faster tree pattern matching recently r kosaraju gave an o nmo 75polylog m step algorithm for tree pattern matching we improve this result by designing a simple o n6 polylog m algorithm

improved parallel construction of wavelet trees and rank select structures abstract existing parallel algorithms for wavelet tree construction have a work complexity of o n log this paper presents parallel algorithms for the problem with improved work complexity our first algorithm is based on parallel integer sorting and has either o n log log n log log n log log n work and polylogarithmic depth or o n log log n work and sub linear depth we also describe another algorithm that has o n log log n work and o log n depth we then show how to use similar ideas to construct variants of wavelet trees arbitrary shaped binary trees and multiary trees as well as wavelet matrices in parallel with lower work complexity than prior algorithms finally we show that the rank and select structures on binary sequences and multiary sequences which are stored on wavelet tree nodes can be constructed in parallel with improved work bounds matching those of the best existing sequential algorithms for constructing rank and select structures

on parallel integer merging the problem of merging two sorted arrays a a1 a2 an1 and b b1 b2 bn2 is considered for input elements that are drawn from a domain of integers 1 s we present an algorithm that runs in o log log log s time using n log log log s crew pram processors optimal speed up and o ns space where n n1 n2 for input elements that are drawn from a domain of integers 1 n we present a second algorithm that runs in o n time where n is the inverse of ackermann s function using n n crew pram processors and linear space this second algorithm is non uniform however it can be made uniform at a price of a certain loss of speed or by using a crcw pram

an efficient strategy for generating all descendant subtree patterns from phylogenetic trees with its implementation abstract phylogenetic trees are an important tool to help in the understanding of relationships between objects that evolve through time in particular molecular sequences in this paper we efficiently solve two subtree comparison problems on a set of phylogenetic trees which have practical applications to analyze the evolution and co evolution genes clustering of genomic sequences let t 1 t 2 t k be a set of k phylogenetic trees such that the leaves of each tree are drawn from 1 2 n and the leaves for two arbitrary trees are not necessary the same where n is the maximum number of the leaves among the k trees we present a linear time algorithm to find all the leaf agreement descendant subtrees by further extending this result we present a linear time algorithm to find all the leaf agreement isomorphic descendant subtrees based on our algorithms a web based system using input tree files from treebase is also implemented

brief paper interval observer design for consistency checks of nonlinear continuous time systems this paper deals with fault detection for nonlinear continuous time systems a procedure based on interval analysis is proposed to build a guaranteed qlpv quasi linear parameter varying approximation of the nonlinear model the interval qlpv approximation makes it possible to derive two point observers which estimate respectively the lower and the upper bound of the state vector using cooperativity theory a set guaranteed to contain the actual value of the residual is then designed the modelling uncertainties and measurement errors are taken into account at the design stage the proposed methodology is illustrated through numerical simulations

high gain interval observer for partially linear systems with bounded disturbances in this paper a high gain interval observer is proposed for a class of partially linear systems affected by unknown but bounded additive disturbances term and measurements noise the proposed obse

fixed point properties of semigroups of non expansive mappings abstract in recent years there have been considerable interests in the study of when a closed convex subset k of a banach space has the fixed point property i e whenever t is a non expansive mapping from k into k then k contains a fixed point for t in this paper we shall study fixed point properties of semigroups of non expansive mappings on weakly compact convex subsets of a banach space or more generally a locally convex space by considering the classes of bicyclic semigroups we answer two open questions one posted earlier by the first author in 1976 dalhousie and the other posted by t mitchell in 1984 virginia we also provide a characterization for the existence of a left invariant mean on the space of weakly almost periodic functions on separable semitopological semigroups in terms of fixed point property for non expansive mappings related to another open problem raised by the first author in 1976

improved deterministic parallel integer sorting abstract we consider the problem of deterministic sorting of integers on a parallel ram pram the best previous result t hagerup 1987 inform and comput 75 39 51 states that n integers of size polynomial in n can be sorted in time o log n on a priority crcw pram with o n log log n log n processors we prove that n integers drawn from a set 0 m 1 can be sorted on an arbitrary crcw pram in time o log n log log n log log m with a time processor product of o n log log m in particular if m n log n o 1 the time and number of processors used are o log n log log n and o n log log n 2 log n respectively this improves the previous result in several respects the new algorithm is faster it works on a weaker pram model and it is closer to optimality for input numbers of superpolynomial size if log log m o log n log log n the new algorithm is optimally fast for any polynomial number of processors and if log log m 1 1 log log n and log log m 0 log n it has optimal speedup relative to the fastest known sequential algorithm the space needed is o nme for arbitrary but fixed e 0 the sorting algorithm derives its speed from a fast solution to a special list ranking problem of possible independent interest the monotonic list ranking problem in monotonic list ranking each list element has an associated key and the keys are known to increase monotonically along the list we show that monotonic list ranking problems of size n can be solved optimally in time o log n log log n we also discuss and attempt to solve some of the problems arising in the precise description and implementation of parallel recursive algorithms as part of this effort we introduce a new pram variant the allocated pram

structural properties of xpath fragments we study structural properties of each of the main sublanguages of navigational xpath w3c recommendation commonly used in practice first we characterize the expressive power of these language fragments in terms of both logics and tree patterns second we investigate closure properties focusing on the ability to perform basic boolean operations while remaining within the fragment we give a complete picture of the closure properties of these fragments treating xpath expressions both as functions of arbitrary nodes in a document tree and as functions that are applied only at the root of the tree finally we provide sound and complete axiom systems and normal forms for several of these fragments these results are useful for simplification of xpath expressions and optimization of xml queries

improved fast integer sorting in linear space we present a fast deterministic algorithm for integer sorting in linear space our algorithm sorts n integers in the range 0 1 2 m 1 in linear space in o n log log n log log log n time when log m log2 n 0 we can further achieve o n log log n time this improves the o n log log n 2 time bound given in m thorup 1998 in proc 1998 acm siam symp on discrete algorithms soda 98 pp 550 555 this result is obtained by combining our new technique with that of thorup s signature sorting a andersson t hagerup s nilsson and r raman 1995 in proc 1995 symposium on theory of computing pp 427 436 a andersson s result 1996 in proc 1996 ieee symp on foundations of computer science pp 135 141 r raman s result 1996 lecture notes in computer science vol 1136 pp 121 137 springer verlag berlin new york and our previous result y han and x shen 1999 in proc 1999 tenth annual acm siam symposium on discrete algorithms soda 99 baltimore md january pp 419 428 are also used for the design of our algorithms we provide an approach and techniques which are totally different from previous approaches and techniques for the problem as a consequence our technique can be extended to apply to nonconservative sorting and parallel sorting our nonconservative sorting algorithm sorts n integers in 0 1 m 1 in time o n log log n 2 log k log log log n using word length k log m n where k log n our erew parallel algorithm sorts n integers in 0 1 m 1 in o log n 2 time and o n log log n 2 log log log n operations provided log m log n 2

an optimal o log n time parallel string matching algorithm an optimal o log log n time parallel algorithm for string matching on crow pram is presented it improves previous results of galil inform and control 67 1985 pp 144 157 and vishkin inform and control 67 1985 pp 91 113

finding maximal leaf agreement isomorphic descendent subtrees from phylogenetic trees with different species phylogenetic trees are an important tool to help in the understanding of relationships between objects that evolve through time in particular molecular sequences in this paper we consider two descendent subtree comparison problems on phylogenetic trees given a set of k phylogenetic trees whose leaves are drawn from 1 2 n and the leaves for two arbitrary trees are not necessary the same we first present a linear time algorithm to final all the maximal leaf agreement descendent subtrees based on this result we also present a linear time algorithm to find all the maximal leaf agreement isomorphic descendent subtrees

on finding common subtrees abstract let t and r be two arbitrary ordered trees t r whose nodes are labelled over an alphabet a we devise a simple solution for detecting all the common subtrees in o t time and space if the size of a is finite and o t log min a t time otherwise we solve the problem of finding in t and r all occurrences if any of any given tree b in either o t b or o b t b time this requires to set up a simple data structure in o t time that allows to find all maximal subtrees of b in o b time and to solve other related problems

interval estimation for continuous time switched linear systems this paper deals with the design of interval observers for switched linear systems sls a class of hybrid systems under the assumption that the disturbances and the measurement noise are bounded upper and lower bounds for the state are calculated new conditions of cooperativity in discrete time instants are firstly proposed then some techniques for interval estimation are developed in continuous time it is shown that it is possible to calculate the observer gains making the estimation error dynamics cooperative and stable via some change of coordinates under arbitrary switching sequences the performances of the developed techniques are illustrated through numerical examples

finite dimensional invariant subspaces for algebras of linear operators and amenable banach algebras abstract we study a finite dimensional invariant subspace property similar to fan s theorem on semigroups for arbitrary banach algebras a in terms of amenability of x a the closed subalgebra of a generated by the set of all maximal elements in a with respect to a character as a consequence we offer some applications to the measure algebra m g and the generalized fourier algebra a p g of a locally compact group g

parallel algorithms with optimal speedup for bounded treewidth we describe the first parallel algorithm with optimal speedup for constructing minimum width tree decompositions of graphs of bounded treewidth on n vertex input graphs the algorithm works in o log n 2 time using o n operations on the erew pram we also give faster parallel algorithms with optimal speedup for the problem of deciding whether the treewidth of an input graph is bounded by a given constant and for a variety of problems on graphs of bounded treewidth including all decision problems expressible in monadic second order logic on n vertex input graphs the algorithms use o n operations together with o log n log n time on the erew pram or o log n time on the crcw pram

common fixed point properties and amenability of a class of banach algebras abstract let a be a lau algebra and let s a be the semigroup of all positive functionals in a with norm one we obtain some equivalent conditions for left amenability of a in terms of a common fixed point property and the hahn banach property we then apply these results for certain lau algebras on a locally compact group g to give characterizations for amenability of g

an efficient parallel algorithm for the single function coarsest partition problem we describe an efficient parallel algorithm to solve the single function coarsest partition problem the algorithm runs in o log n time using o n log log n operations on the arbitrary crcw pram the previous best known algorithms run in o log2 n time using o n log2n operations on the crew pram and o log n time using o n log n operations on the arbitrary crcw pram our solution is based on efficient algorithms for solving several subproblems that are of independent interest in particular we present efficient parallel algorithms to find a minimal starting point of a circular string with respect to lexicographic ordering and to sort lexicographically a list of strings of different lengths

alternating two way ac tree automata we explore the notion of alternating two way tree automata modulo the theory of finitely many associative commutative ac symbols this was prompted by questions arising in cryptographic protocol verification in particular in modeling group key agreement schemes based on diffie hellman like functions where the emptiness question for intersections of such automata is fundamental this also has independent interest we show that the use of general push clauses or of alternation leads to undecidability already in the case of one ac symbol with only functions of arity zero on the other hand emptiness is decidable in the general case of several function symbols including several ac symbols provided push clauses are unconditional and intersection clauses are final this class of automata is also shown to be closed under intersection

asymptotically non expansive actions of strongly amenable semigroups and fixed points abstract in this paper we deal with some fixed point properties for a semi topological semigroup s acting on a compact convex subset k of a banach space we first focus on the space l m c s of left multiplicatively continuous functions on s and its strong left amenability the existence of a compact left ideal group in the lmc compactification of s we then study the relation between left amenability and strong left amenability of l m c s with a common fixed point property for non expansive and asymptotically non expansive actions of s our results improve a result of t mitchell in 1970 and answer an open problem of a t m lau in 2010 for the class of strongly left amenable semi topological semigroups

nonlinear pattern matching in trees tree pattern matching is a fundamental operation that is used in a number of programming tasks such as mechanical theorem proving term rewriting symbolic computation and nonprocedural programming languages in this paper we present new sequential algorithms for nonlinear pattern matching in trees our algorithm improves upon know tree pattern matching algorithms in important aspects such as time performance ease of integration with several reduction strategies and ability to avoid unnecessary computation steps on match attempts that fail the expected time complexity of our algorithm is linear in the sum of the sizes of the two trees

fixed point properties for semigroups of nonlinear mappings and amenability abstract in this paper we study fixed point properties for semitopological semigroup of nonexpansive mappings on a bounded closed convex subset of a banach space we also study a schauder fixed point property for a semitopological semigroup of continuous mappings on a compact convex subset of a separated locally convex space such semigroups properly include the class of extremely left amenable semitopological semigroups the free commutative semigroup on one generator and the bicyclic semigroup s 1 a b a b 1

generalised f algebras as predual algebras of jbw triples and characterisations of the fourier algebras on locally compact groups abstract we introduce the notion of a generalised f algebra as a banach algebra a whose banach space dual is a j b w triple with a certain additional condition on a distinguished character of a this generalises the well known notion of f algebras which in turn includes as special cases many important classes of banach algebras on locally compact groups and semigroups our main use of this new notion is to give some axiomatic characterisations of the fourier algebras on locally compact groups strengthening our previous work 37 but we also quickly review some well known results in f algebras that can be extended to the context of generalised f algebras

improved parallel integer sorting without concurrent writing we show thatnintegers in the range 1 ncan be sorted stably on an erew pram usingo t time ando n lognloglogn logn 2 t operations for arbitrary givent lognloglogn and on a crew pram usingo t time ando n logn logn 2t logn operations for arbitrary givent logn in addition we are able to sortnarbitrary integers on a randomized crew pram within the same resource bounds with high probability in each case our algorithm is a factor of almost logn closer to optimality than all previous algorithms for the stated problem in the stated model and our third result matches the operation count of the best previous sequential algorithm we also show thatnintegers in the range 1 mcan be sorted ino logn 2 time witho n operations on an erew pram using a nonstandard word length ofo lognloglognlogm bits thereby greatly improving the upper bound on the word length necessary to sort integers with a linear time processor product even sequentially our algorithms were inspired by and in one case directly use the fusion trees of fredman and willard

patterns and pattern matching in trees an analysis this paper presents general results on the probabilities of occurrences of patterns in trees which serve to analyze a commonly used pattern matching algorithm on trees it appears that for a wide class of statistics on trees pattern matching has a linear expected time complexity in contrast to a quadratic worst case behaviour the methods used are both combinatorial and analytic and prove useful in the evaluation of a wide class of tree algorithms

on character amenability of banach algebras abstract we continue our work e kaniuth a t lau j pym on amenability of banach algebras math proc cambridge philos soc 144 2008 85 96 in the study of amenability of a banach algebra a defined with respect to a character of a various necessary and sufficient conditions of a global and a pointwise nature are found for a banach algebra to possess a mean of norm 1 we also completely determine the size of the set of means for a separable weakly sequentially complete banach algebra a with no mean in a itself a number of illustrative examples are discussed

brief guaranteed state estimation by zonotopes this paper presents a new approach to guaranteed state estimation for non linear discrete time systems with a bounded description of noise and parameters the main result is an algorithm to compute a set that contains the states consistent with the measured output and the given noise and parameters this set is represented by a zonotope the size of the zonotope is minimized each sample time by an analytic expression or by solving a convex optimization problem interval arithmetic is used to calculate a guaranteed trajectory of the process state two examples have been provided to clarify the algorithm

finite dimensional invariant subspace property and amenability for a class of banach algebras anthony to ming lau and yong zhangabstract motivated by a result of ky fan in 1965 we establish a charac terization of a left amenable f algebra which includes the group algebra andthe fourier algebra of a locally compact group and quantum group algebras or more generally the predual algebra of a hopf von neumann algebra interms of a nite dimensional invariant subspace property this is done by rstrevealing a xed point property for the semigroup of norm one positive lin ear functionals in the algebra our result answers an open question posted intokyo in 1993 by the rst author see 25 problem 5 we also show that theleft amenability of an ideal in an f algebra may determine the left amenabilityof the algebra

construction of interval observers for continuous time systems with discrete measurements we consider continuous time systems with input output and additive disturbances in the particular case where the measurements are only available at discrete instants and have disturbances to solve a state estimation problem we construct continuous discrete interval observers that are asymptotically stable in the absence of disturbances these interval observers are composed of two copies of the studied system and of a framer accompanied with appropriate outputs which give componentwise upper and lower bounds for the solutions of the studied system

extensions and isomorphisms for the generalized fourier algebras of a locally compact group abstract it is shown that for amenable groups all finite dimensional extensions of ap g algebras split strongly furthermore each extension of ap g which splits algebraically also splits strongly we also show that if g is an almost connected locally compact group or a subgroup of gln v v being a finite dimensional vector space and if for a fixed p 1 all finite dimensional singular extensions of ap g split strongly then g is amenable continuous order isomorphisms for the pointwise order of ap g algebras are characterized as weighted composition maps similarly order isomorphisms for the pointwise order of bp g algebras are characterized as algebra isomorphisms followed by multiplication by an invertible positive multiplier in addition it is shown that for amenable groups an order isomorphism for the pointwise order between ap g algebras that preserve cozero sets is necessarily continuous and hence induces an algebra isomorphism

interval observers for linear time invariant systems with disturbances it is shown that for any time invariant exponentially stable linear system with additive disturbances time varying exponentially stable interval observers can be constructed the technique of construction relies on the jordan canonical form that any real matrix admits and on time varying changes of coordinates for elementary jordan blocks which lead to cooperative linear systems the approach is applied to detectable linear systems

linear work suffix array construction suffix trees and suffix arrays are widely used and largely interchangeable index structures on strings and sequences practitioners prefer suffix arrays due to their simplicity and space efficiency while theoreticians use suffix trees due to linear time construction algorithms and more explicit structure we narrow this gap between theory and practice with a simple linear time construction algorithm for suffix arrays the simplicity is demonstrated with a c implementation of 50 effective lines of code the algorithm is called dc3 which stems from the central underlying concept of difference cover this view leads to a generalized algorithm dc that allows a space efficient implementation and moreover supports the choice of a space time tradeoff for any v 1 n it runs in o vn time using o n v space in addition to the input string and the suffix array we also present variants of the algorithm for several parallel and hierarchical memory models of computation the algorithms for bsp and erew pram models are asymptotically faster than all previous suffix tree or array construction algorithms

zonotopes and kalman observers state bounding observation based on zonotopes is the subject of this paper dealing with zonotopes is motivated by set operations resulting in simple matrix calculations with regard to the often huge number of facets and vertices of the equivalent polytopes discrete time ltv lpv systems with state and measurement uncertainties are considered based on a new zonotope size criterion called f w radius and by merging optimal and robust observer gain designs a zonotopic kalman filter zkf is proposed with a proof of robust convergence the notion of covariation is introduced and results in an explicit bridge between the zonotopic set membership and the stochastic paradigms for kalman filtering no intersection is used and the influence of the reduction operator limiting to a tunable maximum the size of the matrices involved in the zonotopic set computations is fully taken into account in the lmi based robust stability analysis a numerical example illustrates the effectiveness of the proposed zkf

the c algebra generated by operators with compact support on a locally compact group abstract let g be a locally compact group and vn g be the von neumann algebra generated by the left regular representation of g let ucb denote the c subalgebra generated by operators in vn g with compact support when g is abelian ucb corresponds to the space of bounded uniformly continuous functions on the dual group of g in this paper we prove among other things that for a large class of locally compact groups which include the heisenberg group the ax b group and the motion group the centre of the banach algebra ucb is the fourier stieltjes algebra b g

on ideals in the bidual of the fourier algebra and related algebras let g be a compact nonmetrizable topological group whose local weight b g has uncountable cofinality let h be an amenable locally compact group a g h the fourier algebra of g h and uc2 g h the space of uniformly continuous functionals in vn g h a g h we use weak factorization of operators in the group von neumann algebra vn g h to prove that there exist at least 22b g left ideals of dimensions at least 22b g in a g h and in uc2 g h we show that every nontrivial right ideal in a g h and in uc2 g h has dimension at least 22b g

optimal and sublogarithmic time randomized parallel sorting algorithms this paper assumes a parallel ram random access machine model which allows both concurrent reads and concurrent writes of a global memory the main result is an optimal randomized parallel algorithm for integer sort i e for sorting n integers in the range 1 n this algorithm costs only logarithmic time and is the first known that is optimal the product of its time and processor bounds is upper bounded by a linear function of the input size also given is a deterministic sublogarithmic time algorithm for prefix sum in addition this paper presents a sublogarithmic time algorithm for obtaining a random permutation of n elements in parallel and finally sublogarithmic time algorithms for general sort and integer sort are presented our sub logarithmic general sort algorithm is also optimal

interval state observer for nonlinear time varying systems this paper is devoted to the design of interval observers for linear time varying ltv systems and a class of nonlinear time varying systems in the output canonical form an interval observer design is feasible if it is possible to calculate the observer gains making the estimation error dynamics cooperative and stable it is shown that under some mild conditions the cooperativity of an ltv system can be ensured by a static linear transformation of coordinates the efficiency of the proposed approach is demonstrated through numerical simulations

a survey on tree edit distance and related problems we survey the problem of comparing labeled trees based on simple local operations of deleting inserting and relabeling nodes these operations lead to the tree edit distance alignment distance and inclusion problem for each problem we review the results available and present in detail one or more of the central algorithms for solving the problem

automata driven efficient subterm unification syntactic unification has widespread use in computing there are several operations used in deductive computing such as critical pair generation paramodulation and narrowing that require unifying a term s with every subterm of another term p this subterm unification problem can be solved naively by repeatedly unifying s with each subterm of p in isolation the drawback of doing unification in isolation is that commonality among subterms of p is ignored we present an algorithm for efficient subterm unification by exploiting this commonality the central idea used in our algorithm is to reduce the common part computation in unification into a string matching problem and solve it efficiently using a string matching automaton the automaton succinctly captures the commonality between subterms of p the string matching approach in conjunction with two new techniques called bidirectional reduce and marking enables efficient unification of s with every subterm of p

tree pattern matching to subset matching in linear time in this paper we show an o n m time turing reduction from the tree pattern matching problem to another problem called the subset matching problem subsequent works have given efficient deterministic and randomized algorithms for the subset matching problem together these works yield an o nlog2m m time deterministic algorithm and an o n log n m time monte carlo algorithm for the tree pattern matching problem

amenability of hopf von neumann algebras and kac algebras abstract let m be a hopf von neumann algebra the operator predualm ofmis a completely contractive banach algebra with multiplicationm m m m we call m operator amenableif the completely contractive banach algebram isoperator amenable i e for every operatorm bimodulev every completely bounded derivation fromm into the dualm bimodulev is inner there is a weaker notion of amenability introduced by d voiculescu we say that a hopf von neumann algebra m isvoiculescu amenableif there exists a left invariant mean onm we show that if a hopf von neumann algebra m is operator amenable then it is voiculescu amenable for kac algebras there is astrong voiculescu amenability we show that for discrete kac algebras these amenabilities are all equivalent in fact if we letk m be a discrete kac algebra and letk m be its compact dual kac algebra then the following are equivalent 1 kis operator amenable 2 kis voiculescu amenable 3 the von neumann algebramis hyperfinite 4 kis strong voiculescu amenable 5 kis operator amenable 6 m has a bounded approximate identity

optimal parallel algorithms for forest and term matching abstract forest matching is a fundamental step in solving various problems defined on terms such as term matching we describe the first optimal speedup parallel algorithm for solving the forest matching problem our algorithm runs in time o log n using n log n processors on a crcw pram given a forest of n nodes as input we use this algorithm to design the first optimal speedup parallel algorithm for solving the term matching problem we also extend these algorithms to run on the weaker crew pram with optimal speedup as well this will involve a simple randomization scheme for simulating concurrent writes through a use of hashing

fourier stieltjes algebra of a topological group abstract this paper is an invitation to the study of the fourier stieltjes algebra b g the linear span of the continuous positive definite complex valued functions on a topological group g we study b g when g has a host algebra or a group c algebra the analogue of the group c algebra of a locally compact group our main challenge is that a topological group g cannot have a positive regular borel measure which is left translation invariant unless g is locally compact

a linear time solution to the single function coarsest partition problem abstract the problem of finding the coarsest partition of a set s with respect to another partition of s one or more functions on s has several applications one of which is the state minimization of finite state automata in 1971 hopcroft presented an algorithm to solve the many function coarsest partition problem for sets of n elements in o n log n time and o n space in 1974 aho hopcroft and ullman presented an o n log n algorithm that solves the special case of this problem for only one function both these algorithms use a negative strategy that repeatedly refines the original partition until a solution is found we present a new algorithm to solve the single function coarsest partition problem in o n time and space using a different constructive approach our algorithm can be applied to the automated manufacturing of woven fabric