reducts of the random partial order abstract we determine up to the equivalence of first order interdefinability all structures which are first order definable in the random partial order it turns out that there are precisely five such structures we achieve this result by showing that there exist exactly five closed permutation groups which contain the automorphism group of the random partial order and thus expose all symmetries of this structure our result lines up with previous similar classifications for the random graph and the order of the rationals it also provides further evidence for a conjecture due to simon thomas which states that the number of structures definable in a homogeneous structure in a finite relational language is up to first order interdefinability always finite in the proof we use the new technique of canonical functions originally invented in the context of theoretical computer science which allows for a systematic ramsey theoretic analysis of functions acting on the random partial order the technique identifies patterns in arbitrary functions on the random partial order which makes them accessible to finite combinatorial arguments

net and prune a linear time algorithm for euclidean distance problems we provide a general framework for getting expected linear time constant factor approximations and in many cases fptas s to several well known problems in computational geometry such as k center clustering and farthest nearest neighbor the new approach is robust to variations in the input problem and yet it is simple elegant and practical in particular many of these well studied problems which fit easily into our framework either previously had no linear time approximation algorithm or required rather involved algorithms and analysis a short list of the problems we consider include farthest nearest neighbor k center clustering smallest disk enclosing k points kth largest distance kth smallest m nearest neighbor distance kth heaviest edge in the mst and other spanning forest type problems problems involving upward closed set systems and more finally we show how to extend our framework such that the linear running time bound holds with high probability

space time block codes from orthogonal designs we introduce space time block coding a new paradigm for communication over rayleigh fading channels using multiple transmit antennas data is encoded using a space time block code and the encoded data is split into n streams which are simultaneously transmitted using n transmit antennas the received signal at each receive antenna is a linear superposition of the n transmitted signals perturbed by noise maximum likelihood decoding is achieved in a simple way through decoupling of the signals transmitted from different antennas rather than joint detection this uses the orthogonal structure of the space time block code and gives a maximum likelihood decoding algorithm which is based only on linear processing at the receiver space time block codes are designed to achieve the maximum diversity order for a given number of transmit and receive antennas subject to the constraint of having a simple decoding algorithm the classical mathematical framework of orthogonal designs is applied to construct space time block codes it is shown that space time block codes constructed in this way only exist for few sporadic values of n subsequently a generalization of orthogonal designs is shown to provide space time block codes for both real and complex constellations for any number of transmit antennas these codes achieve the maximum possible transmission rate for any number of transmit antennas using any arbitrary real constellation such as pam for an arbitrary complex constellation such as psk and qam space time block codes are designed that achieve 1 2 of the maximum possible transmission rate for any number of transmit antennas for the specific cases of two three and four transmit antennas space time block codes are designed that achieve respectively all 3 4 and 3 4 of maximum possible transmission rate using arbitrary complex constellations the best tradeoff between the decoding delay and the number of transmit antennas is also computed and it is shown that many of the codes presented here are optimal in this sense as well

tree compression with top trees we introduce a new compression scheme for labeled trees based on top trees our compression scheme is the first to simultaneously take advantage of internal repeats in the tree as opposed to the classical dag compression that only exploits rooted subtree repeats while also supporting fast navigational queries directly on the compressed representation we show that the new compression scheme achieves close to optimal worst case compression can compress exponentially better than dag compression is never much worse than dag compression and supports navigational queries in logarithmic time

lines and free line segments tangent to arbitrary three dimensional convex polyhedra motivated by visibility problems in three dimensions we investigate the complexity and construction of the set of tangent lines in a scene of three dimensional polyhedra we prove that the set of lines tangent to four possibly intersecting convex polyhedra in mathbb r 3 with a total of n edges consists of theta n 2 connected components in the worst case in the generic case each connected component is a single line but our result still holds for arbitrarily degenerate scenes more generally we show that a set of k possibly intersecting convex polyhedra with a total of n edges admits in the worst case theta n 2k 2 connected components of maximal free line segments tangent to at least four polytopes furthermore these bounds also hold for possibly occluded lines rather than maximal free line segments finally we present an o n 2 k 2 log n time and o nk 2 space algorithm that given a scene of k possibly intersecting convex polyhedra computes all the minimal free line segments that are tangent to any four of the polytopes and are isolated transversals to the set of edges they intersect in particular we compute at least one line segment per connected component of tangent lines

computing maximally separated sets in the plane let s be a set of n points in reals 2 given an integer 1 le k le n we wish to find a maximally separated subset i subseteq s of size k this is a subset for which the minimum among the k choose 2 pairwise distances between its points is as large as possible the decision problem associated with this problem is to determine whether there exists i subseteq s i k so that all k choose 2 pairwise distances in i are at least 2 this problem can also be formulated in terms of disk intersection graphs let d be the set of unit disks centered at the points of s the disk intersection graph g of d has as edges all pairs of disks with nonempty intersection any set i with the above properties is then the set of centers of disks that form an independent set in the graph g this problem is known to be np complete if k is part of the input in this paper we first present a linear time eps approximation algorithm for any constant k next we give exact algorithms for the cases k 3 and k 4 that run in time o n 4 3 polylog n we also present a simpler n o sqrt k time exact algorithm as compared with the recent algorithm in j alber and j fiala j algorithms 52 2004 pp 134 151 for arbitrary values of k

adaptive multiregression in reproducing kernel hilbert spaces the multiaccess mimo channel case this paper introduces a wide framework for online i e time adaptive supervised multiregression tasks the problem is formulated in a general infinite dimensional reproducing kernel hilbert space rkhs in this context a fairly large number of nonlinear multiregression models fall as special cases including the linear case any convex continuous and not necessarily differentiable function can be used as a loss function in order to quantify the disagreement between the output of the system and the desired response the only requirement is the subgradient of the adopted loss function to be available in an analytic form to this end we demonstrate a way to calculate the subgradients of robust loss functions suitable for the multiregression task as it is by now well documented when dealing with online schemes in rkhs the memory keeps increasing with each iteration step to attack this problem a simple sparsification strategy is utilized which leads to an algorithmic scheme of linear complexity with respect to the number of unknown parameters a convergence analysis of the technique based on arguments of convex analysis is also provided to demonstrate the capacity of the proposed method the multiregressor is applied to the multiaccess multiple input multiple output channel equalization task for a setting with poor resources and nonavailable channel information numerical results verify the potential of the method when its performance is compared with those of the state of the art linear techniques which in contrast use space time coding more antenna elements as well as full channel information

assessing the uncertainty associated with intermittent rainfall fields 1 in many practical situations where spatial rainfall estimates are needed rainfall occurs as a spatially intermittent phenomenon an efficient geostatistical method for rainfall estimation in the case of intermittency has previously been published and comprises the estimation of two independent components a binary random function for modeling the intermittency and a continuous random function that models the rainfall inside the rainy areas the final rainfall estimates are obtained as the product of the estimates of these two random functions however the published approach does not contain a method for estimation of uncertainties the contribution of this paper is the presentation of the indicator maximum likelihood estimator from which the local conditional distribution of the rainfall value at any location may be derived using an ensemble approach from the conditional distribution representations of uncertainty such as the estimation variance and confidence intervals can be obtained an approximation to the variance can be calculated more simply by assuming rainfall intensity is independent of location within the rainy area the methodology has been validated using simulated and real rainfall data sets the results of these case studies show good agreement between predicted uncertainties and measured errors obtained from the validation data

supervised learning and co training co training under the conditional independence assumption is among the models which demonstrate how radically the need for labeled data can be reduced if a huge amount of unlabeled data is available in this paper we explore how much credit for this saving must be assigned solely to the extra assumptions underlying the co training model to this end we compute general almost tight upper and lower bounds on the sample size needed to achieve the success criterion of pac learning in the realizable case within the model of co training under the conditional independence assumption in a purely supervised setting the upper bounds lie significantly below the lower bounds for pac learning without co training thus co training saves labeled data even when not combined with unlabeled data on the other hand the saving is much less radical than the known savings in the semi supervised setting

minimum variance linear receivers for multiaccess mimo wireless systems with space time block coding we consider the problem of joint space time decoding and multiaccess interference mai rejection in multiuser multiple input multiple output mimo wireless communication systems we address the case when both the receiver and multiple transmitters are equipped with multiple antennas and when space time block codes stbcs are used to send the data simultaneously from each transmitter to the receiver a new linear receiver structure is developed to decode the data sent from the transmitter of interest while rejecting mai self interference and noise the proposed receivers are designed by minimizing the output power subject to constraints that zero force self interference and or preserve a unity gain for all symbols of the transmitter of interest simulation results show that in multiaccess scenarios the proposed techniques have substantially lower symbol error rates as compared with the matched filter mf receiver which is equivalent to the maximum likelihood ml space time decoder in the point to point mimo communication case

constellation space invariance of orthogonal space time block codes in this correspondence we prove an interesting property of orthogonal space time block codes ostbcs for flat block fading channels it is shown that the internal structure of the vector space of the input constellation remains invariant to the effects of both the ostbc and the channel except for certain scaling factors this property sheds light on the mechanism of maximum likelihood ml decoding of ostbcs and in particular provides an alternative explanation of why optimal decoding can be reduced to symbol by symbol decoding new simple expressions for the ml decoder are obtained which clarify its intrinsic structure

ray shooting and parametric search efficient algorithms for the ray shooting problem are presented given a collection gamma of objects in mathbb r d build a data structure so that for a query ray the first object of gamma hit by the ray can be quickly determined using the parametric search technique this problem is reduced to the segment emptiness problem for various ray shooting problems space query time trade offs of the following type are achieved for some integer b and a parameter m n leqslant m leqslant n b the queries are answered in time o n m 1 b log o 1 n with o m 1 varepsilon space and preprocessing time varepsilon 0 is arbitrarily small but fixed constant b lfloor d 2 rfloor is obtained for ray shooting in a convex d polytope defined as an intersection of n half spaces b d for an arrangement of n hyperplanes in mathbb r d and b 3 for an arrangement of n half planes in mathbb r 3 this approach also yields fast procedures for fin

an optimal algorithm for approximate nearest neighbor searching fixed dimensions consider a set of s of n data points in real d dimensional space r d where distances are measured using any minkowski metric in nearest neighbor searching we preprocess s into a data structure so that given any query point q r d is the closest point of s to q can be reported quickly given any positive real e data point p is a 1 e approximate nearest neighbor of q if its distance from q is within a factor of 1 e of the distance to the true nearest neighbor we show that it is possible to preprocess a set of n points in r d in o dn log n time and o dn space so that given a query point q r d and e 0 a 1 e approximate nearest neighbor of q can be computed in o c d e log n time where c d e d 1 6d e d is a factor depending only on dimension and e in general we show that given an integer k 1 1 e approximations to the k nearest neighbors of q can be computed in additional o kd log n time

comparing approaches to deal with non gaussianity of rainfall data in kriging based radar gauge rainfall merging merging radar and rain gauge rainfall data is a technique used to improve the quality of spatial rainfall estimates and in particular the use of kriging with external drift ked is a very effective radar rain gauge rainfall merging technique however kriging interpolations assume gaussianity of the process rainfall has a strongly skewed positive probability distribution characterized by a discontinuity due to intermittency in ked rainfall residuals are used implicitly calculated as the difference between rain gauge data and a linear function of the radar estimates rainfall residuals are non gaussian as well the aim of this work is to evaluate the impact of applying ked to non gaussian rainfall residuals and to assess the best techniques to improve gaussianity we compare box cox transformations with parameters equal to 0 5 0 25 and 0 1 box cox with time variant optimization of normal score transformation and a singularity analysis technique the results suggest that box cox with 0 1 and the singularity analysis are not suitable for ked normal score transformation and box cox with optimized or 0 25 produce satisfactory results in terms of gaussianity of the residuals probability distribution of the merged rainfall products and rainfall estimate quality when validated through cross validation however it is observed that box cox transformations are strongly dependent on the temporal and spatial variability of rainfall and on the units used for the rainfall intensity overall applying transformations results in a quantitative improvement of the rainfall estimates only if the correct transformations for the specific dataset are used

shorter arithmetization of nondeterministic computations arithmetizing computation is a crucial component of many fundamental results in complexity theory including results that gave insight into the power of interactive proofs multi prover interactive proofs and probabilistically checkable proofs informally an arithmetization is a way to encode a machine s computation so that its correctness can be easily verified via few probabilistic algebraic checks we study the problem of arithmetizing nondeterministic computations for the purpose of constructing short probabilistically checkable proofs pcps with polylogarithmic query complexity in such a setting a pcp s proof length depends at least linearly on the length in bits of the encoded computation thus minimizing the number of bits in the encoding is crucial for minimizing pcp proof length in this paper we show how to arithmetize any t step computation on a nondeterministic turing machine by using a polynomial encoding of length o t log t 2 previously the best known length was t log t 4 for nondeterministic random access machines our length is o t log t 2 o 1 while prior work only achieved t log t 5 the polynomial encoding that we use is the reed solomon code when combined with the best pcps of proximity for this code our result yields quasilinear size pcps with polylogarithmic query complexity that are shorter by at least two logarithmic factors than in all prior work our arithmetization also enjoys additional properties first it is succinct i e the encoding of the computation can be probabilistically checked in log t o 1 time this property is necessary for constructing short pcps with a polylogarithmic time verifier furthermore our techniques extend in a certain well defined sense to the arithmetization of yet other nexp complete languages

approximate polytope membership queries in the polytope membership problem a convex polytope k in mathbb r d is given and the objective is to preprocess k into a data structure so that given any query point q in mathbb r d it is possible to determine efficiently whether q in k we consider this problem in an approximate setting given an approximation parameter varepsilon the query can be answered either way if the distance from q to k s boundary is at most varepsilon times k s diameter we assume that the dimension d is fixed and k is presented as the intersection of n halfspaces previous solutions to approximate polytope membership were based on straightforward applications of classic polytope approximation techniques by dudley approx theory 10 1974 pp 227 236 and bentley faust and preparata commun acm 25 1982 pp 64 68 the former is optimal in the worst case with respect to space and the latter is optimal with respect to query time we present four main results first we show how

streaming with minimum space an algorithm for covering by two congruent balls in this paper we design a simple streaming algorithm for maintaining two smallest balls of equal radius in d dimension to cover a set of points in an on line fashion different from most of the traditional streaming models at any step we use the minimum amount of space by only storing the locations and the common radius of the balls previously such a geometric algorithm is only investigated for covering with one ball one center by zarrabi zadeh and chan 2006 16 we give an analysis of our algorithm which is significantly different from the one center algorithm due to the obvious possibility of grouping points wrongly under this streaming model we show that our algorithm has an approximation ratio 2 for d 1 and at most 5 611 for any fixed d 1 we also present lower bounds of 1 5 and 1 604 for the problem in the d 1 and d 1 cases respectively

a dynamic data structure for 3 d convex hulls and 2 d nearest neighbor queries we present a fully dynamic randomized data structure that can answer queries about the convex hull of a set of n points in three dimensions where insertions take o log3n expected amortized time deletions take o log6n expected amortized time and extreme point queries take o log2n worst case time this is the first method that guarantees polylogarithmic update and query cost for arbitrary sequences of insertions and deletions and improves the previous o ne time method by agarwal and matousek a decade ago as a consequence we obtain similar results for nearest neighbor queries in two dimensions and improved results for numerous fundamental geometric problems such as levels in three dimensions and dynamic euclidean minimum spanning trees in the plane

semiblind multiuser mimo channel estimation using capon and music techniques channel state information csi is required at the receiver side of multiple input multiple output mimo systems for decoding space time codes in this paper new semiblind techniques are developed to jointly estimate the receiver csi of multiple multiantenna transmitters that use orthogonal space time block codes ostbcs the proposed techniques are based on the extension of the concepts of the popular capon and music spectral estimators to the problem of multiuser channel estimation our methods blindly estimate the subspace that contains the user channel matrices and then use only a few training symbol blocks to extract the user csi from this subspace it is demonstrated that in addition to improving the bandwidth efficiency the proposed techniques offer better channel estimation accuracy as compared with the standard nonblind least squares ls channel estimation method moreover it is shown that using the proposed capon and music based semiblind channel estimators along with the coherent maximum likelihood ml or the minimum variance mv multiuser mimo receivers results in a substantially better performance as compared with the case when the standard ls channel estimates are used

an upper bound for the choice number of star edge coloring of graphs abstract the star chromatic index of a multigraph g denoted s g is the minimum number of colors needed to properly color the edges of g such that no path or cycle of length four is bi colored a multigraph g is star k edge colorable if s g k dvo ak et al 2013 proved that every subcubic multigraph is star 7 edge colorable they conjectured in the same paper that every subcubic multigraph should be star 6 edge colorable in this paper we consider this problem in a more general setting we investigate star list edge coloring of general graph g and obtain an upper bound for the choice number of star edge coloring of graphs namely we proved that s l 2 3 2 1 2 1 2 2

distributed coloring algorithms for triangle free graphs vertex coloring is a central concept in graph theory and an important symmetry breaking primitive in distributed computing whereas degree graphs may require palettes of 1 colors in the worst case it is well known that the chromatic number of many natural graph classes can be much smaller in this paper we give new distributed algorithms to find k coloring in graphs of girth 4 triangle free graphs girth 5 and trees the parameter k can be at most 1 4 o 1 ln in triangle free graphs and at most 1 o 1 ln in girth 5 graphs and trees where o 1 is a function of specifically for sufficiently large we can find such a coloring in o k log n time moreover for any we can compute such colorings in roughly logarithmic time for triangle free and girth 5 graphs and in o log log log n time on trees as a byproduct our algorithm shows that the chromatic number of triangle free graphs is at most 4 o 1 ln which improves on jamall s recent bound of 67 o 1 ln finally we show that 1 coloring for triangle free graphs can be obtained in sublogarithmic time for any

disjunctive kriging 1 overview of estimation and conditional probability the disjunctive kriging method described in this paper produces a nonlinear unbiased estimator with the characteristic minimum variance of errors disjunctive kriging is as good or otherwise better than linear estimators in the sense of reduced kriging variance and exactness of estimation it does not suffer from the difficulties associated with computing the conditional expectation and can be thought of as its estimator disjunctive kriging also provides an estimate of the conditional probability that a random variable located at a point or averaged over a block in two dimensional space is above some specified cutoff or tolerance level and this can be written in terms of the probability distribution or the density function the method has important implications in aiding management decisions by providing a quantitative input which is not readily obtained from the linear kriging estimators based on the available data which is the best nonlinear unbiased estimator short of the conditional expectation a major disadvantage in using disjunctive kriging is the increased computational time this however is mitigated by increased information about the estimate

approximating the radii of point sets we consider the problem of computing the outer radii of point sets in this problem we are given integers n d and k where k le d and a set p of n points in re d the goal is to compute the outer k radius of p denoted by cal r k p which is the minimum over all d k dimensional flats f of max p in p d p f where d p f is the euclidean distance between the point p and flat f computing the radii of point sets is a fundamental problem in computational convexity with many significant applications the problem admits a polynomial time algorithm when the dimension d is constant u faigle w kern and m streng math program 73 1996 pp 1 5 here we are interested in the general case in which the dimension d is not fixed and can be as large as n where the problem becomes np hard even for k 1 it is known that r k p can be approximated in polynomial time by a factor of 1 varepsilon for any varepsilon 0 when d k is a fixed constant m babdoiu s har peled and p indyk in proceedings of the acm symposium on the theory of computing 2002 s har peled and k varadarajan in proceedings of the acm symposium on computing geometry 2002 a polynomial time algorithm that guarantees a factor of o sqrt log n approximation for r 1 p the width of the point set p is implied by the results of nemirovski roos and terlaky math program 86 1999 pp 463 473 and nesterov handbook of semidefinite programming theory algorithms kluwer academic publishers norwell ma 2000 in this paper we show that r k p can be approximated by a ratio of o sqrt log n for any 1 leq k leq d thus matching the previously best known ratio for approximating the special case r 1 p the width of point set p our algorithm is based on semidefinite programming relaxation with a new mixed deterministic and randomized rounding procedure we also prove an inapproximability result that gives evidence that our approximation algorithm is doing well for a large range of k we show that there exists a constant delta 0 such that the following holds for any 0 eps 1 there is no polynomial time algorithm that approximates r k p within log n delta for all k such that k leq d d varepsilon unless np subseteq dtime 2 log m o 1 our inapproximability result for r k p extends a previously known hardness result of brieden discrete comput geom 28 2002 pp 201 209 and is proved by modifying brieden s construction using basic ideas from probabilistically checkable proofs pcp theory

a fully polynomial time approximation scheme for the smallest diameter of imprecise points abstract given a set d d 1 d n of imprecise points modeled as disks the minimum diameter problem is to locate a set p p 1 p n of fixed points where p i d i such that the furthest distance between any pair of points in p is as small as possible this introduces a tight lower bound on the size of the diameter of any instance p in this paper we present a fully polynomial time approximation scheme fptas for computing the minimum diameter of a set of disjoint disks that runs in o n 2 1 time then we relax the disjointness assumption and we show that adjusting the presented fptas will cost o n 2 2 time we also show that our results can be generalized in r d when the dimension d is an arbitrary fixed constant

fast detection of polyhedral intersection abstract methods are given for unifying and extending previous work on detecting intersections of suitably preprocessed polyhedra new upper bounds of o log n and o log2 n are given on plane polyhedron and polyhedron polyhedron intersection problems

linear receivers for the multiple input multiple output multiple access channel we consider a multiuser multiple input multiple output mimo communication system using code division multiple access cdma and multiuser detection to discriminate the different users our focus is on the cdma uplink of a frequency nonselective rayleigh fading channel we study two types of receivers joint receivers which address simultaneously both spatial and multiple access interference and separate receivers addressing the two types of interference individually this approach allows assessing the benefits of adding mimo processing capabilities to existing multiuser single input single output systems for both receiver types we analyze solutions based on linear matched filter decorrelator minimum mean square error and maximum likelihood receivers for all the receivers considered we provide closed form expressions as expectations of given functions of the resulting pairwise error probabilities performance results are obtained in terms of frame error rate versus eb n0 following two different approaches an analytic approach using large system asymptotic methods whereby the system parameters number of users and antennas spreading gain are assumed to grow to infinity with finite limiting ratios a computer simulation approach is used to illustrate the differences between asymptotic and simulation results

space time block codes a maximum snr approach in tarokh et al 1999 space time block codes were introduced to obtain coded diversity for a multiple antenna communication system in this work we cast space time codes in an optimal signal to noise ratio snr framework and show that they achieve the maximum snr and in fact they correspond to a generalized maximal ratio combiner the maximum snr framework also helps in calculating the distribution of the snr and in deriving explicit expressions for bit error rates we bring out the connection between the theory of amicable orthogonal designs and space time codes based on this we give a much simpler proof to one of the main theorems on space time codes for complex symbols we present a rate 1 2 code for complex symbols which has a smaller delay than the code already known we also present another rate 3 4 code which is simpler than the one already known in the sense it does not involve additions or multiplications we also point out the connection between generalized real designs and generalized orthogonal designs

approximating extent measures of points we present a general technique for approximating various descriptors of the extent of a set p of n points in rd when the dimension d is an arbitrary fixed constant for a given extent measure and a parameter e 0 it computes in time o n 1 eo 1 a subset q p of size 1 eo 1 with the property that 1 e p q p the specific applications of our technique include e approximation algorithms for i computing diameter width and smallest bounding box ball and cylinder of p ii maintaining all the previous measures for a set of moving points and iii fitting spheres and cylinders through a point set p our algorithms are considerably simpler and faster in many cases than previously known algorithms

disjunctive kriging 2 examples the disjunctive kriging dk method described in detail in the previous paper of this series is illustrated by two examples the first example is for the electrical conductivity ec which is approximately lognormally distributed in the second example the natural logarithm of the ec is used to produce an approximately normally distributed data set the data set was chosen since the hermite coefficients for a normal and lognormal distribution could be determined analytically as well as to facilitate a comparison between ordinary and disjunctive kriging the capability of dk to be a nonlinear estimator and an estimator of the conditional probability is explored the results indicate that dk is a better estimator than linear estimators i e ordinary kriging in the sense of reduced variance of errors and average kriging variance even when the data are approximately normally or lognormally distributed also using dk one can obtain an estimate of the conditional probability

on translational motion planning of a convex polyhedron in 3 space let b be a convex polyhedron translating in 3 space amidst k convex polyhedral obstacles a1 ak with pairwise disjoint interiors the free configuration space space of all collision free placements of b can be represented as the complement of the union of the minkowski sums p i a i oplus b for i 1 k we show that the combinatorial complexity of the free configuration space of b is o nk log k and that it can be omega nk alpha k in the worst case where n is the total complexity of the individual minkowski sums p1 pk we also derive an efficient randomized algorithm that constructs this configuration space in expected time o nk log k log n

finding transversals for sets of simple geometric figures abstract a straight line that intersects all members of a set s of objects in the real plane is called a transversal of s geometric transforms are described that reduce transversal problems for various types of objects to convex hull problems for points these reductions lead to efficient algorithms for finding transversals which are also described applications of the algorithms are found in computer graphics reproduce the line displayed by a collection of pixels and in statistics find the line that minimizes the maximum distance from a collection of weighted points in the plane

disjunctive kriging 3 cokriging the disjunctive kriging dk method described in the first paper of this series is extended to account for more than one random function in the derivation contained herein two random functions are considered but this is easily generalized to any number an example is presented using disjunctive cokriging dck where the surface gravimetric moisture content is estimated using the bare soil temperature as an auxiliary random function the results indicate that the dck procedure produces a better estimator than ordinary cokriging in terms of reduced variance of errors and exactness of estimation also using dck an estimate of the conditional probability that the level of a property is greater than a known cutoff value can be obtained in general this conditional probability is better than the dk probability by virtue of the additional information contained in the second auxiliary random function

an optimal algorithm for intersecting three dimensional convex polyhedra this paper describes a linear time algorithm for computing the intersection of two convex polyhedra in 3 space applications of this result to computing intersections convex hulls and voronoi diagrams are also given

biased search trees we consider the problem of storing items from a totally ordered set in a search tree so that the access time for a given item depends on a known estimate of the access frequency of the item we describe two related classes of biased search trees whose average access time is within a constant factor of the minimum and that are easy to update under insertions deletions and more radical update operations we present and analyze efficient update algorithms for biased search trees we list several applications of such trees

fast construction of nets in low dimensional metrics and their applications we present a near linear time algorithm for constructing hierarchical nets in finite metric spaces with constant doubling dimension this data structure is then applied to obtain improved algorithms for the following problems approximate nearest neighbor search well separated pair decomposition spanner construction compact representation scheme doubling measure and computation of the approximate lipschitz constant of a function in all cases the running preprocessing time is near linear and the space being used is linear

space time tradeoffs for approximate nearest neighbor searching nearest neighbor searching is the problem of preprocessing a set of n point points in d dimensional space so that given any query point q it is possible to report the closest point to q rapidly in approximate nearest neighbor searching a parameter e 0 is given and a multiplicative error of 1 e is allowed we assume that the dimension d is a constant and treat n and e as asymptotic quantities numerous solutions have been proposed ranging from low space solutions having space o n and query time o log n 1 ed 1 to high space solutions having space roughly o n log n ed and query time o log n e we show that there is a single approach to this fundamental problem which both improves upon existing results and spans the spectrum of space time tradeoffs given a tradeoff parameter where 2 1 e we show that there exists a data structure of space o n d 1 log 1 e that can answer queries in time o log n 1 e d 1 2 when e 2 this yields a data structure of space o n log 1 e that can answer queries in time o log n 1 e d 1 2 when e 1 e it provides a data structure of space o n ed 1 log 1 e that can answer queries in time o log n e our results are based on a data structure called a t e avd which is a hierarchical quadtree based subdivision of space into cells each cell stores up to t representative points of the set such that for any query point q in the cell at least one of these points is an approximate nearest neighbor of q we provide new algorithms for constructing avds and tools for analyzing their total space requirements we also establish lower bounds on the space complexity of avds and show that up to a factor of o log 1 e our space bounds are asymptotically tight in the two extremes e 2 and e 1 e

three valued semantics for hybrid mknf knowledge bases revisited abstract knorr et al 2011 9 formulated a three valued formalism for the logic of minimal knowledge and negation as failure mknf and proposed a well founded semantics for hybrid mknf knowledge bases the main results state that if a hybrid mknf knowledge base has a three valued mknf model its well founded mknf model exists which is unique and can be computed by an alternating fixpoint construction however we show that these claims are erroneous the goal of this paper is two fold first we provide insight into why these claims fail to hold this leads to a classification of hybrid mknf knowledge bases into a hierarchy of four classes of which the smallest one is what works for the well founded semantics proposed by knorr et al after that we characterize three valued mknf models into what we call stable partitions which are similar to partial stable models in logic programming the intuitive notion of stable partitions allows us to discover a new proof theoretic method to determine whether a three valued mknf model exists for a given hybrid mknf knowledge base we can guess partial partitions and verify their stability by computing alternating fixpoints and by performing a consistency check this algorithm can be applied to compute all three valued mknf models as well as all two valued ones originally formulated by motik and rosati for query answering as a result our work provides a uniform characterization of well founded two valued and all three valued mknf models in terms of stable partitions and the alternating fixpoint construction

closed form blind mimo channel estimation for orthogonal space time block codes in this paper a new computationally simple approach to blind decoding of orthogonal space time block codes ostbcs is proposed using specific properties of ostbcs the authors approach estimates the channel matrix in a closed form and in a fully blind fashion this channel estimate is then used in the maximum likelihood ml receiver to decode the information symbols the proposed estimation technique provides consistent channel estimates and as a result the performance of the authors blind ml receiver approaches that of the coherent ml receiver which exploits the exact channel state information csi simulation results demonstrate the performance improvements achieved by the proposed blind decoding algorithm relative to the popular differential space time modulation scheme

computing some distance functions between polygons abstract we present algorithms for computing some distance functions between two possibly intersecting polygons in both the convex and nonconvex cases the interest for such distance functions comes from applications in robot vision pattern recognition and contour fitting we present an optimal erew pram parallel algorithm for the case when the input polygons are convex and an essentially quadratic sequential algorithm for the case of arbitrary polygons possibly with holes

computing a minimum width square annulus in arbitrary orientation in this paper we address the problem of computing a minimum width square annulus in arbitrary orientation that encloses a given set of n points in the plane a square annulus is the region between two concentric squares we present an o n 3 log n time algorithm that finds such a square annulus over all orientations

a decomposition of multidimensional point sets with applications to k nearest neighbors and n body potential fields we define the notion of a well separated pair decomposition of points in d dimensional space we then develop efficient sequential and parallel algorithms for computing such a decomposition we apply the resulting decomposition to the efficient computation of k nearest neighbors and n body potential fields

intersection of convex objects in two and three dimensions one of the basic geometric operations involves determining whether a pair of convex objects intersect this problem is well understood in a model of computation in which the objects are given as input and their intersection is returned as output for many applications however it may be assumed that the objects already exist within the computer and that the only output desired is a single piece of data giving a common point if the objects intersect or reporting no intersection if they are disjoint for this problem none of the previous lower bounds are valid and algorithms are proposed requiring sublinear time for their solution in two and three dimensions

multiaccess interference suppression in orthogonal space time block coded mimo systems by adaptive projected subgradient method this paper introduces adaptive filters that are effective to suppress multiple access interference mai in orthogonal space time block coded multiple input multiple output ostbc mimo systems we define an optimal linear filter that minimizes the mean square error between the filter output and a scaled version of the desired output under a constraint defined by the available channel state information csi the adaptive filters refine a given estimate of the optimal filter by suppressing a sequence of closed convex functions with the adaptive projected subgradient method apsm at each iteration to provide robustness against imperfect csi the adaptive filters use not only the available csi but also estimates of previously transmitted symbols which usually belong to a small finite set in digital communication systems the resulting algorithms employ computationally efficient projections onto hyperplanes or hyperslabs and do not require any matrix inversion an efficient recursive scheme based on such an algorithm is also presented convergence analysis and simulation results show the excellent performance of the proposed schemes

dynamic planar convex hull operations in near logarithmic amortized time we give a data structure that allows arbitrary insertions and deletions on a planar point set p and supports basic queries on the convex hull of p such as membership and tangent finding updates take o log 1 e n amori tzed time and queries take o log n time each where n is the maximum size of p and e is any fixed positive constant for some advanced queries such as bridge finding both our bounds increase to o log 3 2 n the only previous fully dynamic solution was by overmars and van leeuwen from 1981 and required o log 2 n time per update and o log n time per query

stochastic mv pure estimator robust reduced rank estimator for stochastic linear model this paper proposes a novel linear estimator named stochastic mv pure estimator developed for the stochastic linear model and designed to provide improved performance over the linear minimum mean square error mmse wiener estimator in cases prevailing in practical real world settings where at least some of the second order statistics of the random vectors under consideration are only imperfectly known the proposed estimator shares its main mathematical idea and terminology with the recently introduced minimum variance pseudo unbiased reduced rank estimator mv pure developed for the linear regression model the proposed stochastic mv pure estimator minimizes the mean square error mse of its estimates subject to rank constraint and inducing minimum distortion to the target random vector therefore the stochastic mv pure combines the techniques of the reduced rank wiener filter named in this paper rr mmse and the distortionless constrained estimator named in this paper c mmse in order to achieve greater robustness against noise or model errors than rr mmse and c mmse furthermore to ensure that the stochastic mv pure estimator combines the reduced rank and minimum distortion approaches in the mse optimal way we propose a rank selection criterion which minimizes the mse of the estimates obtained by the stochastic mv pure as a numerical example we employ the stochastic mv pure rr mmse c mmse and mmse estimators as linear receivers in a mimo wireless communication system this example is chosen as a typical signal processing scenario where the statistical information on the data on which the estimates are built is only imperfectly known we verify that the stochastic mv pure achieves the lowest mse and symbol error rate ser in such settings by employing the proposed rank selection criterion

robust linear receivers for space time block coded multiaccess mimo systems with imperfect channel state information recently several linear receiver algorithms have been developed for space time block coded multiaccess multiple input multiple output mimo wireless communication systems all these techniques are based on the assumption that the channel state information csi at the receiver side is perfect however in practical situations the available csi may be imperfect because of channel estimation errors and or outdated training in this paper we develop new robust linear receiver techniques for joint space time decoding and interference rejection in multiaccess mimo systems that use orthogonal space time block codes and erroneous csi the proposed receivers are based on worst case performance optimization they are shown to provide a substantially improved robustness against csi mismatches as compared with the existing linear multiaccess mimo receivers

blind and semiblind channel and carrier frequency offset estimation in orthogonally space time block coded mimo systems in this paper the problem of joint channel and carrier frequency offset cfo estimation is studied in the context of multiple input multiple output mimo communications based on orthogonal space time block codes ostbcs a new blind approach is proposed to jointly estimate the channel matrix and the cfo parameters using a relaxed maximum likelihood ml estimator that for the sake of simplicity ignores the finite alphabet constraint although the proposed technique can be applied to the majority of ostbcs there are however a few codes that suffer from an intrinsic ambiguity in the joint channel cfo and symbol estimates for such specific ostbcs a semiblind modification of the proposed approach is developed that resolves the aforementioned estimation ambiguity our simulation results demonstrate that although the finite alphabet constraint is relaxed the performance of the proposed techniques approaches that of the informed fully frequency synchronized and coherent receiver provided that a sufficient number of data blocks is available for each channel realization

a subexponential algorithm for abstract optimization problems an abstract optimization problem aop is a triple h phi where h is a finite set a total order on 2 h and phi an oracle that for given f subseteq g subseteq h either reports that f min f mid f subseteq g or returns a set f subseteq g with f e 2 sqrt n o sqrt 4 n ln n oracle calls n h in contrast any deterministic algorithm needs to make 2 n 1 oracle calls in the worst case the algorithm is applied to the problem of finding the distance between two n vertex or n facet convex polyhedra in d space and to the computation of the smallest ball containing n points in d space for both problems we give the first subexponential bounds in the arithmetic model of computation

efficient search for approximate nearest neighbor in high dimensional spaces we address the problem of designing data structures that allow efficient search for approximate nearest neighbors more specifically given a database consisting of a set of vectors in some high dimensional euclidean space we want to construct a space efficient data structure that would allow us to search given a query vector for the closest or nearly closest vector in the database we also address this problem when distances are measured by the l1 norm and in the hamming cube significantly improving and extending recent results of kleinberg we construct data structures whose size is polynomial in the size of the database and search algorithms that run in time nearly linear or nearly quadratic in the dimension depending on the case the extra factors are polylogarithmic in the size of the database

algorithms for a minimum volume enclosing simplex in three dimensions we develop a combinatorial algorithm for determining a minimum volume simplex enclosing a set of points in cal r 3 if the convex hull of the points has n vertices then our algorithm takes theta n 4 time combining our exact but slow algorithm with a simple but crude approximation technique we also develop an varepsilon approximation algorithm the algorithm computes in o n 1 varepsilon 6 time a simplex whose volume is within 1 varepsilon factor of the optimal for any varepsilon 0