distribution free consistent independence tests via center outward ranks and signs this article investigates the problem of testing independence of two random vectors of general dimensions for this we give for the first time a distribution free consistent test our approach com

efficient tests for top down termination of logical rules considered is the question of whether top down prolog like evaluation of a set of logical rules can be guaranteed to terminate the nail system is designed to process programs consisting of logical rules and to select for each fragment of the program the best from among many possible strategies for its evaluation in the context of such a system it is essential that termination tests be fast thus the uniqueness property of logical rules is introduced this property is satisfied by many of the common examples of rules and is easily recognized for rules with this property a set of inequalities whose satisfaction is sufficient for termination of the rules can be generated in polynomial time then a polynomial test for satisfaction of constraints generated by this process is given

minimal representation of directed hypergraphs in this paper the problem of minimal representations for particular classes of directed hypergraphs is analyzed various concepts of minimal representations of directed hypergraphs called minimal equivalent hypergraphs are introduced as extensions to the concepts of transitive reduction and minimum equivalent graph of directed graphs in particular we consider equivalent hypergraphs which are minimal with respect to all parameters which may be adopted to characterize a given hypergraph number of hyperarcs number of adjacency lists required for the representation length of the overall description etc the relationships among the various concepts of minimality are discussed and their computational properties are analyzed in order to derive such results a graph representation of hypergraphs is introduced

on line computation of minimal and maximal length paths abstract we consider the problem of maintaining minimum length paths in a directed graph g v e with n nodes while inserting new arcs a data structure which supports the following operations is presented an add operation which inserts an arc in the digraph and a minpath operation which returns a minimal length path between a pair of nodes the data structure supports each minpath operation in o k worst case time where k n is the length of the returned path moreover if we assume that the weights of the arcs are integer numbers in the range 1 w then the expected cost of any sequence of add operations is o min n 4 n 3 max w log n time the space complexity is o n 2 the same algorithm can be used for solving the problem of maintaining maximum length paths when the digraph is acyclic and add operations preserve acyclicity

optimal covering tours with turn costs we give the first algorithmic study of a class of covering tour problems related to the geometric traveling salesman problem find a polygonal tour for a cutter so that it sweeps out a specified region pocket in order to minimize a cost that depends mainly on the number of turns these problems arise naturally in manufacturing applications of computational geometry to automatic tool path generation and automatic inspection systems as well as arc routing postman problems with turn penalties we prove the np completeness of minimum turn milling and give efficient approximation algorithms for several natural versions of the problem including a polynomial time approximation scheme based on a novel adaptation of the m guillotine method

fully dynamic planarity testing with applications this paper introduces compressed certificates for planarity biconnectivity and triconnectivity in planar graphs and proves many structural properties of certificates in planar graphs as an application of our compressed certificates we develop efficient dynamic planar algorithms in particular we consider the following three operations on a planar graph g i insert an edge if the resultant graph remains planar ii delete an edge and iii test whether an edge could be added to the graph without violating planarity we show how to support each of the above operations in o n 2 3 time where n is the number of vertices in the graph the bound for tests and deletions is worst case while the bound for insertions is amortized this is the first algorithm for this problem with sub linear running time and it affirmatively answers a question posed in epstein et al 1992 we use our compressed certificates for biconnectivity and triconnectivity to maintain the biconnected and triconnected components of a dynamic planar graph the time bounds are the same o n 2 3 worst case time per edge deletion o n 2 3 amortized time per edge insertion and o n 2 3 amortized time per edge insertion and o n 2 3 worst case time to check whether two vertices are either biconnected or triconnected

an asymptotic property of factorizable completely positive maps and the connes embedding problem we establish a reformulation of the connes embedding problem in terms of an asymptotic property of factorizable completely positive maps we also prove that the holevo werner channels w n are factorizable for all odd integers n neq 3 furthermore we investigate factorizability of convex combinations of w 3 and w 3 a family of channels studied by mendl and wolf and discuss asymptotic properties for these channels

well posed constraint preserving boundary conditions for the linearized einstein equations in this paper we address the problem of specifying boundary conditions for einstein s equations when linearized around minkowski space using the generalized einstein christoffel symmetric hyperbolic system of evolution equations the boundary conditions we work out guarantee that the constraints are satisfied provided they are satisfied on the initial slice and ensures a well posed initial boundary value formulation we consider the case of a manifold with a non smooth boundary as is the usual case of the cubic boxes commonly used in numerical relativity the techniques discussed should be applicable to more general cases as linearizations around more complicated backgrounds and may be used to establish well posedness in the full non linear case

schur multipliers and mixed unitary maps we consider the tensor product of the completely depolarising channel on d d matrices with the map of schur multiplication by a k k correlation matrix and characterise via matrix theory methods when such a map is a mixed random unitary channel when d 1 this recovers a result of o meara and pereira and for larger d is equivalent to a result of haagerup and musat that was originally obtained via the theory of factorisation through von neumann algebras we obtain a bound on the distance between a given correlation matrix for which this tensor product is nearly mixed unitary and a correlation matrix for which such a map is exactly mixed unitary this bound allows us to give an elementary proof of another result of haagerup and musat about the closure of such correlation matrices without appealing to the theory of von neumann algebras

tent spaces associated with semigroups of operators abstract we study tent spaces on general measure spaces we assume that there exists a semigroup of positive operators on l p satisfying a monotone property but do not assume any geometric metric structure on the semigroup plays the same role as integrals on cones and cubes in euclidean spaces we then study bmo spaces on general measure spaces and get an analogue of fefferman s h 1 bmo duality theory we also get a h 1 bmo duality inequality without assuming the monotone property all the results are proved in a more general setting namely for noncommutative l p spaces

conditional expectations in von neumann algebras and a theorem of takesaki conditional expectations play an important role in classical probability theory in the general context of von neumann algebras they were impliciteiy used by von neumann 41 chap ii and by dixmier 14 nakamura and turumaru 27 and umegaki 36 391 introduced an axiomatic definition of the concept of conditional expectation in the framework of von neumann or c algebras and established many properties of these objects especially in the context of von neumann algebras with a finite trace their starting point was the characterization given by moy 26 of the classical conditional expectations as operators on spaces of measurable functions tomiyama showed 33 that conditional expectations in the sense of the above mentioned authors can be characterized as norm one projection in c algebras the importance of norm one projection in the classification problem of von neumann algebras was recognized by hakeda and tomiyama 23 and subsequent research on this argument confirmed the usefulness of these objects this line of thought culminated in the fundamental work of connes 121 in which approximately finite von 245 0022 1236 82 020245 29 02 00 o

dynamical entropy of c algebras and von neumann algebras the definition of the dynamical entropy is extended for automorphism groups ofc algebras as an example the dynamical entropy of the shift of a lattice algebra is studied and it is shown that in some cases it coincides with the entropy density

dilations of semigroups on von neumann algebras and noncommutative lp spaces abstract we prove that any weak continuous semigroup t t t 0 of factorizable markov maps acting on a von neumann algebra m equipped with a normal faithful state can be dilated by a group of markov automorphisms analogous to the case of a single factorizable markov operator which is an optimal result we also give a version of this result for strongly continuous semigroups of operators acting on noncommutative l p spaces and examples of semigroups to which the results of this paper can be applied our results imply the boundedness of the mcintosh s h functional calculus of the generators of these semigroups on the associated noncommutative l p spaces generalising some previous work from junge le merdy and xu finally we also give concrete dilations for poisson semigroups which are even new in the case of r n

relaxed most negative cycle and most positive cut canceling algorithms for minimum cost flow this paper presents two new scaling algorithms for the minimum cost network flow problem one a primal cycle canceling algorithm the other a dual cut canceling algorithm both algorithms scale a relaxed optimality parameter and create a second inner relaxation the primal algorithm uses the inner relaxation to cancel a most negative node disjoint family of cycles w r t the scaled parameter the dual algorithm uses it to cancel most positive cuts w r t the scaled parameter we show that in a network with n nodes and m arcs both algorithms need to cancel only omn objects per scaling phase furthermore we show how to efficiently implement both algorithms to yield weakly polynomial running times that are as fast as any other cycle or cut canceling algorithms our algorithms have potential practical advantages compared to some other canceling algorithms as well along the way we give a comprehensive survey of cycle and cut canceling algorithms for min cost flow we also clarify the formal duality between cycles and cuts

an extensional treatment of lazy data flow deadlock in an extensional treatment of dataflow deadlock wa81 wadge introduced an elegant non operational test for proving that many of kahn s data flow message passing networks ka74 must be free of deadlock a test that should extend to a much wider context in the study of program correctness such a context has now been provided with the introduction of partial metric spaces ma92 these spaces can be used to describe semantic domains such as those used in lazy data flow languages w a85 this paper develops wadge s ideas on establishing an extensional theory of program correctness by using partial metric spaces to give a non operational treatment of lazy data flow deadlock

factorization and dilation problems for completely positive maps on von neumann algebras we study factorization and dilation properties of markov maps between von neumann algebras equipped with normal faithful states i e completely positive unital maps which preserve the given states and also intertwine their automorphism groups the starting point for our investigation has been the question of existence of non factorizable markov maps as formulated by c anantharaman delaroche we provide simple examples of non factorizable markov maps on m n mathbb c for all n 3 as well as an example of a one parameter semigroup t t t 0 of markov maps on m 4 mathbb c such that t t fails to be factorizable for all small values of t 0 as applications we solve in the negative an open problem in quantum information theory concerning an asymptotic version of the quantum birkhoff conjecture as well as we sharpen the existing lower bound estimate for the best constant in the noncommutative little grothendieck inequality

single source shortest paths in h minor free graphs we present an algorithm for the single source shortest paths sssp problem in directedh minor free graphs for every fixed h if g is a graph with n vertices having integer edge lengths and s is a designated source vertex of g the algorithm runs in o n 1 1 5 2logl o n 1 3 9 2logl time where l is the absolute value of the smallest edge length the algorithm computes the shortest paths and the distances from s to all vertices of the graph or else provides a certificate that g is not h minor free our result improves an earlier o n 1 5logl time algorithm for this problem which follows from a general sssp algorithm of goldberg

an on line edge deletion problem there is given an undirected graph g v e from which edges are deleted one at a time and about which questions of the type are the vertices u and v in the same connected component have to be answered on line there is presented an algorithm which maintains a data structure in which each question is answered in constant time and for which the total time involved in answering q questions and maintaining the data structure is o q i vi led

dynamic reachability in planar digraphs with one source and one sink abstract in this paper we investigate the reachability problem on spherical st graphs which are planar acyclic digraphs with exactly one source and exactly one sink these digraphs find specific applications to visibility representations planarity testing planar graph embedding graph drawing and motion planning let n be the number of vertices first we show that reachability queries in a spherical st graph can be answered in o 1 time using an o n space data structure that can be constructed in o n time next we present a dynamic data structure which uses o n space and supports reachability queries and updates in o log n time finally we show how to extend these results to planar digraphs that have one source and one sink and may have directed cycles

faster scaling algorithms for general graph matching problems an algorithm for minimum cost matching on a general graph with integral edge costs is presented the algorithm runs in time close to the fastest known bound for maximum cardinality matching specifically let n m and n denote the number of vertices number of edges and largest magnitude of a cost respectively the best known time bound for maximum cardinal ity matching m 0 am the new algorithm for minimum cost matching has time bound 0 in a m n iog n m log nn a slight modification of the new algorithm finds a maximum cardinality matching in 0 fire time other applications of the new algorlthm are given mchrding an efficient implementa tion of christofides traveling salesman approximation algorithm and efficient solutions to update problems that require the linear programming duals for matching

a decomposition theorem for maximum weight bipartite matchings let g be a bipartite graph with positive integer weights on the edges and without isolated nodes let n n and w be the node count the largest edge weight and the total weight of g let k x y be log x log x2 y we present a new decomposition theorem for maximum weight bipartite matchings and use it to design an o sqrt n w k n w n time algorithm for computing a maximum weight matching of g this algorithm bridges a long standing gap between the best known time complexity of computing a maximum weight matching and that of computing a maximum cardinality matching given g and a maximum weight matching of g we can further compute the weight of a maximum weight matching of g u for all nodes u in o w time

trade offs for fully dynamic transitive closure on dags breaking through the o n 2 barrier we present an algorithm for directed acyclic graphs that breaks through the o n2 barrier on the single operation complexity of fully dynamic transitive closure where n is the number of edges in the graph we can answer queries in o ne worst case time and perform updates in o n 1 e 1 epn1pe worst case time for any e 0 1 where 1 e 1 is the exponent of the multiplication of an n ne matrix by an ne n matrix the current best bounds on 1 e 1 imply an o n0 575 query time and an o n1 575 update time in the worst case our subquadratic algorithm is randomized and has one sided error as an application of this result we show how to solve single source reachability in o n1 575 time per update and constant time per query

dynamic maintenance of directed hypergraphs abstract in this paper we are concerned with the on line maintenance of directed hypergraphs a generalization of directed graphs previously introduced in the literature in particular we show how to maintain efficiently information about hyperpaths while new hyperarcs are inserted we present a data structure which allows us to check whether there exists a hyperpath between an arbitrarily given pair of nodes in constant time and to return such a hyperpath in a time which is linear in its size the total time required to maintain the data structure during the insertion of new hyperarcs is o mn where m is the total size of the description of the hyperarcs and n is the number of nodes this generalizes a previous result known for directed graphs and has applications in several areas of computer science such as rewriting systems database schemes logic programming and problem solving an extension of these results to hyperpaths between sets of nodes is also presented

grothendieck s theorem for operator spaces we prove several versions of grothendieck s theorem for completely bounded linear maps t e f when e and f are operator spaces we prove that if e f are c algebras of which at least one is exact then every completely bounded t e f can be factorized through the direct sum of the row and column hilbert operator spaces equivalently t can be decomposed as t t r t c where t r resp t c factors completely boundedly through a row resp column hilbert operator space this settles positively at least partially some earlier conjectures of effros ruan and blecher on the factorization of completely bounded bilinear forms on c algebras moreover our result holds more generally for any pair e f of exact operator spaces this yields a characterization of the completely bounded maps from a c algebra or from an exact operator space to the operator hilbert space oh as a corollary we prove that up to a complete isomorphism the row and column hilbert operator spaces and their direct sums are the only operator spaces e such that both e and its dual e are exact we also characterize the schur multipliers which are completely bounded from the space of compact operators to the trace class

a shortest path algorithm for real weighted undirected graphs we present a new scheme for computing shortest paths on real weighted undirected graphs in the fundamental comparison addition model in an efficient preprocessing phase our algorithm creates a linear size structure that facilitates single source shortest path computations in o m log alpha time where alpha alpha m n is the very slowly growing inverse ackermann function m the number of edges and n the number of vertices as special cases our algorithm implies new bounds on both the all pairs and single source shortest paths problems we solve the all pairs problem in o mn log alpha m n time and if the ratio between the maximum and minimum edge lengths is bounded by n log n o 1 we can solve the single source problem in o m n log log n time both these results are theoretical improvements over dijkstra s algorithm which was the previous best for real weighted undirected graphs our algorithm takes the hierarchy based approach invented by thorup

linear time approximation for maximum weight matching the maximum cardinality and maximum weight matching problems can be solved in o m n time a bound that has resisted improvement despite decades of research here m and n are the number of edges and vertices in this article we demonstrate that this m n barrier can be bypassed by approximation for any e 0 we give an algorithm that computes a 1 e approximate maximum weight matching in o me 1 log e 1 time that is optimal linear time for any fixed e our algorithm is dramatically simpler than the best exact maximum weight matching algorithms on general graphs and should be appealing in all applications that can tolerate a negligible relative error

the modular symmetry of markov maps abstract a state preserving automorphism of a von neumann algebra induces a canonical unitary operator on the gns hilbert space of the state which fixes the vacuum this unitary commutes with both the modular operator of the state and its modular conjugation we prove an extension of this result for state preserving unital completely positive maps

on ergodic theorems for free group actions on noncommutative spaces we extend in a noncommutative setting the individual ergodic theorem of nevo and stein concerning measure preserving actions of free groups and averages on spheres s 2 n of even radius here we study state preserving actions of free groups on a von neumann algebra a and the behaviour of s 2 n x for x in noncommutative spaces l p a for the cesaro means this problem was solved by walker our approach is based on ideas of bufetov we prove a noncommutative version of rota alternierende verfahren theorem to this end we introduce specific dilations of the powers of some noncommutative markov operators

amortized efficiency of a path retrieval data structure a data structure is presented for the problem of maintaining a digraph under an arbitrary sequence of two kinds of operations an add operation that inserts an arc in the digraph and a searchpath operation that checks the presence of a path between a pair of nodes our data structure supports both operations in o n amortized time and requires o n2 space where n is the number of nodes in the digraph

bounds on the distance between a unital quantum channel and the convex hull of unitary channels motivated by the recent resolution of asymptotic quantum birkhoff conjecture aqbc we attempt to estimate the distance between a given unital quantum channel and the convex hull of unitary channels we provide two lower bounds on this distance by employing techniques from quantum information and operator algebras respectively we then show how to apply these results to construct some explicit counterexamples to aqbc we also point out an interesting connection between the grothendieck s inequality and aqbc

sparse dynamic programming for evolutionary tree comparison constructing evolutionary trees for species sets is a fundamental problem in biology unfortunately there is no single agreed upon method for this task and many methods are in use current practice dictates that trees be constructed using different methods and that the resulting trees should be compared for consensus it has become necessary to automate this process as the number of species under consideration has grown we study one formalization of the problem the maximum agreement subtree mast problem the mast problem is as follows given a set a and two rooted trees ct 0 and ct 1 leaf labeled by the elements of a find a maximum cardinality subset b of a such that the topological restrictions of ct 0 and ct 1 to b are isomorphic in this paper we will show that this problem reduces to unary weighted bipartite matching uwbm with an o n 1 o 1 additive overhead we also show that uwbm reduces linearly to mast thus our algorithm is optimal unless uwbm can be solved in near linear time the overall running time of our algorithm is o n 1 5 log n improving on the previous best algorithm which runs in o n 2 we also derive an o n c sqrt log n time algorithm for the case of bounded degrees whereas the previously best algorithm runs in o n 2 as in the unbounded case

quantum channels arising from abstract harmonic analysis we present a new application of harmonic analysis to quantum information by constructing intriguing classes of quantum channels stemming from specific representations of multiplier algebras over locally compact groups g beginning with a representation of the measure algebra m g we unify and elaborate on recent counter examples to a conjecture on the structure of fixed point subalgebras in infinite dimensions as well as present an application to the noiseless subsystems method of quantum error correction using a representation of the completely bounded fourier multiplier algebra mcba g we provide a new class of counter examples to the recently solved asymptotic quantum birkhoff conjecture along with a systematic method of producing the examples using a geometric representation of schur maps further properties of our channels including duality quantum capacity and entanglement preservation are discussed along with potential applications to additivity conjectures

faster scaling algorithms for network problems this paper presents algorithms for the assignment problem the transportation problem and the minimum cost flow problem of operations research the algorithms find a minimum cost solution yet run in time close to the best known bounds for the corresponding problems without costs for example the assignment problem equivalently minimum cost matching in a bipartite graph can be solved in o sqrt nm log nn time where n m and n denote the number of vertices number of edges and largest magnitude of a cost costs are assumed to be integral the algorithms work by scaling as in the work of goldberg and tarjan in each scaled problem an approximate optimum solution is found rather than an exact optimum

reducing rank maximal to maximum weight matching given a bipartite graph g v e email protected email protected b where v n e m and a partition of the edge set into email protected m disjoint subsets e e email protected email protected e email protected email protected email protected email protected e r which are called ranks the rank maximal matching problem is to find a matching m of g such that email protected e 1 is maximized and given that email protected e 1 is maximized email protected e 2 is also maximized and so on such a problem arises as an optimization criteria over a possible assignment of a set of applicants to a set of posts the matching represents the assignment and the ranks on the edges correspond to a ranking of the posts submitted by the applicants the rank maximal matching problem and several other optimization variants e g fair matching and maximum cardinality rank maximal matching can be solved by a reduction to the weight matching problem in time o rnmlogn recently irving et al developed a combinatorial approach which improves the running time for the rank maximal matching problem to o min n r rn m they raised the open questions on a whether such a running time can be achieved by the weight matching reduction and b whether such a running time can be achieved for the other variants of the problem in this work we show how the reduction to the weight matching problem can also be used to achieve the same running time our algorithm is simpler and more intuitive

the essentially commutative dilations of dynamical semigroups on m n for identity and trace preserving one parameter semigroups tt t 0 on then n matricesmn we obtain a complete description of their essentially commutative dilations i e dilations which can be constructed on a tensor product ofmn by a commutativew algebra

temporal stratification tests for linear and branching time deductive databases we consider the problem of extending temporal deductive databases with stratified negation we argue that the classical stratification test for deductive databases is too restrictive when one shifts attention to the temporal case moreover as we demonstrate the more general local stratification approach is impractical detecting whether a temporal deductive database is locally stratified is shown to be co np hard even if one restricts attention to programs that only use one predicate symbol and two constants for these reasons we define temporal stratification an intermediate notion between stratification and local stratification we demonstrate that for the temporal deductive databases we consider temporal stratification coincides with local stratification in certain important cases in which the latter is polynomial time decidable we then develop two algorithms for detecting temporal stratification the first algorithm applies to linear time temporal deductive databases and it is efficient and more general than existing approaches however the algorithm sacrifices completeness for efficiency since it does not cover the whole class of temporally stratified programs the second algorithm applies to branching time temporal deductive databases which include as a special case the linear time ones this algorithm is more expensive from a computational point of view but it covers the whole class of temporally stratified programs we discuss the relative merits of the two algorithms and compare them with other existing approaches

gestalt based feature similarity measure in trademark database motivated by the studies in gestalt principle this paper describes a novel approach on the adaptive selection of visual features for trademark retrieval we consider five kinds of visual saliencies symmetry continuity proximity parallelism and closure property the first saliency is based on zernike moments while the others are modeled by geometric elements extracted illusively as a whole from a trademark given a query trademark we adaptively determine the features appropriate for retrieval by investigating its visual saliencies we show that in most cases either geometric or symmetric features can give us good enough accuracy to measure the similarity of geometric elements we propose a maximum weighted bipartite graph wbg matching algorithm under transformation sets which is found to be both effective and efficient for retrieval

a near linear time e approximation algorithm for geometric bipartite matching for point sets a b rd mam e mbm e n and for a parameter e 0 we present a monte carlo algorithm that computes in o npoly log n 1 e time an e approximate perfect matching of a and b under any lp norm with high probability the previously best known algorithm takes n3 2 time we approximate the lp norm using a distance function d based on a randomly shifted quad tree the algorithm iteratively generates an approximate minimum cost augmenting path under d in time proportional within a polylogarithmic factor to the length of the path we show that the total length of the augmenting paths generated by the algorithm is o n e log n implying that the running time of our algorithm is o npoly log n 1 e

factorizations of quantum channels abstract we find a connection between the existence of a factorization of a quantum channel and the existence of low rank solutions to certain linear matrix equations using this we show that if a quantum channel is factorized by a direct integral of factors it must lie in the convex hull of quantum channels which are factorized respectively by the factors in the direct integral we use this to characterize some non trivial extreme points in the set of factorizable quantum channels and give an example

on non semisplit extensions tensor products and exactness of group c algebras we show the existence of a block diagonal extensionb of the suspensions a of the reduced groupc algebraa c sl 2 such that there is only onec norm on the algebraic tensor productb op b butb is not nuclear even not exact thus the class of exactc algebras is not closed under extensions the existence comes from a new established tensorial duality between the weak expectation property wep of lance and the local variant llp of the lifting property we characterize the local lifting property of separable unitalc algebrasa as follows a has the local lifting property if and only if ext s a is a group wheres a is the suspension ofa if moreovera is the quotient algebra of ac algebra withwep for brevity a isqwep but does not satisfyllp then there exists a quasidiagonal extensionb of the suspensions a by the compact operators such that on the algebraic tensor productb op b there is only onec norm the question if everyc algebra isqwep remains open but we obtain the following results onqwep ac algebrac isqwep if and only ifc isqwep a von neumannii 1 factorn with separable predualn isqwep if and only ifn is a von neumann subfactor of the ultrapower of the hyperfiniteii 1 factor ifg is a maximally almost periodic discrete non amenable group with haagerup s herz schur multiplier constant g 1 then the universal groupc algebrac g is not exact but the reduced groupc albegrac g is exact and isqwep but does not satisfywep andllp we study functiorial properties of the classes ofc algebras satisfyingwep llp resp beingqwep as applications we obtain some unexpected relations between some open questions onc algebras

finding approximate patterns in undirected acyclic graphs abstract we consider an approximate pattern matching problem for undirected acyclic graphs specifically let p be a pattern graph d a data graph and t an integer we present an algorithm to locate a subgraph in d whose distance from p is at most t the distance measure used here is the degree 2 metric published previously the time complexity of our algorithm is o n p n d d d log d where n p and n d are the number of nodes in p and d respectively d min d p d d d p and d d are the maximum degree of p and d respectively central to our algorithm is a procedure for finding approximate patterns in rooted unordered trees and freely allowing cuts we discuss two applications of the algorithms in chemical information search and website management on the internet

testing logic programs for local stratification abstract locally stratified programs are a significant class of logic programs with negation for which both declarative and fixpoint semantics are well defined unfortunately in most cases recognizing local stratification is so hard a task that it has been conjectured that the problem is undecidable indeed in this paper a formal proof of this undecidability is presented and rather general sufficient conditions for local stratification are introduced

markov dilations on w algebras abstract in this paper a systematic study of markov dilations is begun for completely positive operators on w algebras which leave a faithful normal state invariant it is shown that a minimal markov dilation preserves important properties of the underlying completely positive operator afterwards some results are proved concerning the construction of dilations which lead to markov dilations for large classes of operators finally some of the ideas developed here are applied to the study of a simple example over the 2 2 matrices

maintenance of 2 and 3 edge connected components of graphs ii data structures and algorithms are presented to efficiently maintain the 2 and 3 edge connected components of a general graph under insertions of edges and nodes in the graph at any moment the data structure can answer whether two nodes are 2 or 3 edge connected the algorithms run in o n alpha m n time where m is the total number of queries and edge insertions furthermore a linear time algorithm is presented for maintaining the 2 edge connected components in case the initial graph is connected finally a new solution is presented for the 2 vertex connected components of a graph

an efficient cost scaling algorithm for the assignment problem the cost scaling push relabel method has been shown to be efficient for solving minimum cost flow problems in this paper we apply the method to the assignment problem and investigate implementations of the method that take advantage of assignment s special structure the results show that the method is very promising for practical use

decomposable approximations of nuclear c algebras abstract we show that nuclear c algebras have a refined version of the completely positive approximation property in which the maps that approximately factorize through finite dimensional algebras are convex combinations of order zero maps we use this to show that a separable nuclear c algebra a which is closely contained in a c algebra b embeds into b

cavity matchings label compressions and unrooted evolutionary trees we present an algorithm for computing a maximum agreement subtree of two unrooted evolutionary trees it takes o n1 5 log n time for trees with unbounded degrees matching the best known time complexity for the rooted case our algorithm allows the input trees to be mixed trees i e trees that may contain directed and undirected edges at the same time our algorithm adopts a recursive strategy exploiting a technique called label compression the backbone of this technique is an algorithm that computes the maximum weight matchings over many subgraphs of a bipartite graph as fast as it takes to compute a single matching

stratified negation in temporal logic programming and the cycle sum test we consider stratified negation in temporal logic programming we demonstrate that the cycle sum test which was initially proposed for detecting deadlocks in the context of temporal functional programming can also be used as a syntactic stratification test for temporal logic programming therefore on the one hand we exhibit a class of temporal logic programs with negation which have a well defined semantics and on the other hand we provide further evidence that the cycle sum test is a fundamental one in the area of temporal programming

finding minimum cost circulations by canceling negative cycles a classical algorithm for finding a minimum cost circulation consists of repeatedly finding a residual cycle of negative cost and canceling it by pushing enough flow around the cycle to saturate an arc we show that a judicious choice of cycles for canceling leads to a polynomial bound on the number of iterations in this algorithm this gives a very simple strongly polynomial algorithm that uses no scaling a variant of the algorithm that uses dynamic trees runs in o nm log n min log nc m log n time on a network of n vertices m arcs and arc costs of maximum absolute value c this bound is comparable to those of the fastest previously known algorithms

exact and approximation algorithms for weighted matroid intersection in this paper we propose new exact and approximation algorithms for the weighted matroid intersection problem our exact algorithm is faster than previous algorithms when the largest weight is relatively small our approximation algorithm delivers a 1 epsilon approximate solution with a running time significantly faster than most known exact algorithms the core of our algorithms is a decomposition technique we decompose an instance of the weighted matroid intersection problem into a set of instances of the unweighted matroid intersection problem the computational advantage of this approach is that we can make use of fast unweighted matroid intersection algorithms as a black box for designing algorithms more precisely we show that we can solve the weighted matroid intersection problem via solving w instances of the unweighted matroid intersection problem where w is the largest given weight assuming that all given weights are integral furthermore we can find a 1 epsilon approximate solution via solving o epsilon 1 log r instances of the unweighted matroid intersection problem where r is the smaller rank of the two given matroids our algorithms make use of the weight splitting approach of frank j algorithms 2 4 328 336 1981 and the geometric scaling scheme of duan and pettie j acm 61 1 1 2014 our algorithms are simple and flexible they can be adapted to special cases of the weighted matroid intersection problem using specialized unweighted matroid intersection algorithms in addition we give a further application of our decomposition technique we solve efficiently the rank maximal matroid intersection problem a problem motivated by matching problems under preferences

fibonacci heaps and their uses in improved network optimization algorithms in this paper we develop a new data structure for implementing heaps priority queues our structure fibonacci heaps abbreviated f heaps extends the binomial queues proposed by vuillemin and studied further by brown f heaps support arbitrary deletion from an n item heap in o log n amortized time and all other standard heap operations in o 1 amortized time using f heaps we are able to obtain improved running times for several network optimization algorithms in particular we obtain the following worst case bounds where n is the number of vertices and m the number of edges in the problem graph o n log n m for the single source shortest path problem with nonnegative edge lengths improved from o m log m n 2 n o n 2 log n nm for the all pairs shortest path problem improved from o nm log m n 2 n o n 2 log n nm for the assignment problem weighted bipartite matching improved from o nm log m n 2 n o m m n for the minimum spanning tree problem improved from o m log log m n 2 n where m n min i u log i n m n note that m n log n if m n of these results the improved bound for minimum spanning trees is the most striking although all the results give asymptotic improvements for graphs of appropriate densities

the general structure of edge connectivity of a vertex subset in a graph and its incremental maintenance odd case let g v e be an undirected graph s be a subset of its vertices frak c s be the set of minimum edge cuts partitioning s and lambda s be the cardinality of such a cut we suggest a graph structure called the connectivity carcass of s that represents both cuts in frak c s and the partition of v by all these cuts its size is o min e lambda s v in this paper we present general constructions and study in detail the case lambda s odd the specifics of the case lambda s even are considered elsewhere for an adequate description of the connectivity carcass we introduce a new type of graph locally orientable graphs which generalize digraphs the connectivity carcass consists of a locally orientable quotient graph of g a cactus tree in case lambda s odd just a tree representing all distinct partitions of s by cuts in frak c s and a mapping connecting them one can build it in o s max flow computations in g for an arbitrary sequence of u edge insertions not changing lambda s the connectivity carcass can be maintained in time o v min e lambda s v u for two vertices of g queries asking whether they are separated by a cut in frak c s are answered in o 1 worst case time per query another possibility is to maintain the carcass in o s min e lambda s v u time but to answer the queries in o 1 time only if at least one of the vertices belongs to s

solving linear programs from sign patterns this paper is an attempt to provide a connection between qualitative matrix theory and linear programming a linear program max cx mid ax b x geq 0 is said to be sign solvable if the set of sign patterns of the optimal solutions is uniquely determined by the sign patterns of a b and c it turns out to be np hard to decide whether a given linear program is sign solvable or not we then introduce a class of sign solvable linear programs in terms of totally sign nonsingular matrices which can be recognized in polynomial time for a linear program in this class we devise an efficient combinatorial algorithm to obtain the sign pattern of an optimal solution from the sign patterns of a b and c the algorithm runs in o m time where m is the number of rows of a and is the number of all nonzero entries in a b and c

the effros ruan conjecture for bilinear forms on c algebras in 1991 effros and ruan conjectured that a certain grothendieck type inequality for a bilinear form on c algebras holds if and only if the bilinear form is jointly completely bounded in 2002 pisier and shlyakhtenko proved that this inequality holds in the more general setting of operator spaces provided that the operator spaces in question are exact moreover they proved that the conjecture of effros and ruan holds for pairs of c algebras of which at least one is exact in this paper we prove that the effros ruan conjecture holds for general c algebras with constant one more precisely we show that for every jointly completely bounded for short j c b bilinear form on a pair of c algebras a and b there exist states f 1 f 2 on a and g 1 g 2 on b such that for all a a and b b u a b leq u mathrm jcb big f 1 aa 1 2 g 1 b b 1 2 f 2 a a 1 2 g 2 bb 1 2 big while the approach by pisier and shlyakhtenko relies on free probability techniques our proof uses more classical operator algebra theory namely tomita takesaki theory and special properties of the powers factors of type iii 0 1

a similarity metric for edge images the performance of several discrepancy measures for the comparison of edge images is analyzed and a novel similarity metric aimed at overcoming their problems is proposed the algorithm finds an optimal matching of the pixels between the images and estimates the error produced by this matching the resulting pixel correspondence metric pcm can take into account edge strength as well as the displacement of edge pixel positions in the estimation of similarity a series of experimental tests shows the new metric to be a robust and effective tool in the comparison of edge images when a small localization error of the detected edges is allowed

on birkhoff s theorem for doubly stochastic completely positive maps of matrix algebras abstract a study is made of the extreme points of the convex set of doubly stochastic completely positive maps of the matrix algebra m n if n 2 the extreme points are precisely the unitary maps but if n 3 there are nonunitary extreme points examples of which are exhibited a tilde operation is defined on the linear maps of m n and used to give an elementary derivation of a result of kummerer and maassen

the initial boundary value problem for einstein s vacuum field equation we study the initial boundary value problem for einstein s vacuum field equation we prescribe initial data on an orientable compact 3 dimensional manifold s with boundary and boundary conditions on the manifold t re 0 we assume the boundaries and 0 of s and t to be identified in the natural way furthermore we prescribe certain gauge source functions which determine the evolution of the fields provided that all data are smooth and certain consistency conditions are met on we show that there exists a smooth solution to einstein s equation ric g 0 on a manifold which has after an identification a neighbourhood of s in t s as a boundary the solution is such that s is space like the initial data are induced by the solution on s and in the region of t where the solution is defined t is time like and the boundary conditions are satisfied

finding minimum cost circulations by successive approximation we develop a new approach to solving minimum cost circulation problems our approach combines methods for solving the maximum flow problem with successive approximation techniques based on cost scaling we measure the accuracy of a solution by the amount that the complementary slackness conditions are violated we propose a simple minimum cost circulation algorithm one version of which runs in on3lognc time on an n vertex network with integer arc costs of absolute value at most c by incorporating sophisticated data structures into the algorithm we obtain a time bound of onm logn2 mlognc on a network with m arcs a slightly different use of our approach shows that a minimum cost circulation can be computed by solving a sequence of on lognc blocking flow problems a corollary of this result is an on2log nlognc time m processor parallel minimum cost circulation algorithm our approach also yields strongly polynomial minimum cost circulation algorithms our results provide evidence that the minimum cost circulation problem is not much harder than the maximum flow problem we believe that a suitable implementation of our method will perform extremely well in practice

non closure of quantum correlation matrices and factorizable channels that require infinite dimensional ancilla with an appendix by narutaka ozawa we show that there exist factorizable quantum channels in each dimension ge 11 which do not admit a factorization through any finite dimensional von neumann algebra and do require ancillas of type hbox ii 1 thus witnessing new infinite dimensional phenomena in quantum information theory we show that the set of n times n matrices of correlations arising as second order moments of projections in finite dimensional von neumann algebras with a distinguished trace is non closed for all n ge 5 and we use this to give a simplified proof of the recent result of dykema paulsen and prakash that the set of synchronous quantum correlations c q s 5 2 is non closed using a trick originating in work of regev slofstra and vidick we further show that the set of correlation matrices arising from second order moments of unitaries in finite dimensional von neumann algebras with a distinguished trace is non closed in each dimension ge 11 from which we derive the first result above

new algorithms for maximum weight matching and a decomposition theorem we revisit the classical maximum weight matching problem in general graphs with nonnegative integral edge weights we present an algorithm that operates by decomposing the problem into w unweighted versions of the problem where w is the largest edge weight our algorithm has running time as good as the current fastest algorithms for the maximum weight matching problem when w is small one of the highlights of our algorithm is that it also produces an integral optimal dual solution thus our algorithm also returns an integral certificate corresponding to the maximum weight matching that was computed our algorithm yields a new proof to the total dual integrality of edmonds matching polytope and it also gives rise to a decomposition theorem for the maximum weight of a matching in terms of the maximum size of a matching in certain subgraphs we also consider the maximum weight capacitated b matching problem in bipartite graphs with nonnegative integral edge weights and show that it can also be decomposed i

worst case analysis of set union algorithms this paper analyzes the asymptotic worst case running time of a number of variants of the well known method of path compression for maintaining a collection of disjoint sets under union we show that two one pass methods proposed by van leeuwen and van der weide are asymptotically optimal whereas several other methods including one proposed by rein and advocated by dijkstra are slower than the best methods

distributed asynchronous relaxation methods for convex network flow problems we consider the solution of the single commodity strictly convex network flow problem in a distributed asynchronous computation environment the dual of this problem is unconstrained differentiable and well suited for solution via gauss seidel relaxation we show that the structure of the dual allows the successful application of a distributed asynchronous method whereby relaxation iterations are carried out in parallel by several processors in arbitrary order and with arbitrarily large interprocessor communication delays

technical note a note on parametric analysis in linear assignment a classic application of the linear assignment problem is the assignment of people to jobs or jobs to people in this context it is interesting to measure competition for jobs and to generate a suitable list of jobs from which a person can choose the length of the list is a parameter a known list generation procedure is based on an interior point method followed by a parametric analysis we describe a more efficient procedure exploiting linear assignment theory and shortest path computations further we propose an alternative list generation procedure based on a special type of dual values for the linear assignment problem

markov quantum semigroups admit covariant markov c dilations through a daniell kolmogorov type construction to any markov quantum semigroup on ac algebra there is associated a quantum stochastic process which is a dilation of the semigroup and satisfies a covariance rule which implies the weak markov property

a new approach to the maximum flow problem all previously known efficient maximum flow algorithms work by finding augmenting paths either one path at a time as in the original ford and fulkerson algorithm or all shortest length augmenting paths at once using the layered network approach of dinic an alternative method based on the preflow concept of karzanov is introduced a preflow is like a flow except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out the method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated to be shortest paths the algorithm and its analysis are simple and intuitive yet the algorithm runs as fast as any other known method on dense graphs achieving an o n 3 time bound on an n vertex graph by incorporating the dynamic tree data structure of sleator and tarjan we obtain a version of the algorithm running in o nm log n 2 m time on an n vertex m edge graph this is as fast as any known method for any graph density and faster on graphs of moderate density the algorithm also admits efficient distributed and parallel implementations a parallel implementation running in o n 2 log n time using n processors and o m space is obtained this time bound matches that of the shiloach vishkin algorithm which also uses n processors but requires o n 2 space

generalized lcs the longest common subsequence lcs is a well studied problem having a wide range of implementations its motivation is in comparing strings it has long been of interest to devise a similar measure for comparing higher dimensional objects and more complex structures in this paper we study the longest common substructure of two matrices and show that this problem is np hard we also study the longest common subforest problem for multiple trees including a constrained version as well we show np hardness for k 2 unordered trees in the constrained lcs we also give polynomial time algorithms for ordered trees and prove a lower bound for any decomposition strategy for k trees

quantum magic squares dilations and their limitations quantum permutation matrices and quantum magic squares are generalizations of permutation matrices and magic squares where the entries are no longer numbers but elements from arbitrary non commutative algebras the famous birkhoff von neumann theorem characterizes magic squares as convex combinations of permutation matrices in the non commutative case the corresponding question is as follows does every quantum magic square belong to the matrix convex hull of quantum permutation matrices that is does every quantum magic square dilate to a quantum permutation matrix here we show that this is false even in the simplest non commutative case we also classify the quantum magic squares that dilate to a quantum permutation matrix with commuting entries and prove a quantitative lower bound on the diameter of this set finally we conclude that not all arveson extreme points of the free spectrahedron of quantum magic squares are quantum permutation matrices

unital quantum channels convex structure and revivals of birkhoff s theorem the set of doubly stochastic quantum channels and its subset of mixtures of unitaries are investigated we provide a detailed analysis of their structure together with computable criteria for the separation of the two sets when applied to o d covariant channels this leads to a complete characterization and reveals a remarkable feature instances of channels which are not in the convex hull of unitaries can become elements of this set by either taking two copies of them or supplementing with a completely depolarizing channel these scenarios imply that a channel whose noise initially resists any environment assisted attempt of correction can become perfectly correctable

detecting ill posed boundary conditions in general relativity a persistent challenge in numerical relativity is the correct specification of boundary conditions in this work we consider a many parameter family of symmetric hyperbolic initial boundary value formulations for the linearized einstein equations and analyze its well posedness using the laplace fourier technique by using this technique ill posed modes can be detected and thus a necessary condition for well posedness is provided we focus on the following types of boundary conditions i boundary conditions that have been shown to preserve the constraints ii boundary conditions that result from setting the ingoing constraint characteristic fields to zero and iii boundary conditions that result from considering the projection of einstein s equations along the normal to the boundary surface while we show that in case i there are no ill posed modes our analysis reveals that unless the parameters in the formulation are chosen with care there exist ill posed constraint violating modes in the remaining cases

noncommutative riesz transforms a probabilistic approach for 2 p 0 in the classical setting this is certainly satisfied for the maps tt f f 1 t where t is a semigroup of measure preserving maps on a probability space in that case n l then the maps tt act on all noncommutative lp spaces lp n and in particular on the hilbert space l2 l2 n let a be the negative generator i e tt e ta for technical reasons we have to assume that there is a weakly dense algebra a n which lies in the domain of the unbounded operator a i e a a a the algebra a plays the role of smooth functions in the classical setting this assumption might be too restrictive for some classical applications but it is easily verified in the new noncommutative examples for elements x y a we may define the gradient form 2 x y a x y x a y a x y the correct definition of is the one given by sauvageot as a bilinear form with values in l1 again our arguments require stronger assumptions in fact in all our examples we will assume that the tt s are selfadjoint i e ttxy xtty and unital i e tt 1 1 then a is indeed a positive unbounded operator under these circumstances we can formulate p a meyer s problem is it true that x x 2 p c p a 1 2 x p 0 1 holds for all selfadjoint elements x a let us illustrate this question by considering the laplace operator a f f where i 2 x2 i then it is easily verified that

an improved dijkstra s shortest path algorithm for sparse network abstract on a network with nonnegative length edges dijkstra s shortest path algorithm computes single source shortest path in o m n log n time the time bound assumes that a fibonacci heap is used during the implementation of dijkstra s algorithm as the process of building heaps needs a little complex work it makes the algorithm not easy to be used in this paper we make some very simple but useful changes in the original dijkstra algorithm and obtain a new improved dijkstra s shortest path algorithm that avoids the process of building heap and runs in o m d max log n time here m n and d max are the number of edges vertices and the maximal number of edges incident with vertex respectively thus the new algorithm is very competitive for those sparse networks especially in road traffic networks in which d max is often a small number

well posed constraint preserving boundary conditions for the aa formulation of einstein s equations in this paper we address the problem of artificial boundary conditions for the symmetric linearized hyperbolic formulation of einstein s equations introduced in a m alekseenko d n arnold new first order formulation for the einstein equations phys rev d 3 68 6 2003 064013 6 pp we prescribe simple boundary conditions that make the problem well posed and preserve the constraints