extrapolation effects on coupled computational fluid dynamics computational structural dynamics simulations between them passing loads from the e ow code to the structural code and displacements back theother way forunsteady problems the sequencing is done within the pseudotime loop used for the e ow solver and removes sequencing errors the mesh movement for the aerodynamic solver is done using transe nite interpolation of displacements 7 we restrict ourselves in this note to the case of a wing modeled structurally by a plate this case is interesting as a building block to more complex structural descriptions transformation of data between the two grids is broken into two components in and out of the plane of the structural model the outplane treatment follows the considerations of ref 5 the in plane treatment turns out to have a much stronger ine uence on the test case considered next the two approaches used are the ine nite plate spline ips 8 and linear interpolation for ips a solution of the thin plate equation is forced to pass through the known structural points and is then evaluated at the projected aerodynamic points for the required displacements for linear interpolation each projected e uid point is associated with a triangle on the structural mesh and the deformation is calculated using a linear approximation within the triangle in both cases the relationship between displacements on the e uid and structural grids is linear and the principle of virtual work is then applied for transferring forces iii test cases

a simple optimal representation for balanced parentheses we consider succinct or highly space efficient representations of a static string consisting of n pairs of balanced parentheses which support natural operations such as finding the matching parenthesis for a given parenthesis or finding the pair of parentheses that most tightly enclose a given pair this problem was considered by jacobson space efficient static trees and graphs in proc of the 30th focs 1989 pp 549 554 and munro and raman succinct representation of balanced parentheses and static trees siam j comput 31 2001 762 776 who gave o n bit and 2n o n bit representations respectively that supported the above operations in o 1 time on the ram model of computation this data structure is a fundamental tool in succinct representations and has applications in representing suffix trees ordinal trees planar graphs and permutations we consider the practical performance of parenthesis representations first we give a new 2n o n bit representation that supports all the above operations in o 1 time this representation is conceptually simpler its space bound has a smaller o n term and it also has a simple and uniform o n time and space construction algorithm we implement our data structure and a variant of jacobson s and evaluate their practical performance speed and memory usage when used in a succinct representation of trees derived from xml documents as a baseline we compare our representations against a widely used implementation of the standard dom document object model representation of xml documents both succinct representations use orders of magnitude less space than dom and tree traversal operations are usually only slightly slower than in dom

deforming mesh for computational aeroelasticity using a nonlinear elastic boundary element method a nonlinear elastic boundary element method nbem approach is developed as an innovative deforming mesh generator for computational aeroelastic simulation the computational fluid dynamics cfd mesh is assumed to be embedded in an infinite nonlinear elastic medium of a hardening material leading to the formulation of a pseudononlinear elastostatic problem whereas the cfd surface mesh is treated as a boundary element model and the cfd flowfield grid as domain sample points the nbem approach solves navier s equations using a particular solution scheme that removes the requirement of the domain integral in the conventional nbem formulation the nbem approach has a unified feature that is applicable to all mesh systems including unstructured multiblock structured and overset grids an optimization strategy is employed to determine the optimum hardening material properties by minimizing the mesh distortion in the viscous region where grid orthogonality must be preserved three test cases are performed to demonstrate the robustness and effectiveness of the nbem approach for deforming mesh generation

compressed suffix arrays and suffix trees with applications to text indexing and string matching the proliferation of online text such as found on the world wide web and in online databases motivates the need for space efficient text indexing methods that support fast string searching we model this scenario as follows consider a text t consisting of n symbols drawn from a fixed alphabet sigma the text t can be represented in n lg sigma bits by encoding each symbol with lg sigma bits the goal is to support fast online queries for searching any string pattern p of m symbols with t being fully scanned only once namely when the index is created at preprocessing time the text indexing schemes published in the literature are greedy in terms of space usage they require omega n lg n additional bits of space in the worst case for example in the standard unit cost ram suffix trees and suffix arrays need omega n memory words each of omega lg n bits these indexes are larger than the text itself by a multiplicative factor of omega smash lg sigma n which is significant when sigma is of constant size such as in textsc ascii or textsc unicode on the other hand these indexes support fast searching either in o m lg sigma time or in o m lg n time plus an output sensitive cost o mathit occ for listing the mathit occ pattern occurrences we present a new text index that is based upon compressed representations of suffix arrays and suffix trees it achieves a fast smash o m lg sigma n lg sigma epsilon n search time in the worst case for any constant 0 epsilon leq 1 using at most smash bigl epsilon 1 o 1 bigr n lg sigma bits of storage our result thus presents for the first time an efficient index whose size is provably linear in the size of the text in the worst case and for many scenarios the space is actually sublinear in practice as a concrete example the compressed suffix array for a typical 100 mb textsc ascii file can require 30 40 mb or less while the raw suffix array requires 500 mb our theoretical bounds improve emph both time and space of previous indexing schemes listing the pattern occurrences introduces a sublogarithmic slowdown factor in the output sensitive cost giving o mathit occ smash lg sigma epsilon n time as a result when the patterns are sufficiently long we can use auxiliary data structures in o n lg sigma bits to obtain a total search bound of o m lg sigma n mathit occ time which is optimal

approximate all pairs suffix prefix overlaps finding approximate overlaps is the first phase of many sequence assembly methods given a set of strings of total length n and an error rate e the goal is to find for all pairs of strings their suffix prefix matches overlaps that are within edit distance email protected email protected email protected where is the length of the overlap we propose a new solution for this problem based on backward backtracking lam et al 2008 and suffix filters karkkainen and na 2008 our technique uses nh k o email protected rlogr bits of space where h k is the k th order entropy and s the alphabet size in practice it is more scalable in terms of space and comparable in terms of time than q gram filters rasmussen et al 2006 our method is also easy to parallelize and scales up to millions of dna reads

interfacing of fluid and structural models via innovative structural boundary element method an innovative structural boundary element method bem solver is developed for interfacing the computational fluid dynamics cfd and computational structural dynamics csd grids formulated as a solid mechanics problem with a minimum strain energy requirement the bem solver generates a truly three dimensional universal spline matrix the universal spline matrix is a vector operator that includes the coupling of displacements and forces along all axes based on a similar formulation an exterior bem solver is also developed to account for the flowfield grid deformation thus the bem solver allows a unified treatment of the displacement and force transformation for cfd csd interfacing as well as the computation of the flowfield grid deformation the solution procedure is fully automated and no additional model generation is required therefore is ideally suitable for computational aeroelasticity and multidisciplinary optimization applications

succinct representation of labeled trees we give a representation for labeled ordered trees that supports labeled queries such as finding the i th ancestor of a node with a given label our representation is succinct namely the redundancy is small o of the optimal space for storing the tree this improves the representation of he et al isaac 2012 8 which is succinct only when the entropy of the labels is 1

bidirectional search in a string with wavelet trees and bidirectional matching statistics searching for genes encoding micrornas mirnas is an important task in genome analysis because the secondary structure of mirna but not the sequence is highly conserved the genes encoding it can be determined by finding regions in a genomic dna sequence that match the structure it is known that algorithms using a bidirectional search on the dna sequence for this task outperform algorithms based on unidirectional search the data structures supporting a bidirectional search affix trees and affix arrays however are rather complex and suffer from their large space consumption here we present a new data structure called bidirectional wavelet index that supports bidirectional search with much less space with this data structure it is possible to search for candidates of rna secondary structural patterns in large genomes for example the complete human genome another important application of this data structure is short read alignment as a second contribution we show how bidirectional matching statistics can be computed in linear time

on the construction of classes of suffix trees for square matrices we provide a uniform framework for the study of index data structures for a two dimensional matrixtext1 n 1 n whose entries are drawn from an ordered alphabet an index fortextcan be informally seen as the two dimensional analog of the suffix tree for a string it allows on line searches and statistics to be performed ontextby representing compactly the n3 square submatrices oftextin optimalo n2 space we identify 4n 1families of indices fortext each containing ni 1 2i 1 isomorphic data structures we also develop techniques leading to a single algorithm that efficiently builds any index in any family ino n2logn time ando n2 space such an algorithm improves in various respects the algorithms for the construction of the pat tree and the lsuffix tree the framework and the algorithm easily generalize tod 2 dimensions moreover as part of our algorithm we provide new algorithmic tools that yield a space efficient implementation of the naming scheme of r karpet al in proceedings fourth symposium on theory of computing pp 125 136 for strings and matrices

succinct representation of balanced parentheses and static trees we consider the implementation of abstract data types for the static objects binary tree rooted ordered tree and a balanced sequence of parentheses our representations use an amount of space within a lower order term of the information theoretic minimum and support in constant time a richer set of navigational operations than has previously been considered in similar work in the case of binary trees for instance we can move from a node to its left or right child or to the parent in constant time while retaining knowledge of the size of the subtree at which we are positioned the approach is applied to produce a succinct representation of planar graphs in which one can test adjacency in constant time

succinct data structure for dynamic trees with faster queries abstract navarro and sadakane 19 gave a dynamic succinct data structure for storing an ordinal tree the structure supports tree queries in either o log n log log n or o log n time and insertion or deletion of a single node in o log n time in this paper we improve the result of navarro and sadakane by reducing the time complexities of some queries e g degree and level ancestor from o log n to o log n log log n

new space time tradeoffs for top k document retrieval on sequences we address the problem of indexing a collection d t 1 t 2 t d of d string documents of total length n so that we can efficiently answer top k queries retrieve k documents most relevant to a pattern p of length p given at query time there exist linear space data structures that is using o n words that answer such queries in optimal o p k time for an ample set of notions of relevance however using linear space is not sufficiently good for large text collections in this paper we explore how far the space time tradeoff for this problem can be pushed we obtain three results 1 when relevance is measured as term frequency number of times p appears in a document t i an index occupying csa o n bits answers the query in time o t s e a r c h p klg 2klg en where csa is a compressed suffix array indexing d t s e a r c h p is its time to find the suffix array interval of p and e 0 is any constant 2 with the same measure of relevance an index occupying csa nlgd o email protected nlgd bits answers the query in time o t s e a r c h p klg k where lg k is the iterated logarithm of k 3 when the relevance depends only on the documents an index occupying csa o nlglgn bits answers the query in o t s e a r c h p kt s a time where t s a is the time the csa needs to retrieve a suffix array cell on our way we obtain some other results of independent interest

counting suffix arrays and strings suffix arrays are used in various applications and research areas like data compression or computational biology in this work our goal is to characterise the combinatorial properties of suffix arrays and their enumeration for a fixed alphabet size and string length we divide the set of all strings into equivalence classes of strings that share the same suffix array for each such equivalence class we count the number of strings contained in it we also give exact formulas for computing the number of equivalence classes our methods yield a lower bound for the compressibility of suffix arrays and build the foundation for the efficient generation of appropriate test data sets for suffix array based algorithms we also show that summing up the elements of all equivalence classes forms a particular instance for some summation identities of eulerian numbers

approximate string matching using compressed suffix arrays let t be a text of length n and p be a pattern of length m both strings over a fixed finite alphabet a the k difference k mismatch respectively problem is to find all occurrences of p in t that have edit distance hamming distance respectively at most k from p in this paper we investigate a well studied case in which t is fixed and preprocessed into an indexing data structure so that any pattern query can be answered faster we give a solution using an o n log n bits indexing data structure with o a kmk max k log n occ query time where occ is the number of occurrences the best previous result requires o n log n bits indexing data structure and gives o a kmk 2 occ query time our solution also allows us to exploit compressed suffix arrays to reduce the indexing space to o n bits while increasing the query time by an o log n factor only

time efficient aeroelastic simulations based on radial basis functions aeroelasticity studies the interaction between aerodynamic forces and structural responses and is one of the fundamental problems to be considered in the design of modern aircraft the fluid structure interpolation fsi and mesh deformation are two key issues in the cfd csd coupling approach the partitioned approach which is the mainstream numerical strategy in aeroelastic simulations in this paper a time efficient coupling scheme is developed based on the radial basis function interpolations during the fsi process the positive definite system of linear equations is constructed with the introduction of pseudo structural forces the acting forces on the structural nodes can be calculated more efficiently via the solution of the linear system avoiding the costly computations of the aerodynamic structural coupling matrix the multi layer sequential mesh motion algorithm msm is proposed to improve the efficiency of the volume mesh deformations which is adequate for large scale time dependent applications with frequent mesh updates two dimensional mesh motion cases show that the msm algorithm can reduce the computing cost significantly compared to the standard rbf based method the computations of the agard 445 6 wing flutter and the static deflections of the three dimensional high aspect ratio aircraft demonstrate that the developed coupling scheme is applicable to both dynamic and static aeroelastic problems

space efficient algorithms for computing minimal shortest unique substrings abstract given a string t of length n a substring u t i j of t is called a shortest unique substring sus for an interval s t if a u occurs exactly once in t b u contains the interval s t i e i s t j and c every substring v of t with v u containing s t occurs at least twice in t given a query interval s t 1 n the interval sus problem is to output all the suss for the interval s t in this article we propose a 4 n o n bits data structure answering an interval sus query in output sensitive o o c c time where occ is the number of returned suss additionally we focus on the point sus problem which is the interval sus problem for s t here we propose a log 2 3 1 n o n bits data structure answering a point sus query in the same output sensitive time we also propose space efficient algorithms for computing the minimal unique substrings of t

succinct representations of permutations and functions we investigate the problem of succinctly representing an arbitrary permutation p on 0 n 1 so that p k i can be computed quickly for any i and any positive or negative integer power k a representation taking 1 e nlgn o 1 bits suffices to compute arbitrary powers in constant time for any positive constant e 1 a representation taking the optimal lgn o n bits can be used to compute arbitrary powers in o lgn lglgn time we then consider the more general problem of succinctly representing an arbitrary function f n n so that f k i can be computed quickly for any i and any integer power k we give a representation that takes 1 e nlgn o 1 bits for any positive constant e 1 and computes arbitrary positive powers in constant time it can also be used to compute f k i for any negative integer k in optimal o 1 f k i time we place emphasis on the redundancy or the space beyond the information theoretic lower bound that the data structure uses in order to support operations efficiently a number of lower bounds have recently been shown on the redundancy of data structures these lower bounds confirm the space time optimality of some of our solutions furthermore the redundancy of one of our structures surpasses a recent lower bound by golynski golynski soda 2009 thus demonstrating the limitations of this lower bound

on compressing permutations and adaptive sorting we prove that given a permutation p over 1 n formed of nruns sorted blocks of sizes given by the vector r there exists a compressed data structure encoding p in n 1 h r n i 1 n r u n sr ilog 2nr i

path queries on functions abstract let f 1 n 1 n be a function and l 1 n 1 indicate a label assigned to each element of the domain we design several compact data structures that answer various kinds of summary queries on the labels of paths in f for example we can find either the minimum label in f k i for a given i and any k 0 in a given range k 1 k 2 or the minimum label in f k i for a given i and k 0 using n lg n n lg o n lg n bits and time o n the inverse ackermann function within similar space we can count in time o lg n lg lg n the number of labels within a range and report each element with such labels in o lg n lg lg n additional time several other tradeoffs and possible queries are considered such as selection top r queries and majorities finally we consider queries that allow us navigate on the graph of the function such as the nearest common successor of two elements or the nearest successor or predecessor of an element within a range of labels

the cell probe complexity of succinct data structures we consider time space tradeoffs for static data structure problems in the cell probe model with word size 1 the bit probe model in this model the goal is to represent n bit data with s n r bits such that queries of a certain type about the data can be answered by reading at most t bits of the representation ideally we would like to keep both s and t small but there are tradeoffs between the values of s and t that limit the possibilities of keeping both parameters small in this paper we consider the case of succinct representations where s n r for some email protected n for a boolean version of the problem of polynomial evaluation with preprocessing of coefficients we show a lower bound on the redundancy query time tradeoff of the form r 1 t email protected n logn in particular for very small redundancies r we get an almost optimal lower bound stating that the query algorithm has to inspect almost the entire data structure up to a logarithmic factor we show similar lower bounds for problems satisfying a certain combinatorial properties of a coding theoretic flavor and obtain r 1 t email protected n for certain problems previously no w m lower bounds were known on t in the general model for explicit boolean problems even for very small redundancies by restricting our attention to systematic or index structures f satisfying f x email protected email protected x for some map f where denotes concatenation we show similar lower bounds on the redundancy query time tradeoff for the natural data structuring problems of prefix sum and substring search

suffix arrays a new method for on line string searches a new and conceptually simple data structure called a suffix array for on line string searches is introduced in this paper constructing and querying suffix arrays is reduced to a sort and search paradigm that employs novel algorithms the main advantage of suffix arrays over suffix trees is that in practice they use three to five times less space from a complexity standpoint suffix arrays permit on line string searches of the type is w a substring of a to be answered in time o p log n where p is the length of w and n is the length of a which is competitive with and in some cases slightly better than suffix trees the only drawback is that in those instances where the underlying alphabet is finite and small suffix trees can be constructed in o n time in the worst case versus o n log n time for suffix arrays however an augmented algorithm is given that regardless of the alphabet size constructs suffix arrays in o n expected time albeit with lesser space efficiency it is

improved radial basis function fluid structure coupling via efficient localized implementation previous work by the authors has developed a universal interpolation scheme using radial basis functions rbfs which results in a unified formulation for robust fluid structure interpolation and high quality mesh motion the method has several significant advantages primarily all volume mesh structural mesh and flow solver type dependence is removed entirely as all operations are performed on totally arbitrary point clouds of any form hence all connectivity requirements are removed from both the coupling and mesh motion problems furthermore only matrix vector multiplications are required during unsteady simulation because dependence relations are computed once prior to any simulation and then remain constant this property means that the method is both perfectly parallel and totally independent from the flow solver however the full method is expensive since the dependence matrix between two sets of points is n points1 n points2 the fluid structure coupling behaviour can also be influenced by parameters used in the interpolation to alleviate these difficulties a more efficient form of the rbf fluid structure coupling is presented which also greatly reduces the interpolation parameter influence a pointwise form of the partition of unity approach is developed that localizes the interpolation with results presented for static aeroelastic simulations of the brite euram multi disciplinary optimization wing using a very fine mesh containing 58000 surface points it is shown that a 58 reduction in data size is achieved and equally importantly the interpolation has a much smaller influence on final aeroelastic results

fully functional suffix trees and optimal text searching in bwt runs bounded space indexing highly repetitive texts such as genomic databases software repositories and versioned text collections has become an important problem since the turn of the millennium a relevant compressibility measure for repetitive texts is r the number of runs in their burrows wheeler transforms bwts one of the earliest indexes for repetitive collections the run length fm index used o r space and was able to efficiently count the number of occurrences of a pattern of length m in a text of length n in o m log log n time with current techniques however it was unable to locate the positions of those occurrences efficiently within a space bounded in terms of r in this article we close this long standing problem showing how to extend the run length fm index so that it can locate the occ occurrences efficiently in o occ log log n time within o r space by raising the space to o r log log n our index counts the occurrences in optimal time o m and locates them in optimal time as well o m occ by further raising the space by an o w log factor where is the alphabet size and w e log n is the ram machine size in bits we support count and locate in o m log w and o m log w occ time which is optimal in the packed setting and had not been obtained before in compressed space we also describe a structure using o r log n r space that replaces the text and extracts any text substring of length e in the almost optimal time o log n r e log w within that space we similarly provide access to arbitrary suffix array inverse suffix array and longest common prefix array cells in time o log n r and extend these capabilities to full suffix tree functionality typically in o log n r time per operation our experiments show that our o r space index outperforms the space competitive alternatives by 1 2 orders of magnitude in time competitive implementations of the original fm index are outperformed by 1 2 orders of magnitude in space and or 2 3 in time

fast bwt in small space by blockwise suffix sorting abstract we present a new space and time efficient algorithm for computing the burrow wheeler transform bwt for any choice of a parameter v 3 n 2 3 the computation of bwt for a text of length n takes o n log n v n worst case time and o n log n v n average case time using o n log n v bits of space in addition to the text and the bwt for example if v log 2 n the time is o n log 2 n in the worst case and o n log n on an average with the additional space requirement of o n bits the algorithm is alphabet independent it uses only character comparisons and the complexities do not depend on the alphabet size unless v does a practical implementation is 2 3 times slower than one of the fastest and most space efficient previous algorithms while needing only one third of the main memory the algorithm is based on suffix arrays but unlike any other algorithm it can construct the suffix array a small block at a time without storing the rest of the suffix array anywhere

optimal induced universal graphs and adjacency labeling for trees in this article we show that there exists a graph g with o n nodes such that any forest of n nodes is an induced subgraph of g furthermore for constant arboricity k the result implies the existence of a graph with o nk nodes that contains all n node graphs of arboricity k as node induced subgraphs matching a nk lower bound of alstrup and rauhe our upper bounds are obtained through a log2n o 1 labeling scheme for adjacency queries in forests we hereby solve an open problem being raised repeatedly over decades by authors such as kannan et al chung and fraigniaud and korman

optimal lower bounds for rank and select indexes we develop a new lower bound technique for data structures we show an optimal omega n lg lg n lg n space lower bounds for storing an index that allows to implement rank and select queries on a bit vector b provided that b is stored explicitly these results improve upon miltersen soda 05 we show omega m t lg t lower bounds for storing rank select index in the case where b has m 1 bits in it e g low 0 th entropy and the algorithm is allowed to probe t bits of b we simplify the select index given in raman et al soda 02 and show how to implement both rank and select queries with an index of size 1 o 1 n lg lg n lg n o n lg n i e we give an explicit constant for storage in the ram model with word size lg n

optimal data compression algorithm abstract a practical source coding scheme based on approximate string matching is proposed it is an approximate fixed length string matching data compression combined with a block coder based on the empirical distribution a lemma on approximate string matching which is an extension of the kac lemma is proved it is shown based on the lemma that the deterministic algorithm converts the stationary and ergodic source u into an output process v and under the assumption that v is a stationary process after the scheme has run for an infinite time the optimal compression ratio r d is achieved this reduces the problem of the universal lossy coder to the proof of stationarity of the output process v in the proposed algorithm the main advantages of the proposed method are the asymptotic sequential behavior of the encoder and the simplicity of the decoder

space time trade offs for finding shortest unique substrings and maximal unique matches abstract given a string x 1 n and a position k 1 n a shortest unique substring of x covering k denoted by s k is a substring x i j of x which satisfies the following conditions i i k j ii i is the only position where there is an occurrence of x i j and iii j i is minimized current best known algorithms for finding s k require n words of working space and o n time let be a given parameter we present the following new results given a k 1 n we can compute s k in o n 2 log n time using x and an additional o n words of working space for every k 1 n we can compute s k in o n 2 log n time using x and an additional o n words and 4 n o n bits of working space we present an o n log c 1 n time randomized algorithm that uses n log c n words in addition to that mentioned above where c 0 is an arbitrary constant in this case the reported string is unique and covers k but with probability at most n o 1 may not be the shortest by choosing 1 our results imply the first sub linear space in addition to the input string solution to these problems we also present the following two results an algorithm that finds s k for every k 1 n using o n log bits of working space in o n log n time where n is the number of distinct symbols in x a 4 n o n bit index that can report s k for any k in o 1 time as a consequence of our techniques we also obtain similar space and time tradeoffs for a related problem of finding maximal unique matches of two strings delcher et al 1999 14

alphabet independent linear time construction of compressed suffix arrays using o n log n bit working space the suffix array is a fundamental index data structure in string algorithms and bioinformatics and the compressed suffix array csa and the fm index are its compressed versions many algorithms for constructing these index data structures have been developed recently hon et al w k hon k sadakane w k sung breaking a time and space barrier in constructing full text indices in proceedings of the 44th annual ieee symposium on foundations of computer science 2003 pp 251 260 proposed a construction algorithm using o nloglog time and o nlog bit working space which is the fastest algorithm using o nlog bit working space in this paper we give an efficient algorithm to construct the index data structures our algorithm constructs the suffix array the csa the fm index and burrows wheeler transform using alphabet independent o n time and bit working space where log32 our algorithm takes less time and more space than hon et al s algorithm our algorithm uses least working space among alphabet independent linear time algorithms

verifying and enumerating parameterized border arrays the parameterized pattern matching problem is to check if there exists a renaming bijection on the alphabet with which a given pattern can be transformed into a substring of a given text a parameterized border array p border array is a parameterized version of a standard border array and we can efficiently solve the parameterized pattern matching problem using p border arrays in this paper we present a linear time algorithm to verify if a given integer array is a valid p border array for a binary alphabet we also show a linear time algorithm to compute all binary parameterized strings sharing a given p border array in addition we give an algorithm which computes all p border arrays of length at most n where n is a given threshold this algorithm runs in o b 2 n time where b 2 n is the number of all p border arrays of length n for a binary parameter alphabet the problems with a larger alphabet are much more difficult still we present an o n 1 5 time o n space algorithm to verify if a given integer array of length n is a valid p border array for an unbounded alphabet the best previously known solution to this task takes time proportional to the n th bell number email protected k 0 k nk and hence our algorithm is much more efficient also we show that it is possible to enumerate all p border arrays of length at most n for an unbounded alphabet in o b nn 2 5 time where b n denotes the number of p border arrays of length n

restrictions of rainbow supercharacters abstract the maximal subgroup of unipotent upper triangular matrices of the finite general linear groups is a fundamental family of p groups their representation theory is well known to be wild but there is a standard supercharacter theory replacing irreducible representations by super representations that gives us some control over its representation theory while this theory has a beautiful underlying combinatorics built on set partitions the structure constants of restricted super representations remain mysterious this paper proposes a new approach to solving the restriction problem by constructing natural intermediate modules that help factor the computation of the structure constants we illustrate the technique by solving the problem completely in the case of rainbow supercharacters and some generalizations along the way we introduce a new q analogue of the binomial coefficients that depend on an underlying poset

unified fluid structure interpolation and mesh motion using radial basis functions a multivariate interpolation scheme using radial basis functions is presented which results in a completely unified formulation for the fluid structure interpolation and mesh motion problems the method has several significant advantages primarily all volume mesh structural mesh and flow solver type dependence is removed and all operations are performed on totally arbitrary point clouds of any form hence all connectivity and user input requirements are removed from the computational fluid dynamics computational structural dynamics cfd csd coupling problem as only point clouds are required to determine the coupling also it may equally well be applied to structured and unstructured grids or structural and aerodynamic grids that intersect again because no connectivity information is required furthermore no expensive computations are required during an unsteady simulation just matrix vector multiplications since the required dependence relations are computed only once prior to any simulation and then remain constant this property means that the method is both perfectly parallel since only the data relevant to each structured block or unstructured partition are required to move those points and totally independent from the flow solver hence a completely generic black box tool can be developed which is ideal for use in an optimization approach aeroelastic behaviour of the brite euram mdo wing is analysed in terms of both static deflection and dynamic responses and it is demonstrated that responses are strongly dependent on the exact cfd csd interpolation used mesh quality is also examined during the motion resulting from a large surface deformation global grid quality is shown to be preserved well with local grid orthogonality also being maintained well particularly at and near the moving surface where the original orthogonality is retained copyright 2007 john wiley sons ltd

generalizations of suffix arrays to multi dimensional matrices we propose multi dimensional index data structures that generalize suffix arrays to square matrices and cubic matrices giancarlo proposed a two dimensional index data structure the lsuffix tree that generalizes suffix trees to square matrices however the construction algorithm for lsuffix trees maintains complicated data structures and uses a large amount of space we present simple construction algorithms for multi dimensional suffix arrays by applying a new partitioning technique to lexicographic sorting our contributions are the first efficient algorithms for constructing two dimensional and three dimensional suffix arrays directly

parameterized longest previous factor given a string w the longest previous factor lpf problem is to determine the maximum length of a previously occurring factor for each suffix occurring in w the lpf problem is defined for traditional strings exclusively from the constant alphabet s a parameterized string p string is a string composed of symbols from a constant alphabet s and a parameter alphabet p we formulate the lpf problem in terms of p strings by defining the parameterized longest previous factor plpf problem subsequently we present an expected linear time solution to construct the parameterized longest previous factor plpf array given our plpf solution we show how to construct the plcp parameterized longest common prefix array with the same general algorithm we exploit the properties of the plpf data structure to also construct the standard lpf longest previous factor and lcp longest common prefix arrays all in linear time further we provide insight into the practicality of our construction algorithms

unsteady euler algorithm with unstructured dynamic mesh for complex aircraft aerodynamic analysis an euler solution algorithm is presented for unsteady aerodynamic analysis of complex aircr aft configurations the flow solver involves a multistage runge kutta time stepping scheme that uses a finite volume spatial discretization on an unstructured grid made up of tetrahedra a significant contribution of the research is the development and implementation of a moving mesh algorithm that is employed for problems involving static or dynamic deformation of the aircraft the mesh algorithm is a general procedure that can treat realistic motions and deformations of complex aircraft configurations steady and unsteady results are presented for a supersonic fighter configuration to demonstrate applications of the euler solver and dynamic mesh algorithm the unsteady flow results were obtained for the aircraft oscillating harmonically in a complete vehicle bending mode effects of angle of attack and reduced frequency on instantaneous pressures and force responses were investigated the paper presents descriptions of the euler solver and dynamic mesh algorithm along with results that assess the capability

compressed property suffix trees property matching is a biologically motivated problem where the task is to find those occurrences of an online pattern p in a string text t of size n such that the matched text part satisfies some conceptual property the property of a string is a set p of possibly overlapping intervals s 1 f 1 s 2 f 2 corresponding to the part of text and an occurrence of a pattern p t i i p 1 is a valid output only if t i i p 1 is completely contained in at least one interval s j f j email protected the indexing version of this problem was introduced by a amir 2008 where the text is preprocessed in o email protected nloglogn time and an o nlogn bits index named property suffix tree pst is maintained pst can perform property matching in o p email protected occ p time where occ p is the number of occurrences of p in t satisfying the property t kopelowitz 2010 considered the dynamic version of this problem where intervals can be added or deleted however all these indexes take space linear to the size of text o nlogn bits which can be much more than the size of the text email protected bits in this paper we propose the first index for property matching occupying space close to the entropy compressed space requirement of the text our compressed index takes csa n email protected o 1 bits space and performs query answering in o t p email protected 1 occ p t s a time where csa is the size of compressed suffix array of t t p be the time for searching a pattern of length p in csa t s a is the time for computing the suffix array value and e 0 is a constant we also introduce a dynamic index which takes csa o n p logn bits space and performs query answering in o t p 1 occ p logn t s a logn loglogn time and can update insert delete an interval s f in o f s logn t s a time

linear time computation of similarity measures for sequential data efficient and expressive comparison of sequences is an essential procedure for learning with sequential data in this article we propose a generic framework for computation of similarity measures for sequences covering various kernel distance and non metric similarity functions the basis for comparison is embedding of sequences using a formal language such as a set of natural words k grams or all contiguous subsequences as realizations of the framework we provide linear time algorithms of different complexity and capabilities using sorted arrays tries and suffix trees as underlying data structures experiments on data sets from bioinformatics text processing and computer security illustrate the efficiency of the proposed algorithms enabling peak performances of up to 106 pairwise comparisons per second the utility of distances and non metric similarity measures for sequences as alternatives to string kernels is demonstrated in applications of text categorization network intrusion detection and transcription site recognition in dna

efficient pattern matching for rna secondary structures we propose efficient methods to address key pattern matching problems in rna secondary structures using the notion of structural strings a structural string s string is composed of constant symbols and parameter symbols from the alphabets and respectively an individual symbol in the alphabet may be considered a complement of another unique symbol in the notion of matching constants parameters and complements is referred to as the structural matching s match problem which is helpful in matching rna and previously was solved by the structural suffix tree sst other approaches to rna matching that do not openly consider the s match include the use of affix data structures in this paper we provide new data structures and algorithms to address the s match problem specifically we introduce the structural suffix array and structural longest common prefix array and then identify how to s match with these data structures our new s matching solution is then used as the framework to answer various combinatorial queries encountered in matching rna secondary structures

a quick tour on suffix arrays and compressed suffix arrays suffix arrays are a key data structure for solving a run of problems on texts and sequences from data compression and information retrieval to biological sequence analysis and pattern discovery in their simplest version they can just be seen as a permutation of the elements in 1 2 n encoding the sorted sequence of suffixes from a given text of length n under the lexicographic order yet they are on a par with ubiquitous and sophisticated suffix trees over the years many interesting combinatorial properties have been devised for this special class of permutations for instance they can implicitly encode extra information and they are a well characterized subset of the n permutations this paper gives a short tutorial on suffix arrays and their compressed version to explore and review some of their algorithmic features discussing the space issues related to their usage in text indexing combinatorial pattern matching and data compression

a metric index for approximate string matching we present a radically new indexing approach for approximate string matching the scheme uses the metric properties of the edit distance and can be applied to any other metric between strings we build a metric space where the sites are the nodes of the suffix tree of the text and the approximate query is seen as a proximity query on that metric space this permits us finding the occ occurrences of a pattern of length m permitting up to r differences in a text of length n over an alphabet of size in average time o m1 e occ for any e 0 if r o m log m and m 1 e e log n the index works well up to r 3 2 m log m where it achieves its maximum average search complexity o m1 2 e occ the construction time of the index is o m1 2 e nlog n and its space is o m1 2 en this is the first index achieving average search time polynomial in m and independent of n for r o m log m previous methods achieve this complexity only for r o m log n we also present a simpler scheme needing o n space

parallel computation of the burrows wheeler transform in compact space abstract the burrows wheeler transform bwt has become since its introduction a key tool for representing large text collections in compressed space while supporting indexed searching on a text of length n over an alphabet of size it requires o n lg bits of space instead of the o n lg n bits required by classical indexes a challenge for its adoption is to build it within o n lg bits as well there are some sequential algorithms building it within this space but no such a parallel algorithm in this paper we present a pram crew algorithm to build the bwt using o n lg n work o lg 3 n lg depth and o n lg bits

tight bounds for searching a sorted array of strings given a k character query string and an array of n strings arranged in lexicographical order computing the rank of the query string among the n strings or deciding whether it occurs in the array requires the inspection of theta left frac k log log n log log 4 frac k log log n log n k log n right characters in the worst case