Bisimulation on speed: Lower time bounds Abstract. More than a decade ago, Moller and Tofts published their seminal work on relating processes that are annotated with lower time bounds, with respect to speed. Their paper has left open many questions concerning the semantic theory for their suggested bisimulation-based faster-than preorder, the MT-preorder, which have not been addressed since. The encountered difficulties concern a general compositionality result, a complete axiom system for finite processes, and a convincing intuitive justification of the MT-preorder. This paper solves these difficulties by developing and employing novel tools for reasoning in discrete-time process algebra, in particular a general commutation lemma relating the sequencing of action and clock transitions. Most importantly, it is proved that the MT-preorder is fullyabstract with respect to a natural amortized preorder that uses a simple bookkeeping mechanism for deciding whether one process is faster than another. Together these results reveal the intuitive roots of the MTpreorder as a faster-than relation, while testifying to its semantic elegance. This lifts some of the barriers that have so far hampered progress in semantic theories for comparing the speed of processes. Over the past two decades, the field of process algebra [7] has proved successful for modeling and reasoning about the communication behavior of concurrent processes. Early process algebras, such as Milner's CCS [18] and Hoare's CSP [15] , have been augmented to capture other important system aspects as well, including timing behavior [6] . Many variants of timed process algebra that employ either discrete or continuous notions of time have been proposed, whose semantic theories are usually based on the well-studied concepts of bisimulation [19] , failures [22] , or testing [14] .. While several approaches for comparing the efficiency of processes have been introduced in the literature [4, 21] , theories for comparing timed processes with. Research supported by EPSRC grant GR/M99637. respect to speed are seeded very sparsely. The most seminal paper in the latter category was published over a decade ago [20] . In this paper, the authors Moller and Tofts argue that a faster-than relation on processes can only exist for those process-algebraic settings where the passage of time cannot preempt behavior, and especially not for settings involving timeout operators. For a timeout-less fragment of TCCS [19] , Moller and Tofts then introduced a compositional faster-than preorder based on strong bisimulation [18] , and discussed some of its underlying algebraic laws. Despite the paper's originality, the work is lacking regarding three important aspects. First, the advocated preorder is not intuitively justified but appears to be an ad-hoc remedy for a compositionality problem. Second, the framework possesses technical weaknesses. For example, Moller and Tofts only managed to prove compositionality of their preorder for the class of regular processes, and their proposed laws for characterizing their preorder are incomplete. Third, no semantic theory that abstracts from internal computation, in the sense of observation equivalence [18] , is presented in [20] .. The aim of this paper is to put the faster-than preorder of Moller and Tofts, or MT-preorder for short, on solid semantic grounds and to highlight its intuitive roots, thereby testifying to the elegance of Moller and Tofts' approach. Technically, we add to Milner's CCS a discrete-time clock prefixing operator "σ.", interpreted as lower time bound. Intuitively, process P in σ.P is only activated after the ticking of the abstract clock σ, i.e., after one time unit. The nesting of σ-prefixes then allows the specification of arbitrary delays (written as prefix (n) with n ∈ N in [20] ), which results in a process algebra equivalent to the fragment of TCCS studied by Moller and Tofts. We refer to this algebra as Timed Asynchronous Communicating Systems with lower time bounds, or TACS lt . As our first main result we prove that the MT-preorder is compositional and fully-abstract with respect to a natural amortized preorder that uses a simple bookkeeping mechanism for deciding whether one process is faster than another. The intuition behind this amortized preorder is that the faster process must execute each action no later than the slower process does, while both processes must be functionally equivalent in the usual sense of strong bisimulation. To obtain this result we also establish some powerful semantic tools for reasoning within discrete-time process algebra, in particular a general commutation lemma relating the sequencing of action and clock transitions. As our second main result we provide a sound and complete axiomatization of the MT-preorder for the class of finite processes. This includes the provision of a simple expansion law, which Moller and Tofts had claimed could not exist. The twist is that this expansion law is only valid for finite processes, but interestingly not for arbitrary recursive processes. As our third and final main result we introduce a notion of a weak MT-preorder -a task that turns out to be far more challenging than in other bisimulation-based process-algebraic settings.. Our results shed light on the nature of the MT-preorder and overcome the technical difficulties experienced by Moller and Tofts, thereby completing, generalizing, and strengthening their results and providing groundwork for advancing semantic theories that compare processes with respect to speed. This paper also complements our previous work on bisimulation-based faster-than relations for timed process algebra with upper time bounds [17] . Indeed, several ideas and technical concepts can be carried over from the upper-time-bounds setting of [17] to the lower-time-bounds setting presented here. In previous work [17] , the authors investigated bisimulation-based preorders that relate the speeds of asynchronous processes relative to given upper time bounds, specifying when actions have to be executed at the latest. The present paper considered the case of lower time bounds, specifying when actions may be executed at the earliest, by revisiting the seminal approach of Moller and Tofts [20] . Although Moller and Tofts' work was published more than a decade ago and the first one to introduce a faster-than relation in timed process algebra, it was never followed up in the literature -except for [1] where characteristic formulae are provided. One reason for this might be the absence of strong theoretical results, including the absence of a compositionality result for arbitrary processes, of a full-abstraction result, and of a complete axiomatization for finite processes, as well as the bleak picture drawn in [20] for achieving such results elegantly. This paper established these nontrivial results by introducing some novel process-algebraic techniques, including a commutation lemma between action and clock transitions. In particular, we proved a full-abstraction theorem with respect to a very intuitive amortized preorder that uses bookkeeping for deciding whether one process is faster than another. In addition, an expansion law was established for finite processes, which paved the way for a sound and complete axiomatization of the Moller-Tofts preorder. This not only testifies to the nature of the MT-preorder but also highlights its importance among the sparse related work in the field. Last, but not least, a variant of the MT-preorder that abstracts from internal, unobservable actions was studied.. Future work should proceed along three directions. First, we wish to complete the theory for our weak MT-precongruence by establishing the conjectured fullabstraction result. Second, the developed preorders should be implemented in a formal verification tool, such as the Concurrency Workbench NC [9] . Third, we intend to integrate our theory for lower time bounds with our earlier work on upper time bounds [17] , thereby exploring the appropriateness of our faster-than approaches for settings with restricted asynchrony. Although there is a wealth of literature on timed process algebras [6] , little work has been done in developing theories for relating processes with respect to speed. The approaches closest to ours are obviously the one by Moller and Tofts regarding processes equipped with lower time bounds [20] , and our own one regarding processes equipped with upper time bounds [17] . As these have been referred to and discussed throughout, we refrain from repetitions here.. The probably best-known related work focuses on comparing process efficiency rather than process speed. Arun-Kumar and Hennessy [3, 4] have developed a bisimulation-based theory for untimed processes that is based on counting internal actions, which was later carried over to De Nicola and Hennessy's testing framework [12] by Natarajan and Cleaveland [21] . In these theories, runs of parallel processes are seen to be the interleaved runs of their component processes. Consequently, e.g., (τ.a.0 | τ.a.b.0) \ {a} is as efficient as τ.τ.τ.b.0, whereas, in our setting, (σ.a.0 | σ.a.b.0) \ {a} is strictly faster than σ.σ.τ.b.0.. The sparse work on comparing process speeds largely concentrated on worstcase timing behavior on the basis of upper time bounds. Research by Vogler et al. [16, 23] originally employed the concurrency-theoretic framework of Petri nets and testing semantics; it has only recently been carried over to the process algebra PAFAS [11] and is discussed in [17] . Simultaneously, Corradini et al. [10] pursued a different idea for relating processes with respect to speed, which is known as the ill-timed-but-well-caused approach [2, 13] . This approach allows system components to attach local time stamps to actions. Since actions may occur as in an untimed process algebra, local time stamps may decrease within a sequence of actions which is exhibited by several processes running in parallel. The presence of these "ill-timed" runs makes it difficult to relate the faster-than preorder of Corradini et al. to the one of Moller and Tofts; a modified approach restricting attention to "well-timed" behaviour might allow some insight.

B O O B I I O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Query processing techniques for arrays Arrays are an appropriate data model for images, gridded output from computational models, and other types of data.This paper describes an approach to array query processing.Queries are expressed in AML, a logical algebra that is easily extended with user-defined functions to support a wide variety of array operations.For example, compression, filtering, and algebraic operations on images can be described.We show how AML expressions involving such operations can be treated declaratively and subjected to useful rewrite optimizations.We also describe a plan generator that produces efficient iterator-based plans from rewritten AML expressions.dim. 1 Arrays are an appropriate data model for images, gridded output from computational models, and many other types of data. If arrays are to be supported in a database system, there must be some language in which queries against the stored arrays can be expressed. If such queries are to be answered efficiently, the optimizer must understand enough about arrays and the array query language to generate efficient execution plans. Efficiency is important because arrays may be very large and array operations may be complex and costly. Figure 1 shows an array query example to which we will refer throughout this paper. In the example, the base data form a three dimensional array (array A) representing a multi-spectral image generated from the Landsat Thematic Mapper sensor. Two of the array dimensions are spatial and the third is spectral. The seven slices through the cube along the spectral dimension are images of the same scene, each taken using a sensor sensitive to electro-magnetic radiation Permission to make digital or hard copies of all or part of this work I'w personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the tirst page. To copy otherwise, to republish, to post on servers or to redistrihutc to lists. requires prior specific permission and/or a fee. Figure 1 also shows several other arrays that might be derived from the Thematic Mapper image. Array E in Figure 1 holds the "transformed vegetation index" (TVI) for the scene. A TV1 value at a spatial position in the scene represents the amount of green biomass present there [9] . The TV1 value at any position can can be computed from the values of third and fourth spectral bands at the corresponding position in the Thematic Mapper image using the function: Another useful image that might be derived from array A is a "band ratio" image, computed as the ratio of two of the spectral bands of the Thematic Mapper image. Ratioing can be a useful data analysis tool fnr(~o7%~2,..., because it can compensate for variations in absolute brightness (cell values) in the original image that might be caused by topographic features [9] . Array F in Figure 1 is a ratio of Themat,ic Mapper bands three and seven, defined at each position by. The Thematic Mapper image may include noise from a variety of sources, and it is desirable to try to reduce this noise before deriving arrays such as the TVI. In Figure 1 , both the TV1 array and the band ratio array are defined in terms of noise-reduced versions (arrays B, C, and D) of the Ioriginal Thematic Mapper bands. Many types of noise reduction are possible; different types are suitable for different applications.. For the purposes of the example, noise reduction is achieved using a kind of convolution filter in which the noisereduced value of a particular cell is computed using the original value in that cell and the values of its eight immediate neighbors., The exact calculation, which is adapted from [9] is shown in Figure 2 .. This example illustrates several points. First, there is a wide variety of complex, domain-specific transformations that might be applied to arrays. An array query language that hopes to be able to express them must either be very expressive or extensible. Second, there is considerable room for query optimization.. One opportunity for optimization is the regularity and structure that may exist in co:mplex-looking queries. In Figure 1 , for example, given a particular cell in a derived array such as array E, iit is possible to determine exactly which cells of the original Thematic Mapper image contribute to its value. It is also possible to calculate those cell values in any order. Techniques such as caching and view materialization can be used to eliminate redundant calculations, e.g., both the TV1 array and the band ratio array are derived from array B. Finally, the data transformation functions themselves may have properties that can be exploited by an optimizer that understands them. For example, the noise reduction technique used to produce arrays B, C, and D in Figure 1 is a discrete two-dimensional convolution.. An optimizer with some knowledge of linear systems might be able to infer that adding two noise-reduced images is equivalent to applying noise reduction to their sum.. Array queries like those shown in Figure 1 can be described using AML, the Array Manipulation Language, which was introduced in [lo] . The main contribution of this paper is a collection of optimization techniques for AML queries. We describe how these techniques can be used to turn AML queries into efficient evaluation plans. These techniques do not exploit all of the opportunities for optimization described above, primaDily because AML itself does not (yet) capture everything needed to exploit them. For example, the optimizer does not "understand" convolution.. However, AML is quite good at capturing structural regularity in queries. The optimizer exploits this to reorder query operators, eliminate unnecessary work, and minimize space requirements. We demonstrate the impact of the optimizer by comparing evaluation costs with and without optimization for several of the queries from Figure 1 . We have described an optimizer for array queries expressed in AML. AML provides a mechanism through which uninterpreted user-defined functions can be applied to arrays. Because these functions are applied in a structured way, the optimizer can rewrite AML expressions to eliminate unnecessary function applications and I/O. The optimizer also controls the order in which the cells of the derived array are computed as a means of minimizing the amount of memory required to evaluate a query. Using several examples from the image processing domain, we have shown how these optimizations can lead to imp:roved query evaluation times and reduced memory requirements.. Other than improving our optimizer and evaluator, there are a number of open problems that we hope to address. One is the problem of integrating array and non-array databases .and query languages, which was discussed briefly in Section 8. The other is the problem of describing properties of user-defined functions to an optimizer so that those properties can be reasoned about and exploited.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O


A Preprocessing Procedure for Haplotype Inference by Pure Parsimony Abstract-Haplotype data are especially important in the study of complex diseases since it contains more information than genotype data. However, obtaining haplotype data is technically difficult and costly. Computational methods have proved to be an effective way of inferring haplotype data from genotype data. One of these methods, the haplotype inference by pure parsimony approach (HIPP), casts the problem as an optimization problem and as such has been proved to be NP-hard. We have designed and developed a new preprocessing procedure for this problem. Our proposed algorithm works with groups of haplotypes rather than individual haplotypes. It iterates searching and deleting haplotypes that are not helpful in order to find the optimal solution. This preprocess can be coupled with any of the current solvers for the HIPP that need to preprocess the genotype data. In order to test it, we have used two state-of-the-art solvers, RTIP and GAHAP, and simulated and real HapMap data. Due to the computational time and memory reduction caused by our preprocess, problem instances that were previously unaffordable can be now efficiently solved. T HE human genetic material is organized in 23 pairs of chromosomes. In each pair, one of the chromosomes is inherited from the mother and the other from the father. The sequence of DNA in contiguous positions along a chromosomal region is called a haplotype, while mixed datum of both chromosomes is called a genotype. In order to trace the structure of the human population and improve our ability to map disease genes, haplotype information is more relevant than genotype information. However, due to technology limitations, haplotype information is harder to obtain than genotype data: Instruments can identify whether an individual is heterozygous at a site (alleles in both haplotypes are different) or homozygous (alleles are equal in the two haplotypes). Therefore, if the two alleles are different at a given site, we do not know which allele belongs to which haplotype. Hence, computational methods have been designed to obtain haplotype data from genotype data. This problem has been called haplotype inference (HI). There are several approaches to this problem: Combinatorial, statistical, etc. Reviews about the haplotype inference problem can be found in [1] , [2] , [3] . This paper focuses on one of the most popular approaches to the haplotype inference problem which is known as haplotype inference by pure parsimony (HIPP) [4] . The HIPP is a combinatorial problem. Its goal is to find the set of haplotypes with the smallest cardinality that explains a given set of genotypes. It is based on the fact that due to the process of genetic inheritance, the number of haplotypes in a given population is vastly smaller than the number of possible haplotypes. Despite this simplification of the genetic model, and the fact that some authors have noticed the need to introduce additional properties for the model [7] , when the recombination rate is low, pure parsimony solutions are generally as accurate as those obtained with other approaches which are based on more complex models of evolution such as the statistical program PHASE [5] . Moreover, the HIPP is still a lively approach to HI as shown in the number of recently published papers [8] , [9] , [10] . However, the task of obtaining relevant information from unphased genotypes (for disease association tests, for example) involves greater work than that of the haplotype inference. It should also be remarked that the HI problem is purely the beginning of haplotype phasing.. This combinatorial optimization problem has been proved to be NP-hard [3] [6] . In the literature, we can find several solvers for the problem, particularly, those based on integer linear programming (TIP [4] , RTIP [4] , PolyIP, [11] , [12] , HybridIP [11] , SM, RM, and SMM [8] ), branch and bound (HAPAR [13] ), genetic algorithms (GAHAP [14] ), local search [15] , boolean satisfiability, SAT (SHIPs [16] ), and pseudoboolean optimization (PolyPB, RPoly, and NRPoly [17] , [18] ).. Many of the previously cited solving methods carry out a search over the space of possible resolving haplotype pairs of the genotypes. Therefore, before running the optimization algorithm, these solvers have to preprocess the genotype data by expanding all possible pairs of haplotypes for each genotype. Unfortunately, the number of resolving pairs for a genotype grows exponentially with respect to the number of heterozygous positions that it has. Therefore, due to memory and computational time limitations, these optimization methods cannot be applied to medium-large instances. Particularly, this problem affects some of the most widely applied algorithms, such as TIP [4] and its optimized version RTIP [4] , which cast the problem as an integer linear program (ILP). These formulations generate an exponential number of constraints on the number of ambiguous positions of the genotypes. It is also the case of GAHAP [14] , the genetic algorithm, which requires an exponential amount of memory.. In this paper, we propose a new preprocessing step for the HIPP problem. This preprocess drastically reduces the subset of resolving pairs generated for each genotype by detecting, before running the optimization algorithm, that some groups of haplotypes are not relevant. In other words, for every solution that includes elements of these groups, another solution can be built that does not include these elements and has, at most, the same number of different haplotypes. From now on, we will refer to these haplotypes as irrelevant haplotypes.. We have tested our preprocessing algorithm with simulated and real data obtained from the HapMap project [19] . For small instances, our preprocess shows quite a similar time performance to those in the literature. However, for medium-big instances, when starting with the reduced subset of resolving pairs generated with our preprocess, the ILP formulation used in TIP and RTIP can deal with HI problems that were previously unaffordable. Moreover, for those problems of large size that can be solved with the original RTIP, we show a dramatic decrease in the computational time when starting from our reduced set of resolving pairs. Similar performance improvements are achieved when the applied solver is GAHAP.. The rest of the paper is organized as follows: In the next section, we give a more detailed description of the HIPP, providing the background of the problem and presenting the RTIP and GAHAP algorithms. Our proposed algorithm is explained in Section 3. The results are presented and discussed in Section 4. The paper ends with the conclusions and future work. In this paper, we have introduced a new preprocessing procedure which can be coupled with several existing solvers for the haplotype inference by pure parsimony problem. This procedure, which we have called set-based preprocess, deals with sets of haplotypes instead of dealing with single haplotypes. It iterates searching and deleting groups of haplotypes such that, for every solution that includes haplotypes of these groups, another solution can be built that does not include these haplotypes and has, at most, the same number of different haplotypes. The use of groups of haplotypes instead of individual haplotypes reduces the memory needed to represent the initial set of haplotypes. The halting condition can be defined in several ways so one can adapt its behavior for different kinds of problems. The number of haplotypes generated by the set-based preprocess when run until the final stages is always, less than or equal to the number of haplotypes generated by any of the current preprocessing algorithms, usually being much smaller.. We have tested our procedure combining it with two existing and well-known solvers for the HIPP problem using simulated and real data. These experiments showed the efficiency of this procedure in terms of the number of haplotypes generated and time performance, especially for instances with a large number of SNPs, it being possible to preprocess and process instances that were previously unaffordable in a reasonable time. Moreover, we can set a lower limit for the number of ambiguous positions per row and column for which it is worth using our proposed preprocessing procedure since the extra time consumed by it will be saved when processing the data. For these big instances, it is usually not worth running the set-based preprocess until the final stages: The extra computational time required for the final steps is higher than the time saved by the later applied solver with a reduced number of haplotypes. Finally, we have shown that the reduction in computational resources required when using our preprocess coupled with a state-of-the art solver, allows us to solve HapMap problem instances that were previously unaffordable for the same solvers.. The haplotype inference by pure parsimony gives a combinatorial solution to a biological problem. In this kind of problems, the genetic model is simplified, resulting in an abstract goal that is of interest for biologists as well as for mathematical and computational researchers. The final objective of this interdisciplinary collaboration is to contribute in the understanding of the genetic influence in diseases, individual development, etc. In this way, it is possible to adapt this preprocess so that it can be applied to several HIPP variations or to other haplotype inference problems. Due to space constraints, we briefly discuss here several variations [21] and the specific changes the preprocess should have.. A common variation of the HIPP considers the knowledge of a parental relation between two individuals in the genotype sample. In this case, these two genotypes share a haplotype. This information can be considered by the set-based preprocess to generate this specific haplotype (or base) and its complementary haplotype (or base, respectively) for both genotypes. It should also avoid generating any other haplotype for these genotypes.. There are some other HIPP variations for which the setbased preprocess could be applied and which require a larger number of changes in the preprocess. This is the case of considering a genotype matrix with missing or incorrect data. This is a more complicated scenario for which multiple kinds of errors can be considered. For example, the information about some particular locus could be missing. Moreover, one could consider that the given genotype matrix is not absolutely accurate due to technological limitations and that there is an error probability rate for every given genotype. In this scenario, both preprocess and solver, should take this into consideration.. Ekhine Irurozki received the MSc degree in computer science from the University of the Basque Country, Spain, in 2008 and is currently a PhD student at the Intelligent Systems Group at the University of the Basque Country, Spain. Her research interests include combinatorial optimization and its application in computational biology.. Borja Calvo received the MSc degree in biochemistry and the BSc degree in computer science from the University of the Basque Country, Spain, in 1999 and 2004, respectively, and the PhD degree in computer science from the University of the Basque Country, Spain, in 2008. He is, at the moment, member of the Intelligent Systems Group at the same university. His research interest include the machine learning and its application in computational biology.. Jose A. Lozano received the MSc degree in mathematics and the MSc degree in computer science from the University of the Basque Country, Spain, in 1991 and 1992, respectively, and the PhD degree in computer science from the University of the Basque Country, Spain, in 1998. Since 2008, he is a full professor of the University of the Basque Country, Spain, where he leads the Intelligent System Group. He is the coauthor of more than 50 ISI journal publications and coeditor of the first book published about estimation of distribution algorithms. His major research interests include machine learning, pattern analysis, evolutionary computation, data mining, metaheuristic algorithms, and real-world applications. He is an associate editor of the IEEE Transactions on Evolutionary Computation and member of the editorial board of Evolutionary Computation, Soft Computing, and three other journals. He is a member of the IEEE. In this section, we compare, on the one hand, the results of RTIP and SBTIP and, on the other hand, the ones of GAHAP and SBGAHAP. The comparisons are made in terms of haplotypes generated by the preprocessing procedures and execution time. As a general comment, we will show that, as the size of the instances grow (i.e., for bigger values of k_avg and l_avg) the instances preprocessed with the set-based are solved much faster. However, for small size instances, it is not always worth preprocessing the instances with our proposed procedure. Before analyzing the results in detail, it is important to take into account the following facts. As we have already stated, GAHAP preprocesses the input genotype matrix before running the genetic algorithm using the RTIP preprocess and an additional cut. Therefore, the number of haplotypes generated by GAHAP is always less than or equal to the number of haplotypes generated by RTIP for every instance. This cut is implicitly performed by the set-based preprocess, so the number of haplotypes generated by the set-based preprocess when run until the final stage (EL0) is always less than or equal to the number of haplotypes generated by GAHAP. GAHAP needs to generate the haplotypes and then test if they match the requirement of the cut, while the set-based only generates haplotypes that do not match the cut prerequisite. Note also that the number of haplotypes generated by SBTIP and SBGAHAP are not the same, although the applied preprocess is the same. This is because GAHAP does not consider haplotypes that cover only one genotype, if they are ever needed they can be easily calculated (remember that under this notation, a genotype is the sum of its two resolving haplotypes). Therefore, when preprocessing the data to which the GAHAP algorithm is going to be applied, our preprocessing procedure does not consider those haplotypes either.

O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Automatically Conflating Road Vector Data with Orthoimagery Abstract Recent growth of the geospatial information on the web has made it possible to easily access a wide variety of spatial data. The ability to combine various sets of geospatial data into a single composite dataset has been one of central issues of modern geographic information processing. By conflating diverse spatial datasets, one can support a rich set of queries that could have not been answered given any of these sets in isolation. However, automatically conflating geospatial data from different data sources remains a challenging task. This is because geospatial data obtained from various data sources may have different projections, different accuracy levels and different formats (e.g., raster or vector format), thus resulting in various positional inconsistencies. Most of the existing algorithms only deal with vector to vector data conflation or require human intervention to accomplish vector data to imagery conflation. In this paper, we describe a novel geospatial data fusion approach, named AMS-Conflation, which achieves automatic vector to imagery conflation. We describe an efficient technique to automatically generate control point pairs from the orthoimagery and vector data by exploiting the information from the vector data to perform localized image processing on the orthoimagery. We also evaluate a filtering technique to automatically eliminate inaccurate pairs from the generated control points. We show that these conflation techniques can automatically align the roads in orthoimagery, such that 75% of the conflated roads are within 3.6 meters from the real road axes compared to 35% for the original vector data for partial areas of the county of St. Louis, MO. With the rapid improvement of geospatial data collection techniques and the growth of Internet, large amount of geospatial data are now readily available on the web. The examples of well-known vector datasets are US Census TIGER/Line files 1 and NAVSTREETS from NAVTEQ. 2 The National Map, 3 Google Map, 4 and Microsoft TerraService 5 [3] are good examples of map or satellite imagery repositories. The users of these data products often want these geospatial data and other related data to be displayed in some integrated fashion for knowledge discovery. Instead of simply being able to display all of the related data in a single framework, we need to actually fuse the data to provide additional inferred information that is not contained in any single information source.. In fact, geospatial data fusion has been one of the central issues in GIS 6 [24] . Geospatial data fusion requires that the various datasets be integrated, and then a single composite dataset from the integrated elements be created. Towards geospatial data fusion, a vital step is reducing the spatial inconsistencies among multiple datasets. Figure 1 shows an example of combining a road network (NAVTEQ NAVSTREETS) and an image (geo-referenced USGS color imagery with 0.3 m/pixel resolution). Certain geospatial inconsistencies between the road network and imagery are noticeable (as shown in Figure 1(a) ). An integrated view of the imagery with the aligned road network of the area (as Figure 1(b) ) can annotate streets in the imagery with detailed attribution information often contained in vector dataset. In addition, recent advances in satellite imaging technology are making it possible to capture imagery with ever increasing precision and resolution (0.3 m/pixel or better). Once the road network is aligned to higher accuracy imagery, its relatively poorer positional accuracy can be improved.. One cannot rely on a manual approach to align diverse geospatial datasets, as the area of interest may be anywhere in the world and manually aligning a large region (e.g., the continental United States) is very time consuming and error-prone. Moreover, performing alignment offline on two geospatial datasets is also not a viable option in online GIS-related applications as both datasets may be obtained by querying different information sources at run-time. However, automatically and accurately aligning geospatial datasets is a difficult task. Essentially, the challenge is that various geospatial datasets may not align due to multiple reasons: they may use different spheroids, projections or coordinate systems; they may have been collected in different ways or with different precisions or resolutions, etc. If the geographic projections of both datasets are known, then both datasets can be converted to the same geographic projections. However, the geographic projection for a wide variety of geospatial data online is not known. Furthermore, converting datasets into the same projection does not address the issue of different inaccuracies between two spatial datasets.. Conflation is often a term used to describe the integration or alignment of different geospatial datasets. 7 The conflation process can be divided into the following subtasks: (1) Feature matching: Find a set of conjugate point pairs, termed control point pairs, in two datasets, (2) Match checking: Detect inaccurate control point pairs from the set of control point pairs for quality control, and (3) Alignment: Use the accurate control points to align the rest of the geospatial objects (such as points or lines) in both datasets by using the triangulation and rubber-sheeting techniques. Please note that finding accurate control point pairs is a very important step in this kind of feature-based conflation process as all the other points in both datasets are aligned based on the control point pairs.. Traditionally, the problems of vector and imagery conflation have been in the domain of image processing and GIS. The focus of the image processing techniques has been on automatic identification of objects in the image in order to resolve vector-image inconsistencies. However, these techniques require significant CPU time to process an image in its entirety and still may result in inaccurate results. Moreover, various GIS systems, such as ESRI ArcView, 8 ESEA MapMerger, 9 and Able R2V 10 provide the functionality to perform different layers of geospatial dataset integration. However, these products do not provide automatic vector and imagery conflation, and manual intervention is needed to consolidate multiple geospatial datasets. The goal of our research is to develop an automatic, efficient and accurate vector to imagery conflation technique to align vector and imagery for GIS-related applications. Once the vector datasets are aligned to higher accuracy imagery, their positional information can be updated. Furthermore, the aligned vector data can annotate spatial objects in the imagery with detailed attributions information often contained in vector datasets. Particularly, in this paper, we consider the automatic conflation of road network and orthoimagery (i.e., this imagery is altered from original photos so that it has the geometric properties of a map). We propose our approach, a geospatial information integration approach, named Automatic Multi-Source conflation (AMS-conflation), to automatically integrate vector data and imagery. AMS-conflation exploits information from each of the sources to be integrated to automatically identify control points for aligning datasets. Furthermore, rather than processing each source of information separately in isolation, AMS-conflation processes the sources and exchanges information obtained from one source to help the processing of the other source and vice-versa. Essentially, there are three general sources of information for automatically identifying control points: (1) inferences on the data source (e.g., analyzing road vector to detect intersections or classifying imagery to identify road regions), (2) metadata/attributes about the data sources (e.g., resolutions/coordinates of imagery and road width information of vector data), (3) other sources of data that can be linked to the source (e.g., the online telephone books that store the addresses of a named point in the imagery). These automatically exploited information are dynamically exchanged and matched across these geospatial datasets to accurately identify corresponding spatial features as control points in AMS-conflation. Figure 2 shows the overall approach for conflating vector and imagery. AMSconflation is a multi-step data alignment process that involves identification of matching features as control points, filtering of misidentified control points and local transformation of other spatial objects. In fact, AMS-conflation is based on the preliminary techniques that we proposed in [7] . We enhanced our techniques in several ways: (1) we proposed a histogram-based classifier to more accurately identify road intersections as control points on median resolution (about 1 m/pixel) to high resolution (up to 0.3 m/pixel) color orthoimages, 11 (2) we improved our localized image processing technique by exploiting road vector directions and widths to generate templates to match against the orthoimages, (3) we presented a novel evaluation methodology evaluate our conflation results based on three different metrics, and (4) we used different accuracy level real-world vector datasets and images of different resolutions for evaluation.. The remainder of this paper is organized as follows. Section 2 describes the algorithm to automatically identify control point pairs in two types of geospatial 11 Our approach could apply to low resolution imagery as well. However, low resolution imagery is not the focus of our research. This is because natural objects in the imagery become vague with the decrease of imagery resolution. Furthermore, high resolution imagery becomes more and more available today and provides clearer ground truth information (hence often poses more challenging automatic spatial object recognition issues). In addition, the misalignments between vector data and low resolution imagery are rather imperceptible. datasets. Section 3 describes the algorithm to filter out inaccurate control point pairs from the automatically generated control point pairs. Section 4 describes an enhanced conflation process to align two geospatial datasets. Section 5 presents our evaluation methodology and provides results of utilizing our approach to align real world data. Section 6 discusses the related work and Section 7 concludes the paper by discussing our future plans. The main contribution of this paper is the design and implementation of a novel data fusion approach to automatically integrate vector data and imagery of median to high resolutions. AMS-conflation is the first technique that exploits different sources of information and metadata from each of the sources to be integrated to automatically generate control points for conflation. Moreover, we propose an effective filtering algorithm to automatically eliminate inaccurate pairs from the generated control points. Experimental results on the county of St. Louis, MO, and city of El Segundo, CA, demonstrate that our approach can automatically and accurately align and annotate orthoimages with vector data. We are further enhancing our approach by improving both LTM technique and the VMF filtering technique. More precisely, we are improving road classifications by utilizing a machine learning classifiers, called Support Vector Machines (SVM) to categorize images pixels based on all available image color information/channels (e.g., RGB or HSV). This better classification consequence results in better intersection detection by LTM. As stated in Section 3, there is often no systematic behavior of the offsets (i.e., no global transformation) between the geospatial datasets. The revised classifier can help to identify more accurate control point pairs. Hence, we can produce more accurate local transformations to reduce the positional inconsistencies between different datasets. Meanwhile, we are enhancing our VMF filtering technique by investigating the differences of angular distances (i.e., both vector direction and magnitude) between control-point vectors. This is because angular distance provides the essential information to dynamically determine different thresholds (i.e., the parameter k of VMF) for diverse regions. More precisely, for the majority of the scenarios, the similar vectors tend to form clusters around the median vectors. From this observation, we can modify the filtering technique to accommodate more vectors that are close to the median vector. The revised filter can retain more accurate control points that are detected by improved classifier and LTM (i.e., the enhanced filter can increase the recall rate of identified control points without losing precision).. Our approach for conflating road networks with imagery can be generalized to a wide variety of geospatial data sources. The basic idea is to use whatever information is available about the different geospatial products to automatically determine a set of control point pairs. Thus, we can apply this approach to conflating images with map, vector, and point data. In particular, consider applying our approach to conflate vector data and geo-referenced maps. The same types of image processing on vectors and can performed on maps. In fact, for many maps, finding the roads on the maps is an easier problem. Once a set of vector data is aligned to two different sets of images or maps, then the same set of control points can be utilized to conflate image with image, map with map, or map with image [5] . Several important application domains that can benefit from such integration are the crisis management applications, city traffic planning and military intelligence applications.. His current research interests include information integration, automated planning, machine learning, and constraint reasoning and the application of these techniques to geospatial data integration. He is a Fellow of the American Association of Artificial Intelligence. Conflation was first proposed and implemented in 1988 by Saalfeld [22] , and the initial focus of conflation was to eliminate the spatial inconsistency between two overlapping vector maps in order to improve the spatial accuracy of vector maps. From then, various conflation techniques have been proposed and many GIS systems have been implemented to achieve the alignments of geospatial datasets with different resolutions or different types.. Geospatial datasets conflation is a complex process that may utilize work from a broad range of disciplines that include GIS, cartography, computational geometry, Original MO-DOT Conflated MO-DOT (using VMF-filtered control points) Conflated MO-DOT (using unfiltered control points) Many vector to vector conflation techniques have been proposed [8] , [23] , [25] , [28] and various GIS systems (such as ESEA MapMerger ) have been implemented to achieve the alignments of vector datasets with different accuracies. However, there are few research activities on vector to imagery data conflation. Due to recent advances in remote sensing technology to capture high resolution imagery, vector to imagery conflation has become one of the central issues in GIS. Utilizing vector to imagery conflation, this accurate imagery can be used to update vector datasets. Moreover, the abundant information often contained in diverse vector data can be utilized to annotate objects, such as roads and buildings, in the imagery.. In this section, we review related work on vector to imagery data integration. In particular, Section 6.1 reviews the techniques that detect some counterpart elements on the datasets and apply traditional conflation algorithm (i.e., establishing the correspondence between the matched entities and transforming other objects accordingly). Section 6.2 describes the approaches that utilize active counter models [19] to align each vector road segment to corresponding road edge in the imagery.. 6.1 Aligning vector data and imagery using some (automatically) identified features Hild and Fritsch [16] process vector data to extract vector polygons and performed image segmentation on imagery to find image polygons. Then, a polygon matching algorithm is applied on both images and vector to find a set of 2D conjugate points. In order to obtain a successful matching between an image and vector data, the datasets must contain polygonal features like forest, villages, grassland or lakes. This approach will fail when polygonal features cannot be found, such as in high resolution urban areas.. Filin and Doytsher [9] propose a linear conflation algorithm to align vector and imagery. First, all edges (such as road edges and building edges) are detected from the imagery (without using the existing vector data as prior knowledge) and converted to vector format. Then, their approach matches the detected edges with vector data to identify real road edges. Based on the influence regions formed by the matched edges, their system then transforms other vector data where there is no corresponding edge detected in the imagery. However, their approach suffers from the difficulties of extracting and converting features directly from imagery as vectors. There exists many algorithms for extracting roads utilizing the characteristics of roads and context of imagery as prior knowledge [17] , [21] , while none of them give good results in all circumstance [1] , [15] and most of them are heavily CPU intensive.. Flavie et al. [10] try to find all the junction points of all detected lines in the imagery , then match the junction points of the road vector with the image junctions. Then, the vector lines are moved according to the matched junctions (i.e., no space partition method is used to build the influence regions of matched junctions). Finally, their system applies the active contour models technique [19] (discussed next) to refine the matched road segments. However, their method sufferers from the high computation cost of finding all possible junctions of detected lines on images.. Our AMS-conflation significantly differs from the work mentioned above in terms of our approach to locate matched entities. To the best of knowledge, AMSconflation is the first vector to imagery conflation approach that automatically exploits auxiliary structured data (such as image color, image metadata, road directions, road intersections and road coordinates provided by vector data) to improve the feature recognition techniques on imagery. In addition, AMS-conflation performs a template matching around each road intersection (i.e., a localized area, instead of the entire image). This will improve both the accuracy and efficiency. We used the following two different datasets for our experiments:. (1) Orthoimagery. The imagery used in the experiments is the geo-referenced USGS color orthoimagery (0.3 m/pixel resolution) and geo-referenced USGS gray-scale DOQ imagery with lower resolution (1 m/pixel). In particular, we tested the color imagery that covers some areas of county of St. Louis, MO, and the grayscale imagery that covers some areas of the city of El Segundo, CA. This imagery is available online and queryable from Microsoft TerraService web service [3] . (2) Vector data (road networks) Three road networks from different data providers were used as the vector data:. & TIGER/Lines from U.S. Census: The TIGER system was developed by the U.S.. Bureau of the Census. The Bureau provides the public with the TIGER/Line files, which are extractions of selected geographic and cartographic information from the TIGER database. In particular, we focus on the road networks queried from TIGER/Line files (called TIGER/Lines henceforth). & NAVSTREETS from NAVTEQ: NAVSTREETS is a commercial product and is high quality vector data with highly accurate geometry. It is regularly updated by NAVTEQ using some base maps acquired from a variety of sources including local governments, commercial mapping agencies and other public agencies. Many online street map services, such as Google Map, utilize NAVSTREETS as the base dataset for road route planning. & Road network data (called MO-DOT henceforth) from department of transportation, St. Louis, MO [24] . It is also a high quality road vector dataset.. In general, all these road network data listed above have rich attribution; however, TIGER/Lines has both poor positional accuracy and road geometry. With TIGER/ Lines and MO-DOT, the number of lanes can be inferred from the attribute BCFCC (Census Feature Class Codes)^associated with each road segment, while the number of lanes can be obtained from the attribute BLANE_CAT^in NAVSTREETS. Furthermore, the locations of road intersections and the road directions around each intersection are calculated by analyzing these road networks using the algo- Figure 13 An example of rubber-sheeting. rithms described in Section 2.1. In general, NAVSTREETS and MO-DOT are high quality road vectors, but with various accuracy levels. As some sample images shown in Figure 14 , there are some spatial inconsistencies between the USGS high resolution color imagery and the three different vectors.. Our automatic conflation system was developed in C#. The algorithm allows the user to specify the two datasets to conflate (e.g., Bimagery and TIGER/Lines^, Bimagery and NAVSTREETS^or Bimagery and MO-DOT^). The output of our conflation system was a set of conflated roads for the three different types of vector datasets. The experiment platform is Pentium III 1.2 GHz processor with 512 MB memory on Windows XP (with .NET framework installed). In order to evaluate our approach on various real world data, we applied AMS-conflation to diverse areas as summarized in Table 1 . In addition, we manually plotted the real road axes (called reference roads) as the ground truth with which we compare our conflated roads.

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O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I 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O O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O 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Self-modifying cartesian genetic programming In nature, systems with enormous numbers of components (i.e. cells) are evolved from a relatively small genotype. It has not yet been demonstrated that artificial evolution is sufficient to make such a system evolvable. Consequently researchers have been investigating forms of computational development that may allow more evolvable systems. The approaches taken have largely used re-writing, multi-cellularity, or genetic regulation. In many cases it has been difficult to produce general purpose computation from such systems. In this paper we introduce computational development using a form of Cartesian Genetic Programming that includes self-modification operations. One advantage of this approach is that ab initio the system can be used to solve computational problems. We present results on a number of problems and demonstrate the characteristics and advantages that self-modification brings. In evolutionary computation there has been increasing interest in the notion of the genotype-phenotype mapping. The term mapping is really a synonym for the concept of a mathematical function, i.e. an algorithm that calculates an output from a set of inputs. A genotype-phenotype mapping therefore implies an algorithm that transforms an input string of numbers encoding a genotype into another string of numbers that comprises the phenotype of an individual. However, the inputs in the transformation of natural genotypes into their phenotypes are not merely the string of bases in the DNA. Such a view would be akin to the once dominant, but now obsolete view in molecular biology known as Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. GECCO'07, July 7-11, 2007 'the central dogma of biology'. Nowadays, the process of transformation from genotype to phenotype is more properly regarded as a complex interaction in which a genotype, together with the cellular machinery and the environment gives rise to a stage of the phenotype, which itself influences the decoding of the genotype for the next stage [1] . One can regard this process as one of self-modification which could take place both at the genotype or cellular level. Implicit in this notion is the concept of time or iteration. In this paper we take the view that development can be equated to the time-dependent process whereby genotype and phenotype, in interaction with each other and an external environment, produce a phenotype that can be selected for. Kampis [9] has conducted an impressive philosophical analysis of the notion and importance of self-modification in biology and its relevance to 'emergent computation'. In our approach the modifications that can be made (within the scope of the self-modification functions defined) are entirely under the control of evolution. Indeed, it is possible for the genome to destroy itself or create copies of itself.. In section 2 we review work that has investigated the benefits of evolving developmental representations when compared with direct representations. To this day, however, it is still not clear how and whether developmental representations have advantages in a more general computational sense. This is the case because, firstly, investigations have concentrated on particular systems such as neural networks, structural design, digital circuits or sorting networks. Secondly, often by their own admission, authors have chosen rather naive direct representations in comparison with developmental representations. It is our aim in this paper to describe a developmental system that is capable of general computation in the sense of genetic programming. However in doing this we did not want to dictate in advance, whether the representation should be developmental or not. We wanted to leave that to be decided by evolution itself.. The approach we have taken is to introduce into a genetic programming technique, namely Cartesian Genetic Programming (CGP), operators that modify the computational genotype itself. In this way evolution is free to use selfmodifying operators or not. In the latter case the developmental system would reduce to non-developmental CGP. In evolutionary computation, the idea of self-modification has its origins in the ontogenetic programming system of Spector and Stoffel [18] , the graph re-writing system of Gruau [5] and the developmental method of evolving graphs and circuits of Miller [15] . In this paper we have introduced a form of Cartesian Genetic Programming that has the property of self-modification. The advantage of this approach is that it is a general automated technique for solving computational problems while at the same time being developmental in nature. This allows us to evaluate the advantages of self-modification on a wide range of computational problems and to compare the approach with traditional GP techniques. We presented first experimental results on evolving solutions to a number of problems. We have shown that the use of self-modification can perform tasks that a non-modifying system could not achieve, and that self-modification is even advantageous on problems where self-modification is not necessary.. The results obtained are not always better than a nonmodifying encoding for the same problem. However, the encoding presented here can solve the same problems -and others that standard CGP cannot solve -without modification to the algorithm. We feel this feature makes the algorithm robust over many different problem domains, including those that we do not know a-priory if a self-modifying encoding is necessary or gives an advantage.. A similar encoding between the standard and the selfmodifying CGP also allows us to compare behavior of the two systems fairly. We hope that further work will give insights into self-modifying and developmental encodings.. In future work we intend to investigate whether the evolutionary algorithm itself could be replaced by survival-based measures for a collection of interacting and self-modifying genomes. Our aim in this is to allow, to some extent, evolution to act on itself and the organization of useful genotypes. We believe that this forms a step in the direction of the computational evolution agenda proposed in [1] . Changes the function of a specified node to the specified function CHC Node, Connection1, Connection2 Changes the connections in the specified node CHP Node, ParameterIndex, New Value Changes the specified parameter and a given node FLR None Clears any entries in the pending modifications list OVR Start, End, Insert Moves each of the nodes between Start and End into the position specified by Insert, overwriting existing nodes DU2 Start, End, Insert Similar to DUPE, but connections are considered to absolute, rather than relative Table 9 : SMCGP overwriting functions set., The following nodes are executed if the first input is greater, or equal to the second. They output 1 if the they are executed, 0 otherwise Recently there has been increasing interest in the benefits of computational development [12] and its potential benefits for evolutionary computation. Many argue that some form of development will be necessary in order to make evolutionary techniques scale up to larger problems (see, e.g. [2] ) and there have been a number of investigations that show that for particular applications developmental or generative techniques scale better.. Early on, Kitano developed a method for evolving the architecture of an artificial neural network using a matrix re-writing system that manipulated adjacency matrices [11] . Kitano found that his method produced superior results to direct methods, i.e., a fixed architecture, directly encoded and evolved. It was later claimed by another study that the two approaches would be really of equal quality [17] .. Gruau devised a graph re-writing method called cellular encoding [5] for local graph transformations that control the division of cells growing into a artificial neural network. Connection strengths (weights), threshold value and the grammar tree that defines the graph re-writing rules were evolved using an evolutionary algorithm. This method was shown to be effective at optimizing both the architecture and weights at the same time, and scaled better, according to [6] than a direct encoding.. Bentley and Kumar examined a number of genotype to phenotype mappings on a problem of creating a tessellating tile pattern [3] . They found that the indirect developmental mapping could evolve tiling patterns much quicker than a variety of other representations (including direct) and further, that they could be subsequently grown to (iterated) much larger sized patterns.. Hornby and Pollack evolved context free L-systems to define three dimensional objects (table designs) [7] . They found that their generative system could produce fitter designs faster than direct methods.. Eggenberger investigated the relative merits of a direct versus a developmental genetic representation for the difficult problem of optical lens design [8] . He found that the direct method in which the location of optical elements was evolved scaled very badly when compared with the developmental approach.. Roggen and Federici compared evolving direct and developmental mappings for the task of producing specific two dimensional patterns of various sizes (the Norwegian Flag and a pattern produced by Wolfram 1D CA rule 90) [16] . They showed in both cases that as the pixel dimensions of the patterns increased the developmental methods outperformed the direct.. Gordon showed that evolved developmental representations were more scalable than direct representations for digital adders and parity functions [4] .. Sekanina and Bidlo showed how a developmental approach could be evolved to design arbitrarily large sorting networks [13] . Kicinger investigated the problem of design in steel structures for tall buildings and found CA-based generative models produced better results quicker than direct representations and that the solutions were more compact [10] .. So a variety of systems have demonstrated the strength of indirect encodings, although none of the systems mentioned performed general purpose computation.

O O B I O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B I O O O B I O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Point counting in families of hyperelliptic curves LetĒΓ be a family of hyperelliptic curves over F alg cl 2 with general Weierstrass equation given over a very small field F. We describe in this paper an algorithm to compute the zeta function ofĒγ forγ in a degree n extension field of F, which has as time complexity O(n 3 ) and memory requirements O(n 2 ). With a slightly different algorithm we can get time O(n 2.667 ) and memory O(n 2.5 ), and the computation of O(n) curves of the family can be done in time and space O(n 3 ). All these algorithms are polynomial in the genus.

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Analytic Methods for the Logic of Proofs The logic of proofs (LP) was proposed as Gödel's missed link between Intuitionistic and S4-proofs, but so far the tableau-based methods proposed for LP have not explored this closeness with S4 and contain rules whose analycity is not immediately evident. We study possible formulations of analytic tableau proof methods for LP that preserve the subformula property. Two sound and complete tableau decision methods of increasing degree of analycity are proposed, KELP and preKELP. The latter is particularly inspired on S4-proofs. The crucial role of proof constants in the structure of LP-proofs methods is analysed. In particular, a method for the abduction of proof constant specifications in strongly analytic preKELP proofs is presented; abduction heuristics and the complexity of the method are discussed. The logic of proofs (LP) was proposed by Artemov [1, 2] as the 'missed link' connecting Intuitionistic Logic to classical proofs, thus filling a gap left by Gödel's original translation from Intuitionistic Logic into S4 modal logic. LP is a propositional multi-modal language, in which modalities are proof terms, also called proof polynomials, such that if t is a proof term and A is a formula, t : A is an LP-formula with the intended meaning 't is a proof of A'.. In Ref. [9] , Melvin Fitting proposed a semantics for Artemov's LP, and presented a sound and complete tableau inference system based on that semantics. Fitting's tableau presentation has a non-analytic rule; however, its correctness was shown with respect to the analytic, cut-free sequent calculus LPG − for LP [2] .. As LP is capable of providing insight into proofs due to its explicit handling of proof terms, it is highly desirable that there exist automated, analytic tableau procedures for it.. This article investigates alternative analytic tableau presentations for LP. This investigation highlights the crucial role played by proof constants in analytic proof construction. Proof constants are a form of atomic proof term, intended to represent evidence for formulas which are valid; they are dealt with in the semantics by a constant specification C. In the semantics, one talks about C-validity, so that constant specifications behave as a semantical parameter. As a counterpart in terms of LP-proof theory, we introduce the concept of C-analycity.. We investigate two possible ways to provide an analytic tableau proof system for LP. Traditional analytic tableaux [20] , as well as Fitting's method for LP, are based on cut-free sequent calculus. Our approach, however, is based on a calculus using analytic cuts, which leads to tableau methods in the style of KE-tableaux [6] . An advantage of using a KE-based calculus is that it is known to provide an exponential speedup in proofs for some classical formulas [5] .. The first KE-based method, KELP, is a C-analytic tableau method for KE. In fact, it is a sound and complete decision procedure for C-valid formulas, whose termination is guaranteed when C is finite. Admittedly, KELP-tableaux turn out to display very similar behaviour to Fittings LP-tableaux in respect to analycity. However, it has the quality of bringing to the light that the problem of computing analytic proofs is not the existence of non-analytic rules, but the way one deals with proof constants. The aim of this section is to position the results obtained in the previous section in the context of recent work described in the literature. In particular, there seems to be a few clarifications in need due to apparent contradiction between the EXPSPACE complexity for abduction and some recent complexity results in the literature, namely:. • A complexity upper bound for the decision problem for LP in the class p 2 in the polynomial hierarchy, obtained by Kuznets [14] . This is considered a much better complexity bound in respect to logic S4, which is known to be PSPACE-complete [15] .. • An NP-complete decision procedure proposed by Krupski [13] for a fragment of LP, known as the Reflected LPs; this fragment has the same expressive power as LP itself.. • A result by Brezhenv and Kuznets, in which a relation between LP theorems can be computed from S4 proofs in polynomial time [4] .. To understand how all these results fit in, one has to recall the definition of the realization of an S4-formula A into an LP-formula A r , that is, to substitute proof polynomials for all occurrences of in A, which yields A r . A central result for this discussion is the following.

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