on tracking control of a class of complementary slackness hybrid mechanical systems abstract in this note we consider the problem of feedback control of n dof degree of freedom rigid manipulators subject to a scalar frictionless unilateral constraint f x 0 x r n is the vector of generalized coordinates the stability analysis relies on a stability concept that incorporates the hybrid and nonsmooth dynamical feature of the overall system it is shown that stability of the closed loop system can be obtained this work generalizes the results in brogliato et al ieee trans automat control 42 2 1997 200 215 which were mainly restricted to the 1 dof case it also clarifies some concepts related to the hybrid nature of closed loop complementary slackness mechanical systems

finding maximal 2 dimensional palindromes abstract this paper extends the problem of palindrome searching into a higher dimension addressing two definitions of 2d palindromes the first definition implies a square while the second definition also known as a centrosymmetric factor can be any rectangular shape we present a linear time algorithm for locating all maximal square 2d palindromes in a given 2d text for the second definition of palindromes rect2dp we present two different algorithms given a text of size n n the first algorithm has time o n 3 which is linear in the worst case output size the second algorithm has time o n 2 log n o c c log n where occ is the number of maximal rect2dp in the output this provides a tradeoff in terms of output size if the output size is small the second algorithm is preferable while the first would be more efficient if the output size is n 3

optimal disturbance rejection control for nonlinear impulsive dynamical systems in this paper we develop an optimality based framework for addressing the problem of nonlinear nonquadratic hybrid control for disturbance rejection of nonlinear impulsive dynamical systems with bounded exogenous disturbances specifically we transform a given nonlinear nonquadratic hybrid performance criterion to account for system disturbances as a consequence the disturbance rejection problem is translatedinto an optimal hybridcontrol problem furthermore the resulting optimal hybrid control law is shown to render the closed loop nonlinear input output map dissipative with respect to general supply rates in addition the lyapunov function guaranteeing closed loop stability is shown to be a solution to a stead y state hybridhamilton jacobi isaacs equation andthus guaranteeing optimality 2005 elsevier ltd all rights reserved

encoding 2d range maximum queries we consider the two dimensional range maximum query 2d rmq problem given an array containing elements from an ordered set encode the array so that the position of the maximum element in any specified range of rows and range of columns can be found efficiently we focus on determining the effective entropy of 2d rmq i e how many bits are needed to encode an array so that 2d rmq queries can be answered without accessing the array we give tight upper and lower bounds on the expected effective entropy for the case when a contains independent identically distributed random values and give new upper and lower bounds for the case when the array contains few rows the latter results improve upon the upper and lower bounds by brodal et al 4 we also give some efficient data structures for 2d rmq whose space usage is close to the effective entropy

decidability for a temporal logic used in discrete event system analysis the type of plant considered is one that can be modelled by a non deterministic finite state machine p the regulator is a deterministic finite state machine r the closed loop system is formed by connecting p and r in a regulator configuration formulae in a propositional temporal language are used to describe the behaviour of the closed loop system it is shown that there is a mechanical procedure which for a given p and r and a temporal formula will determine in a finite number of steps whether or not must be true this decidability result could be proven using other known results on temporal logic the proof given here shows that the behaviour of the closed loop system may safely be assumed to be ultimately periodic formulae of a given complexity say n will be true in all possible runs of the system just in case they are true in all ultimately periodic runs with the period and the onset of periodicity bounded by a certain function of n a synthesis result follows immediately from th

simultaneous encodings for range and next previous larger smaller value queries given an array of n elements from a total order we propose encodings that support various range queries range minimum range maximum and their variants and previous and next smaller larger value queries when query time is not of concern we obtain a 4 088n o n bit encoding that supports all these queries for the case when we need to support all these queries in constant time we give an encoding that takes 4 585n o n bits where n is the length of input array this improves the 5 08n o n bit encoding obtained by encoding the colored 2d min and max heaps proposed by fischer 11 we first extend the original dfuds 8 encoding of the colored 2d min max heap that supports the queries in constant time then we combine the extended dfuds of 2d min heap and 2d max heap using the minmax encoding of gawrychowski and nicholson 15 with some modifications we also obtain encodings that take lesser space and support a subset of these queries

wave simulation in frozen porous media abstract we propose a numerical algorithm for simulation of wave propagation in frozen porous media where the pore space is filled with ice and water the model based on a biot type three phase theory predicts three compressional waves and two shear waves and models the attenuation level observed in rocks attenuation is modeled with exponential relaxation functions which allow a differential formulation based on memory variables the wavefield is obtained using a grid method based on the fourier differential operator and a runge kutta time integration algorithm since the presence of slow quasistatic modes makes the differential equations stiff a time splitting integration algorithm is used to solve the stiff part analytically the modeling is second order accurate in the time discretization and has spectral accuracy in the calculation of the spatial derivatives

rank and select revisited and extended the deep connection between the burrows wheeler transform bwt and the so called rank and select data structures for symbol sequences is the basis of most successful approaches to compressed text indexing rank of a symbol at a given position equals the number of times the symbol appears in the corresponding prefix of the sequence select is the inverse retrieving the positions of the symbol occurrences it has been shown that improvements to rank select algorithms in combination with the bwt turn into improved compressed text indexes this paper is devoted to alternative implementations and extensions of rank and select data structures first we show that one can use gap encoding techniques to obtain constant time rank and select queries in essentially the same space as what is achieved by the best current direct solution and sometimes less second we extend symbol rank and select to substring rank and select giving several space time trade offs for the problem an application of these queries is in position restricted substring searching where one can specify the range in the text where the search is restricted to and only occurrences residing in that range are to be reported in addition arbitrary occurrences are reported in text position order several byproducts of our results display connections with searchable partial sums chazelle s two dimensional data structures and grossi et al s wavelet trees

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

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

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

overlapping decompositions expansions contractions and stability of hybrid systems inclusion and extension principles are defined and studied for hybrid systems the controller design problem for hybrid systems is then considered within the framework of the extension principle it is shown that if the extension principle is used then any controller designed in the expanded spaces is contractible to the original spaces for implementation the stability of hybrid systems is also considered a number of definitions of stability for hybrid systems are given and it is shown that if a system which includes another system is stable then the included system is also stable furthermore it is shown that if a controller designed for the expanded system achieves stability then the contracted controller also achieves stability for the original system decentralized controller design with overlapping decompositions is also discussed within the framework of extension an example is provided to illustrate the proposed approach

sliding mode control in discrete state and hybrid systems the sliding mode control approach is developed for a class of discrete state systems in a metric space a concept of trajectory continuity is introduced which allows the use of sliding mode design techniques similar to that in continuous state systems this approach is then applied to a class of hybrid systems which consists of a continuous plant an interface and a discrete state controller the introduction of the sliding mode concept leads to a design which is invariant to disturbances and also the solution of the stabilization problem

generalized lyapunov function theorems and its applications in switched systems abstract generalized lyapunov theorems of nonlinear systems are developed wherein all regularity assumptions on traditional lyapunov function are removed in particular stability theorems of nonlinear systems are presented by replacing v along the system trajectories is non increasing with v along the system trajectories may increase its value during some proper time intervals furthermore stability theorems of discrete time and continuous time switched system with unstable subsystems are derived using the generalized lyapunov theorems two numerical examples are included to illustrate the effectiveness of the method

compact binary relation representations with rich functionality binary relations are an important abstraction arising in many data representation problems the data structures proposed so far to represent them support just a few basic operations required to fit one particular application we identify many of those operations arising in applications and generalize them into a wide set of desirable queries for a binary relation representation we also identify reductions among those operations we then introduce several novel binary relation representations some simple and some quite sophisticated that not only are space efficient but also efficiently support a large subset of the desired queries

space efficient preprocessing schemes for range minimum queries on static arrays given a static array of n totally ordered objects the range minimum query problem is to build a data structure that allows us to answer efficiently subsequent on line queries of the form what is the position of a minimum element in the subarray ranging from i to j we focus on two settings where 1 the input array is available at query time and 2 the input array is available only at construction time in setting 1 we show new data structures a of size frac 2n c n theta bigl frac n lg lg n c n lg n bigr bits and query time o c n for any positive integer function c n in o bigl n varepsilon bigr for an arbitrary constant 0 varepsilon 1 or b with o nh k o n bits and o 1 query time where h k denotes the empirical entropy of k th order of the input array in setting 2 we give a data structure of size 2n o n bits and query time o 1 all data structures can be constructed in linear time and almost in place

numerical methods based on additive splittings for hyperbolic partial differential equations we derive and analyze several methods for systems of hyperbolic equations with wide ranges of signal speeds these techniques are also useful for problems whose coefficients have large mean values about which they oscillate with small amplitude our methods are based on additive splittings of the operators into components that can be approximated independently on the different time scales some of which are sometimes treated exactly the efficiency of the splitting methods is seen to depend on the error incurred in splitting the exact solution operator this is analyzed and a technique is discussed for reducing this error through a simple change of variables a procedure for generating the appropriate boundary data for the intermediate solutions is also presented

dynamic lca queries on trees we show how to maintain a data structure on trees which allows for the following operations all in worst case constant time insertion of leaves and internal nodes deletion of leaves deletion of internal nodes with only one child determining the least common ancestor of any two nodes we also generalize the dietz sleator cup filling scheduling methodology which may be of independent interest

time optimal top k document retrieval let mathcal d be a collection of d documents which are strings over an alphabet of size sigma of total length n we describe a data structure that uses linear space and reports k most relevant documents that contain a query pattern p which is a string of length p packed in p log sigma n words in time o p log sigma n k this is optimal in the ram model in the general case where log d theta log n and involves a novel ram optimal suffix tree search our construction supports an ample set of important relevance measures such as the number of times p appears in a document called term frequency a fixed document importance and the minimal distance between two occurrences of p in a document when log d o log n we show how to reduce the space of the data structure from o n log n to o n log sigma log d log log n bits and to o n log sigma log d bits in the case of the popular term frequency measure of relevance at the price of an additive term o log varepsilon sigma n in the query time for any constant varepsilon 0 we also consider the dynamic scenario where documents can be inserted and deleted from the collection we obtain linear space and query time o p log log n 2 log sigma n log n k log log k whereas insertions and deletions require o log 1 varepsilon n time per symbol for any constant varepsilon 0 finally we consider an extended static scenario where an extra parameter mathtt par p d is defined and the query must retrieve only documents d such that mathtt par p d in tau 1 tau 2 where this range is specified at query time we solve these queries using linear space and o p log sigma n log 1 varepsilon n k log varepsilon n time for any constant varepsilon 0 our technique is to translate these top k problems into multidimensional geometric search problems as a bonus we describe some improvements to those problems

uniform asymptotic stability of hybrid dynamical systems with delay we formulate a model for hybrid dynamical systems with delay which covers a large class of delay systems under several mild assumptions we establish sufficient conditions for uniform asymptotic stability of hybrid dynamical systems with delay via a lyapunov razumikhin technique to demonstrate the developed theory we conduct stability analyses for delay sampled data feedback control systems including a nonlinear continuous time plant and a linear discrete time controller

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

space efficient frameworks for top k string retrieval the inverted index is the backbone of modern web search engines for each word in a collection of web documents the index records the list of documents where this word occurs given a set of query words the job of a search engine is to output a ranked list of the most relevant documents containing the query however if the query consists of an arbitrary string which can be a partial word multiword phrase or more generally any sequence of characters then word boundaries are no longer relevant and we need a different approach in string retrieval settings we are given a set de d1 d2 d3 m dd of d strings with n characters in total taken from an alphabet set l r and the task of the search engine for a given query pattern p of length p is to report the most relevant strings in d containing p the query may also consist of two or more patterns the notion of relevance can be captured by a function score p dr which indicates how relevant document dr is to the pattern p some example score functions are the frequency of pattern occurrences proximity between pattern occurrences or pattern independent pagerank of the document the first formal framework to study such kinds of retrieval problems was given by muthukrishnan lsoda 2002r he considered two metrics for relevance frequency and proximity he took a threshold based approach on these metrics and gave data structures that use o n log n words of space we study this problem in a somewhat more natural top k framework here k is a part of the query and the top k most relevant highest scoring documents are to be reported in sorted order of score we present the first linear space framework i e using o n words of space that is capable of handling arbitrary score functions with near optimal o p p klog k query time the query time can be made optimal o ppk if sorted order is not necessary further we derive compact space and succinct space indexes for some specific score functions this space compression comes at the cost of higher query time at last we extend our framework to handle the case of multiple patterns apart from providing a robust framework our results also improve many earlier results in index space or query time or both

the range 1 query r1q problem we define the range 1 query r1q problem as follows given a d dimensional d 1 input bit matrix a preprocess a so that for any given region mathcal r of a one can efficiently answer queries asking if mathcal r contains a 1 or not we consider both orthogonal and non orthogonal shapes for mathcal r including rectangles axis parallel right triangles certain types of polygons and spheres we provide space efficient deterministic and randomized algorithms with constant query times in constant dimensions for solving the problem in the word ram model the space usage in bits is sublinear linear or near linear in the size of a depending on the algorithm

some tractable supervisory control problems for discrete event systems modeled by buchi automata discrete event systems des are modeled by buchi automata together with a means of online control in this setting the concept of a controllable language is extended to infinite strings and conditions for the existence of a supervisor controller to implement a prescribed closed loop behavior are derived the focus is on a class of des called product systems these are des composed of a finite set of asynchronous components a control problem for such a system typically requires the synthesis of an online controller so as to achieve some prescribed coordinated behavior of the component subsystems one of the principal difficulties in this task is that the size of the state space increases exponentially with the number of components it is shown that despite this fact several interesting control synthesis problems for such systems are computationally feasible and algorithms are developed for solution

longest common extensions in trees the longest common extension lce of two indices in a string is the length of the longest identical substrings starting at these two indices the lce problem asks to preprocess a string into a compact data structure that supports fast lce queries in this paper we generalize the lce problem to trees and suggest a few applications of lce in trees to tries and xml databases given a labeled and rooted tree t of size n the goal is to preprocess t into a compact data structure that support the following lce queries between subpaths and subtrees in t let v 1 v 2 w 1 and w 2 be nodes of t such that w 1 and w 2 are descendants of v 1 and v 2 respectively lce pp v 1 w 1 v 2 w 2 path path lce return the longest common prefix of the paths v 1 w 1 and v 2 w 2 lce pt v 1 w 1 v 2 path tree lce return maximal path path lce of the path v 1 w 1 and any path from v 2 to a descendant leaf lce tt v 1 v 2 tree tree lce return a maximal path path lce of any pair of paths from v 1 and v 2 to descendant leaves we present the first non trivial bounds for supporting these queries for lce pp queries we present a linear space solution with o log n query time for lce pt queries we present a linear space solution with o log log n 2 query time and complement this with a lower bound showing that any path tree lce structure of size o n polylog n must necessarily use log log n time to answer queries for lce tt queries we present a time space trade off that given any parameter 1 n leads to an o n space and o n query time solution all of these bounds hold on a standard unit cost ram model with logarithmic word size this is complemented with a reduction from the set intersection problem implying that a fast linear space solution is not likely to exist

stability theory of hybrid dynamical systems with time delay by defining the bounded time lag space and other related concepts this note formulates the notion of hybrid dynamical systems with time delay which provides a unified framework for describing a large class of systems and is suitable for qualitative analysis it also investigates stability properties of invariant sets by the method of lyapunov functions and the razumihin techniques criteria on uniform stability and uniform asymptotic stability are established for hybrid dynamical systems with time delay those criteria are then applied to conduct stability analysis for impulsive delay differential systems and nonlinear sampled data feedback control systems with time delay

alignment free sequence comparison using absent words abstract sequence comparison is a prerequisite to virtually all comparative genomic analyses it is often realised by sequence alignment techniques which are computationally expensive this has led to increased research into alignment free techniques which are based on measures referring to the composition of sequences in terms of their constituent patterns these measures such as q gram distance are usually computed in time linear with respect to the length of the sequences in this paper we focus on the complementary idea how two sequences can be efficiently compared based on information that does not occur in the sequences a word is an absent word of some sequence if it does not occur in the sequence an absent word is minimal if all its proper factors occur in the sequence here we present the first linear time and linear space algorithm to compare two sequences by considering all their minimal absent words in the process we present results of combinatorial interest and also extend the proposed techniques to compare circular sequences we also present an algorithm that given a word x of length n computes the largest integer for which all factors of x of that length occur in some minimal absent word of x in time and space o n finally we show that the known asymptotic upper bound on the number of minimal absent words of a word is tight

efficient dynamic range minimum query the range minimum query problem consists in answering efficiently the simple question what is the minimal element between two specified indices of a given array in this paper we present a novel structure that offers a trade off between time and space moreover we show how the structure can be easily maintained whenever an insertion modification or deletion modifies the input sequence

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

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

control of systems integrating logic dynamics and constraints this paper proposes a framework for modeling and controlling systems described by interdependent physical laws logic rules and operating constraints denoted as mixed logical dynamical mld systems these are described by linear dynamic equations subject to linear inequalities involving real and integer variables mld systems include linear hybrid systems finite state machines some classes of discrete event systems constrained linear systems and nonlinear systems which can be approximated by piecewise linear functions a predictive control scheme is proposed which is able to stabilize mld systems on desired reference trajectories while fulfilling operating constraints and possibly take into account previous qualitative knowledge in the form of heuristic rules due to the presence of integer variables the resulting on line optimization procedures are solved through mixed integer quadratic programming miqp for which efficient solvers have been recently developed some examples and a simulation case study on a complex gas supply system are reported

non linear impulsive dynamical systems part i stability and dissipativity in this paper we develop lyapunov and invariant set stability theorems for non linear impulsive dynamical systems furthermore we generalize dissipativity theory to non linear dynamical systems with impulsive effects specifically the classical concepts of system storage functions and supply rates are extended to impulsive dynamical systems providing a generalized hybrid system energy interpretation in terms of stored energy dissipated energy over the continuous time system dynamics and dissipated energy over the resetting instants furthermore extended kalman yakubovich popov conditions in terms of the impulsive system dynamics characterizing dissipativeness via system storage functions are derived finally the framework is specialized to passive and non expansive impulsive systems to provide a generalization of the classical notions of passivity and non expansivity for non linear impulsive systems these results are used in the second part of this paper to develop extensions of the small gain and p

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

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

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

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

a simple linear space data structure for constant time range minimum query we revisit the range minimum query problem and present a new o n space data structure that supports queries in o 1 time although previous data structures exist whose asymptotic bounds match ours our goal is to introduce a new solution that is simple intuitive and practical without increasing asymptotic costs for query time or space

document listing on repetitive collections with guaranteed performance abstract we consider document listing on string collections that is finding in which strings a given pattern appears in particular we focus on repetitive collections a collection of size n over alphabet 1 is composed of d copies of a string of size n and s edits are applied on ranges of copies we introduce the first document listing index with size o n s precisely o n lg s lg 2 n lg d bits and with useful worst case time guarantees given a pattern of length m the index reports the ndoc 0 strings where it appears in time o m lg 1 n ndoc for any constant 0 and tells in time o m lg n if ndoc 0 our technique is to augment a range data structure that is commonly used on grammar based indexes so that instead of retrieving all the pattern occurrences it computes useful summaries on them we show that the idea has independent interest we introduce the first grammar based index that on a text t 1 n with a grammar of size r uses o r lg n bits and counts the number of occurrences of a pattern p 1 m in time o m 2 m lg 2 r for any constant 0 we also give the first index using o z lg n z lg n bits where t is parsed by lempel ziv into z phrases counting occurrences in time o m lg 2 n

an invariance principle for nonlinear hybrid and impulsive dynamical systems in this paper we develop an invariance principle for dynamical systems possessing left continuous flows specifically we show that left continuity of the system trajectories in time for each fixed state point and continuity of the system trajectory in the state for every time in some dense subset of the semi infinite interval are sufficient for establishing an invariance principle for hybrid and impulsive dynamical systems as a special case of this result we state and prove new invariant set stability theorems for a class of nonlinear impulsive dynamical systems namely state dependent impulsive dynamical systems these results provide less conservative stability conditions for impulsive systems as compared to classical results in the literature and allow us to address the stability of limit cycles and periodic orbits of impulsive systems

towards a stability theory of general hybrid dynamical systems in recent work we proposed a general model for hybrid dynamical systems whose states are defined on arbitrary metric space and evolve along some notion of generalized abstract time for such systems we introduced the usual concepts of lyapunov and lagrange stability we showed that it is always possible to transform this class of hybrid dynamical systems into another class of dynamical systems with equivalent qualitative properties but defined on real time r 0 the motions of this class of systems are in general discontinuous this class of systems may be finite or infinite dimensional for the above discontinuous dynamical systems and hence for the above hybrid dynamical systems we established the principal lyapunov stability theorems as well as lagrange stability theorems for some of these we also established converse theorems we demonstrated the applicability of these results by means of specific classes of hybrid dynamical systems in the present paper we continue the work described above in doing so we first develop a general comparison theory for the class of hybrid dynamical systems resp discontinuous dynamical systems considered herein making use of stability preserving mappings we then show how these results can be applied to establish some of the principal lyaponov stability theorems for the latter we also state and prove a converse theorem not considered previously finally to demonstrate the applicability of our results we consider specific examples throughout the paper

compressed range minimum queries abstract given a string s of n integers in 0 a range minimum query rmq i j asks for the index of the smallest integer in s i j it is well known that the problem can be solved with a succinct data structure of size 2 n o n and constant query time in this paper we show how to preprocess s into a compressed representation that allows fast range minimum queries this allows for sublinear size data structures with logarithmic query time the most natural approach is to use string compression and construct a data structure for answering range minimum queries directly on the compressed string we investigate this approach in the context of grammar compression we then consider an alternative approach instead of compressing s using string compression we compress the cartesian tree of s using tree compression we show that this approach can be exponentially better than the former is never worse by more than an o factor i e for constant alphabets it is never asymptotically worse and can in fact be worse by an factor

improved exact algorithms to economic lot sizing with piecewise linear production costs abstract in this article we study a classical single item economic lot sizing problem where production cost functions are assumed to be piecewise linear the lot sizing problem is fundamental in lot sizing research and it is applicable to a wide range of production planning models the intractability of the problem is related to the value of m the number of different breakpoints of the production cost functions when m is arbitrary the problem is known to be np hard florian lenstra rinnooy kan 1980 however if m is fixed then it can be solved in polynomial time koca yaman akturk 2014 so far the most efficient algorithm to solve the problem has a complexity of o t 2 m 3 where t is the number of periods in the planning horizon koca et al 2014 in this article we present an improved exact algorithm for solving the problem where the complexity is reduced to o t m 2 log t as such it also improves upon the computational efficiency of solving some existing lot sizing problems which are important special cases of our model in order to achieve a more efficient implementation our algorithm makes use of a specific data structure named range minimum query rmq

succinct indexes for reporting discriminating and generic words we consider the problem of indexing a collection d of d strings documents of total n characters from an alphabet set of size such that whenever a pattern p of p characters and an integer 1 d come as a query we can efficiently report all i maximal generic words and ii minimal discriminating words as defined below maximal generic word is a maximal extension of p occurring in at least documents minimal discriminating word is a minimal extension of p occurring in at most documents these problems were introduced by kucherov et al spire 8 they proposed indexes occupying o n log n bits with query times o p output and o p log log n output for problem i and problem ii respectively the query time for problem ii is later improved to optimal o p output by gawrychowski et al spire 6 in this paper we describe succinct indexes of n log o n log o n bits space with near optimal query times i e o p log log n output for both these problems

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

error correcting data structures we study data structures in the presence of adversarial noise we want to encode a given object in a succinct data structure that enables us to efficiently answer specific queries about the object even if the data structure has been corrupted by a constant fraction of errors we measure the efficiency of a data structure in terms of its length the number of bits in its representation and query answering time measured by the number of bit probes to the possibly corrupted representation the main issue is the trade off between these two this new model is the common generalization of static data structures and locally decodable error correcting codes ldcs we prove a number of upper and lower bounds on various natural error correcting data structure problems in particular we show that the optimal length of t probe error correcting data structures for the membership problem where we want to store subsets of size s from a universe of size n such that membership queries can be answered effic

lrm trees compressed indices adaptive sorting and compressed permutations lrm trees are an elegant way to partition a sequence of values into sorted consecutive blocks they have been used to encode ordinal trees and to index integer arrays in order to support range minimum queries on them we describe how they yield many other convenient results in a variety of areas compressed indices for range minimum queries on partially sorted arrays a new adaptive sorting algorithm and a compressed data structure for permutations supporting direct and inverse application in time inversely proportional to the compressibility of the permutation

linear time computation of prefix table for weighted strings applications the prefix table of a string is one of the most fundamental data structures of algorithms on strings it determines the longest factor at each position of the string that matches a prefix of the string it can be computed in time linear with respect to the size of the string and hence it can be used efficiently for locating patterns or for regularity searching in strings a weighted string is a string in which a set of letters may occur at each position with respective occurrence probabilities weighted strings also known as position weight matrices or uncertain strings naturally arise in many biological contexts for example they provide a method to realise approximation among occurrences of the same dna segment in this article given a weighted string x of length n and a constant cumulative weight threshold 1 z defined as the minimal probability of occurrence of factors in x we present an o n time algorithm for computing the prefix table of x furthermore we outline a number of applications of this result for solving various problems on non standard strings and present some preliminary experimental results

generalized lyapunov and invariant set theorems for nonlinear dynamical systems in this paper we develop generalized lyapunov and invariant set theorems for nonlinear dynamical systems wherein all regularity assumptions on the lyapunov function and the system dynamics are removed in particular local and global stability theorems are given using lower semicontinuous lyapunov functions furthermore generalized invariant set theorems are derived wherein system trajectories converge to a union of largest invariant sets contained in intersections over finite intervals of the closure of generalized lyapunov level surfaces the proposed results provide transparent generalizations to standard lyapunov and invariant set theorems

encoding nearest larger values in nearest larger value nlv problems we are given an array a 1 n of numbers and need to preprocess a to answer queries of the following form given any index i in 1 n return a nearest index j such that a j a i we consider the variant where the values in a are distinct and we wish to return an index j such that a j a i and j i is minimized the nondirectional nlv nnlv problem we consider nnlv in the encoding model where the array a is deleted after preprocessing and note that nnlv encoding problem has an unexpectedly rich structure the effective entropy optimal space usage of the problem depends crucially on details in the definition of the problem using a new path compressed representation of binary trees that may have other applications we encode nnlv in 1 9n o n bits and answer queries in o 1 time

the stability of a class of discrete event systems using markov chains this paper presents a stability concept of a class of discrete event systems dess using markov chains the dess under consideration are modelled as state machines adopted from ramadge wonham which represent the hybrid dynamic models of constrained motion systems by identifying the probability of firing enabled events of the des p convergence is proposed some properties of p convergence are investigated including the fact that p convergence is a generalization of the convergence proposed by brave and heymann yet it is less restrictive the application of p convergence is shown for a robotic assembly des

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

lyapunov stability of a class of discrete event systems discrete event systems des are dynamical systems which evolve in time by the occurrence of events at possibly irregular time intervals logical des are a class of discrete time des with equations of motion that are most often nonlinear and discontinuous with respect to event occurrences recently there has been much interest in studying the stability properties of logical des and several definitions for stability and methods for stability analysis have been proposed here the authors introduce a logical des model and define stability in the sense of lyapunov and asymptotic stability for logical des then the authors show that more conventional analysis of stability which employs appropriate lyapunov functions can be used for logical des the authors provide a general characterization of the stability properties of automata theoretic des models petri nets and finite state systems furthermore the lyapunov stability analysis approach is illustrated on a manufacturing system that processes batches of n different types of parts according to a priority scheme to prove properties related to the machine s ability to reorient itself to achieve safe operation and a load balancing problem in computer networks to study the ability of the system to achieve a balanced load to minimize underutilization

feedback stabilization of dissipative impulsive dynamical systems in this paper we derive conditions under which a dissipative impulsive dynamical system is asymptotically stabilizable by a feedback controller specializing the obtained results to the case of dissipative linear impulsive dynamical systems with the quadratic supply rate we establish the corresponding sufficient conditions finally simulation results are given to demonstrate the effectiveness of our results

on coding labeled trees we consider the problem of coding labeled trees by means of strings of node labels different codes have been introduced in the literature by prufer neville and deo and micikevicius for all of them we show that both coding and decoding can be reduced to integer radix sorting closing several open problems within a unified framework that can be applied both in a sequential and in a parallel setting our sequential coding and decoding schemes require optimal o n time when applied to n node trees yielding the first linear time decoding algorithm for a code presented by neville these schemes can be parallelized on the erew pram model so as to work in o logn time with cost o n or o nlogn depending on the code and on the operation in all cases they either match or improve the performances of the best ad hoc approaches known so far

accuracy of product formula algorithms abstract to obtain accurate solutions to the time dependent schrodinger equation a product formula algorithm has been proposed in literature which is both explicit and unconditionally stable in this paper the accuracy of this algorithm is considered for a few basic problems in mathematical physics viz the convection equation and the diffusion equation in addition to the schrodinger equation from a theoretical analysis which is confirmed by numerical experiments it is concluded that the product formula method can indeed produce accurate solutions but only for small time steps so that the unconditional stability is not of very much use a comparison is also made with standard finite difference methods such as leap frog and crank nicholson