improved dynamic dictionary matching in the dynamic dictionary matching problem a dictionary d contains a set of patterns that can change over time by insertion and deletion of individual patterns the user also presents text strings and asks for all occurrences of any patterns in the text the two main contributions of this paper are 1 a faster algorithm for dynamic string dictionary matching with bounded alphabets and 2 a dynamic dictionary matching algorithm for two dimensional texts and patterns the first contribution is based on an algorithm that solves the general problem of maintaining a sequence of well balanced parentheses under the operations insert delete and find nearest enclosing parenthesis pair the main new idea behind the second contribution is a novel method to efficiently manipulate failure links for two dimensional patterns

inference for capture recapture experiments in continuous time with variable capture rates summary a two step procedure based on a partial likelihood is proposed to estimate the size of a closed population for multiple recapture studies in continuous time when the capture rates are permitted to depend on covariates associated with individuals the asymptotic and small sample properties of the resulting estimators are investigated the analysis of capture recapture experiments is often based on the assumption that capture probabilities are equal for all individuals in the population being caught it has long been recognised that this assumption is often violated indeed equal capture probability is only a convenient mathematical assumption with no empirical justification manly 1970 gilbert 1973 and carothers 1973 have shown that heterogeneity can cause substantial bias in commonly used estimators burnham overton 1978 and yip 1991 assumed a beta distribution to model the individual capture probabilities chao lee 1992 provided an estimator for a heterogeneous population using sample coverage seber 1982 and otis et al 1978 have pointed out that catchability may vary with characteristics of the individual such as age with physical conditions or with environmental factors for the discrete case with distinct capture occasions huggins 1989 used covariates to model heterogeneity a conditional argument to estimate the parameters associated with the model for the capture probabilities and a method of moments to estimate the population size here we employ a similar two step process in continuous time first using a partial likelihood applied to the counting processes of recaptures of individuals already captured to estimate the parameters in the model for the capture intensity then a method of moments to estimate the population size the work here fits into the model ih classification of pollock 1993 also lee chao 1994 recently suggested a coverage estimator for the population size with heterogeneous and time dependent and behaviour dependent capture probabilities to motivate our work consider a continuous time capture recapture experiment for a closed population of a certain type of bird where the capture intensities depend on covariates assumed to be time independent during the experimental period simulated data from a population of 50 birds with captures occurring over a two unit period where the capture intensities depend on

words and forbidden factors given a finite or infinite word v we consider the set m v of minimal forbidden factors of v we show that the set m v is of fundamental importance in determining the structure of the word v in the case of a finite word w we consider two parameters that are related to the size of m w the first counts the minimal forbidden factors of w and the second gives the length of the longest minimal forbidden factor of w we derive sharp upper and lower bounds for both parameters we prove also that the second parameter is related to the minimal period of the word w we are further interested to the algorithmic point of view indeed we design linear time algorithm for the following two problems i given w construct the set m w and conversely ii given m w reconstruct the word w in the case of an infinite word x we consider the following two functions gx that counts for each n the allowed factors of x of length n and fx that counts for each n the minimal forbidden factors of x of length n we address the following general problem what information about the structure of x can be derived from the pair gx fx we prove that these two functions characterize up to the automorphism exchanging the two letters the language of factors of each single infinite sturmian word

a four russians algorithm for regular expression pattern matching given a regular expression r of length p and a word a of length n the membership problem is to determine if a is in the language denoted by r an o pn lg n time algorithm is presented that is based on a lg n speedup of the standard o pn time simulation of r s nonderministic finite automaton on a using a combination of the node listing and four russians paradigms this result places a new worst case upper bound on regular expression pattern matching moreover in practice the method provides an implementation that is faster than existing software for small regular expressions

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

a unified parametric regression model for recapture studies with random removals in continuous time nous combinons la vraisemblance conditionnelle dans des processus de comptage avec l estimateur de horvitz thompson pour obtenir un estimateur de la taille de la population plus efficient que les estimateurs existants des suppressions aleatoires peuvent etre introduites dans le processus de recapture on presente des etudes de simulation pour determiner la performance des estimateurs proposes on donne des exemples sur une repartition d oiseaux et une petite etude de recapture de mammiferes

semiparametric estimation of random effects using the cox model based on the em algorithm consider a survival experiment where individuals within a certain subset of the population share a common unobservable random frailty such a frailty could be an unobservable genetic or early environmental effect if individuals were in sibling groups or an environmental effect if individuals were grouped by households suppose that if the frailty omega is known the cox proportional hazards model for the observable covariates is valid with the consequence of the random effect being a multiplicative factor on the hazard rate assuming tht the random frailties follow a gamma distribution estimates of the fixed and random effects are obtained by using an em algorithm based on a profile likelihood construction the method developed is applied to the framingham heart study to examine the risks of smoking and cholesterol levels adjusting for potential random effects

from nerode s congruence to suffix automata with mismatches in this paper we focus on the minimal deterministic finite automaton s k that recognizes the set of suffixes of a word w up to k errors as first result we give a characterization of the nerode s right invariant congruence that is associated with s k this result generalizes the classical characterization described in a blumer j blumer d haussler a ehrenfeucht m chen j seiferas the smallest automaton recognizing the subwords of a text theoretical computer science 40 1985 31 55 as second result we present an algorithm that makes use of s k to accept in an efficient way the language of all suffixes of w up to k errors in every window of size r of a text where r is the repetition index of w moreover we give some experimental results on some well known words like prefixes of fibonacci and thue morse words finally we state a conjecture and an open problem on the size and the construction of the suffix automaton with mismatches

the subsequence composition of a string words that appear as constrained subsequences in a text string are considered as possible indicators of the host string structure hence also as a possible means of sequence comparison and classification the constraint consists of imposing a bound on the number w of positions in the text that may intervene between any two consecutive characters of a subsequence a subset of such w sequences is then characterized that consists in intuitive terms of sequences that could not be enriched with more characters without losing some occurrence in the text a compact spatial representation is then proposed for these representative sequences within which a number of parameters can be defined and measured in the final part of the paper such parameters are empirically analyzed on a small collection of text strings endowed with various degrees of structure

full likelihood inference for abundance from continuous time capture recapture data capture recapture experiments are widely used cost effective sampling techniques for estimating population sizes or abundances in biology ecology demography epidemiology and reliability studies for continuous time capture recapture data existing estimation methods are based on conditional likelihoods and an inverse weighting estimating equation the corresponding wald type confidence intervals for the abundance may have severe undercoverage and their lower limits can be below the number of individuals captured we propose a full likelihood inference approach by combining a parametric or partial likelihood with the empirical likelihood under both parametric and semiparametric intensity models we demonstrate that the maximum likelihood estimator attains the semiparametric efficiency lower bound and that the full likelihood ratio statistic for the abundance is asymptotically 2 with 1 degree of freedom simulations indicate that compared with conditional likelihood based methods the maximum full likelihood estimator has a smaller mean square error and the likelihood ratio confidence intervals often have remarkable gains in coverage probability we illustrate the advantages of the proposed approach by analysing illegal immigrant data for the netherlands and prinia flaviventris data from hong kong

reducing space for index implementation this article considers several strategies to implement efficiently full indexes on raw textual data indexes are based on representations of all the suffixes of the original text for which we describe three types of implementations aimed at reducing the memory space the first method is a combination of compaction and minimization that leads to the compact suffix automaton as a second method we show that considering a complement language can be useful especially when it is related to data compression finally approximation of the set of suffixes is the third technique used to reduce the space of the implementation

recognition of the factors of a finite language in a linear time text resume nous donnons ici premierement une construction en ligne d un transducteur l qui reconnait tous les facteurs d un langage fini l et place chacun d eux comme facteur d un des mots de l l peut etre deux fois plus petit que l automate partiel introduit par a blumer j blumer d haussier r mcconnell et a ehrenfeucht 6 8 et qui reconnait les memes mots par contre la construction de l est en o l a min l lgmax ou l et a sont les cardinaux respectifs de l et de son alphabet a l est la somme des longueurs des mots de l et lgmax est la longueur maximum des mots de l et non en o l comme le leur nous construisons ensuite un second transducteur l qui admet les m mes etats que l et qui pour tout facteur u de l et pour toute lettre a de a tels que ua ne soit pas facteur de l determine et place le plus grand facteur droit de ua qui soit facteur de l ce transducteur generalise celui que nous avons introduit en 20 pour un mot unique et sa construction est en o l a a l aide des transducteurs l et l nous obtenons algorithme qui determine toutes les occurences de facteurs de l dans un texte lineairement par rapport a la longueur du texte et independamment de l alphabet du texte cet algorithme peut etre utilise par un informaticien retrouver et modifier toute une famille d identificateurs dans un programme un linguiste peut aussi determiner tous les mots d une meme famille ou relatifs a un meme concept en eliminant eventuellement les mots paronymes

the parenthesis tree we provide a simple and direct dynamic data structure the parenthesis tree to represent a set of nested intervals using o n space updating and querying with an interval nested with respect to those in the tree can be carried out in o log n time this structure provides a simpler alternative to the treap when solving the connected component problem

matching a set of strings with variable length don t cares given an alphabet a a pattern p is a word 1 m where i a and a is a distinguished symbol called a variable length don t care symbol pattern p matches a text t a if t u0 1u1 um 1 mum for some u0 um a we address the following problem given a set p of patterns and a text t test whether one of the patterns of p matches t we describe an algorithm that solves the problem in time o t p log p in contrast to most of the existing string matching algorithms such as that of aho corasick our algorithm is not composed of two successive stages preprocessing the pattern resp the text and reading through the text resp the pattern but has these two stages essentially interleaved our approach is based on using the dawg directed acyclic word graph a data structure studied by a blumer j blumer haussler ehrenfeucht crochemore chen seiferas

a method for detecting structure in polygons abstract in order to efficiently represent any data in a computer it is desirable to have available information about any inherent structure in the data when the data is visual the structural information may also be useful in analyzing a scene or object here an inductive methodology for finding structure is presented and applied to the problem of shape analysis for polygons the polygon structure graph is introduced as a tool for shape analysis based on angles and lengths of sides it not only aids in finding repeated substructures but makes it easy to match parts of the polygon with parts of others an algorithm for computing the polygon structure graph is given and examples are presented

parametric regression models for continuous time removal and recapture studies we use a class of parametric counting process regression models that are commonly employed in the analysis of failure time data to formulate the subject specific capture probabilities for removal and recapture studies conducted in continuous time we estimate the regression parameters by modifying the conventional likelihood score function for left truncated and right censored data to accommodate an unknown population size and missing covariates on uncaptured subjects and we subsequently estimate the population size by a martingale based estimating function the resultant estimators for the regression parameters and population size are consistent and asymptotically normal under appropriate regularity conditions we assess the small sample properties of the proposed estimators through monte carlo simulation and we present an application to a bird banding exercise

on the statistical analysis of capture experiments summary a procedure is given for estimating the size of a closed population in the presence of heterogeneous capture probabilities using capture recapture data when it is possible to model the capture probabilities of individuals in the population using covariates the results include the estimation of the parameters associated with the model of the capture probabilities and the use of these estimated capture probabilities to estimate the population size confidence intervals for the population size using both the asymptotic normality of the estimator and a bootstrap procedure for small samples are given

optimal off line detection of repetitions in a string an algorithm is presented to detect within optimal time o n log n and space o n off line on a ram all of the distinct repetitions in a given textstring on a finite alphabet the proposed strategy is self contained as it depends more heavily on algorithmic design considerations than on the combinatorial properties of the output it is based on a new data structure the leaf tree which is particularly suited to exploit simple properties of the suffix tree associated with the string to be analyzed

compact recognizers of episode sequences given two strings x a1 an and p b1 bm over an alphabet the problem of testing whether p occurs as a subsequence of x is trivially solved in linear time it is also known that a simple o n log time preprocessing of x makes it easy to decide subsequently for any p and in at most p log character comparisons whether p is a subsequence of x these problems become more complicated if one asks instead whether p occurs as a subsequence of some substring y of x of bounded length this paper presents an automaton built on the textstring x and capable of identifying all distinct minimal substrings y of x having p as a subsequence by a substring y being minimal with respect to p it is meant that p is not a subsequence of any proper substring of y for every minimal substring y the automaton recognizes the occurrence of p having the lexicographically smallest sequence of symbol positions in y it is not difficult to realize such an automaton in time and space o n2 for a text of n characters one result of this paper consists of bringing those bounds down to linear or o n log n respectively depending on whether the alphabet is bounded or of arbitrary size thereby matching the corresponding complexities of automata constructions for offline exact string searching having built the automaton the search for all lexicographically earliest occurrences of p in x is carried out in time o i 1mrocci i or o n i 1mrocci i log n depending on whether the alphabet is fixed or arbitrary where rocci is the number of distinct minimal substrings of x having b1 bi as a subsequence note that each such substring may occur many times in x but is counted only once in the bound all log factors appearing in the above bounds can be further reduced to log log by resorting to known integer handling data structures

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

approximate string matching using factor automata given a text t over alphabet and a complete index for t constructed using the finite automaton called the factor automaton or dawg accepting all the substrings factors of text t an answer to the query whether a pattern p occurs in text t with k differences is discussed to be done by an algorithm having the time complexity independent on the length of text t the algorithm searches for the final state of the finite automaton accepting the intersection of languages fac t the set of all factors of t and lk p the set of all strings having at most k differences with respect to pattern p

lexicographical order lexicographical index and linear operators abstract we study the lexicographical index of the elements of r n which we introduce here and the linear operators on r n which preserve the lexicographical order or the lexicographical index as well as those which do not increase or do not decrease the lexicographical index

lexicographical separation in rn we prove a new separation theorem for any two subsets of rn with disjoint convex hulls by linear operators or isomorphisms or isometries in the sense of the lexicographical order of rn or equivalently by generalized half spaces also we prove that if one of the sets is the nonpositive orthant then the isometry can be taken lexicographically nonnegative or the isomorphism nonnegative in the usual order we give some applications

estimating population size for a continuous time frailty model with covariates in a capture recapture study a continuous time frailty capture recapture model is proposed for estimating population size of a closed population with the use of observed covariates to explain individuals heterogeneity in presence of a random effect a conditional likelihood approach is used to derive the estimate of parameters and the horvitz thompson estimator is adopted to estimate the unknown population size asymptotic normality of the estimates is obtained simulation results and a real example show that the proposed method works satisfactorily

general suffix automaton construction algorithm and space bounds suffix automata and factor automata are efficient data structures for representing the full index of a set of strings they are minimal deterministic automata representing the set of all suffixes or substrings of a set of strings this paper presents a novel analysis of the size of the suffix automaton or factor automaton of a set of strings it shows that the suffix automaton or factor automaton of a set of strings u has at most 2q 2 states where q is the number of nodes of a prefix tree representing the strings in u this bound significantly improves over email protected email protected 1 the bound given by blumer et al a blumer j blumer d haussler r m mcconnell a ehrenfeucht complete inverted files for efficient text retrieval and analysis journal of the acm 34 1987 578 589 where email protected is the sum of the lengths of all strings in u more generally we give novel and general bounds for the size of the suffix or factor automaton of an automaton as a function of the size of the original automaton and the maximal length of a suffix shared by the strings it accepts we also describe in detail a linear time algorithm for constructing the suffix automaton s or factor automaton f of u in time o s our algorithm applies in fact to any input suffix unique automaton and strictly generalizes the standard on line construction of a suffix automaton for a single input string our algorithm can also be used straightforwardly to generate the suffix oracle or factor oracle of a set of strings which has been shown to have various useful properties in string matching our analysis suggests that the use of factor automata of automata can be practical for large scale applications a fact that is further supported by the results of our experiments applying factor automata to a music identification task with more than 15 000 songs

on updating suffix tree labels abstract we investigate the problem of maintaining the arc labels in the suffix tree data structure gusfield et al 1992 amir et al 1994 when it undergoes string insertions and deletions in current literature this problem is solved either by a simple accounting strategy to obtain amortized bounds fiala and green 1989 larson 1996 or by a periodical suffix tree reconstruction to obtain worst case bounds according to the global rebuilding technique in overmars 1983 unfortunately the former approach is simple and space efficient at the cost of attaining amortized bounds for the single update the latter is space consuming in practice because it needs to keep two extra suffix tree copies in this paper we obtain a simple realtime algorithm that achieves worst case bounds and only requires small additional space i e a bi directional pointer per suffix tree label we analyze it by introducing a combinatorial coloring problem on the suffix tree arcs

hidden word statistics we consider the sequence comparison problem also known as hidden pattern problem where one searches for a given subsequence in a text rather than a string understood as a sequence of consecutive symbols a characteristic parameter is the number of occurrences of a given pattern w of length m as a subsequence in a random text of length n generated by a memoryless source spacings between letters of the pattern may either be constrained or not in order to define valid occurrences we determine the mean and the variance of the number of occurrences and establish a gaussian limit law and large deviations these results are obtained via combinatorics on words formal language techniques and methods of analytic combinatorics based on generating functions the motivations to study this problem come from an attempt at finding a reliable threshold for intrusion detections from textual data processing applications and from molecular biology

the geometric structure of max plus hemispaces abstract given a set s endowed with a convexity structure a hemispace is a convex subset of s which has convex complement we recall that r max n is a semimodule over the max plus semifield r max r max a convexity structure of current interest is provided by r max n naturally endowed with the max plus or tropical convexity in this paper we provide a geometric description of a max plus hemispace in r max n we show that a max plus hemispace has a conical decomposition as a finite union of disjoint max plus cones these cones can be interpreted as faces of several max plus hyperplanes briec and horvath proved that the closure of a max plus hemispace is bounded by a max plus hyperplane given a hyperplane we give a simple condition for the assignment of the faces between a pair of complementary max plus hemispaces our result allows for counting and enumeration of the associated max plus hemispaces we recall that an n dimensional max plus hyperplane is called strictly affine and nondegenerate if it has a linear equation that contains all variables x 1 x 2 x n and a free term we prove that the number of max plus hemispaces in r max n supported by strictly affine nondegenerate hyperplanes centered in the origin is twice the n th ordered bell number our work can be viewed as a complement to the recent results of katz nitica and sergeev who described generating sets for max plus hemispaces and the results of briec and horvath who proved that closed open max plus hemispaces are max plus closed open halfspaces

transducers and repetitions the factor transducer of a word associates to each of its factors or subwords their first occurrence optimal bounds on the size of minimal factor transducers together with an algorithm for building them are given analogue results and a simple algorithm are given for the case of subsequential suffix transducers algorithms are applied to repetition searching in words le transducteur des facteurs d un mot associe a chacun de ses facteurs leur premiere occurrence on donne des bornes optimales sur la taille du transducteur minimal d un most ainsi qu un algorithme pour sa construction on donne des resultats analogues et un algorithme simple dans le cas du transducteur sous sequentiel des suffixes d un mot on donne une application a la detection de repetitions dans les mots

linear size suffix tries suffix trees are highly regarded data structures for text indexing and string algorithms mcreight 76 weiner 73 for any given string w of length n w a suffix tree for w takes o n nodes and links it is often presented as a compacted version of a suffix trie for w where the latter is the trie or digital search tree built on the suffixes of w here the compaction process replaces each maximal chain of unary nodes with a single arc for this the suffix tree requires that the labels of its arcs are substrings encoded as pointers to w or equivalent information on the contrary the arcs of the suffix trie are labeled by single symbols but there can be n 2 nodes and links for suffix tries in the worst case because of their unary nodes it is an interesting question if the suffix trie can be stored using o n nodes we present the linear size suffix trie which guarantees o n nodes we use a new technique for reducing the number of unary nodes to o n that stems from some results on antidictionaries for instance by using the linear size suffix trie we are able to check whether a pattern p of length m p occurs in w in o m log time and we can find the longest common substring of two strings w 1 and w 2 in o w 1 w 2 log time for an alphabet

lexicographical order and duality in multiobjective programming abstract this paper studies the applications of lexicographical order relation for vectors in the mathematical theory of multiobjective programming we show that any pareto minimum of an unconstrained convex problem is the lexicographical minimum for the problem associated to a matrix multiplier having lexicographical positive columns a similar result is also obtained for inequality constrained problems our approach to the theory of duality follows the pattern of jahn 3 but we substitute vectors by matrices in the formulation of the dual problem and the usual scalar order relation by the lexicographical order relation this allows us to state the strong duality theorem in terms of pareto minima and to eliminate some regularity assumptions

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

complete inverted files for efficient text retrieval and analysis given a finite set of texts s w 1 w k over some fixed finite alphabet s a complete inverted file for s is an abstract data type that provides the functions find w which returns the longest prefix of w that occurs as a subword of a word in s freq w which returns the number of times w occurs in s and locations w which returns the set of positions where w occurs in s a data structure that implements a complete inverted file for s that occupies linear space and can be built in linear time using the uniform cost ram model is given using this data structure the time for each of the above query functions is optimal to accomplish this techniques from the theory of finite automata and the work on suffix trees are used to build a deterministic finite automaton that recognizes the set of all subwords of the set s this automaton is then annotated with additional information and compacted to facilitate the desired query functions the result is a data structure that is smaller and more flexible than the suffix tree

contributions to max min convex geometry ii semispaces and convex sets abstract in this article continuing v nitica i singer contributions to max min convex geometry i segments linear algebra appl 2007 doi 10 1016 j laa 2007 09 032 we give some further contributions to the theory of max min geometry the max min semifield is the set r r endowed with the operations max min in r a subset c of r n is said to be max min convex if the relations x y c r the neutral element of imply x y c where is understood componentwise and x x 1 x n for r x x 1 x n r n in analogy with the definition of semispaces for usual linear spaces see e g p c hammer maximal convex sets duke math j 22 1955 103 106 a max min semispace at a point z r n is a maximal with respect to inclusion max min convex subset of r n z in contrast to the case of linear spaces where there exist an infinity of semispaces at each point we show that in r n there exist at most n 1 max min semispaces at each point and exactly n 1 at each point whose all coordinates are finite we determine these max min semispaces and give some consequences for separation of max min convex sets from outside points we show that max min convexity restricted to the finite part r n of r n is a multi order convexity

efficient dynamic dictionary matching with dawgs and ac automata abstract the dictionary matching is a task to find all occurrences of pattern strings in a set d called a dictionary on a text string t the aho corasick automaton ac automaton which is built on d is a fundamental data structure which enables us to solve the dictionary matching problem in o d log preprocessing time and o n log occ matching time where d is the total length of the patterns in the dictionary d n is the length of the text is the alphabet size and occ is the total number of occurrences of all the patterns in the text the dynamic dictionary matching is a variant where patterns may dynamically be inserted into and deleted from the dictionary d this problem is called semi dynamic dictionary matching if only insertions are allowed in this paper we propose two efficient algorithms that can solve both problems with some modifications for a pattern of length m our first algorithm supports insertions in o m log log d log log d time and pattern matching in o n log occ for the semi dynamic setting this algorithm also supports both insertions and deletions in o m log d log log d time and pattern matching in o n log d log log d log occ log d log log d time for the dynamic dictionary matching problem by some modifications this algorithm is based on the directed acyclic word graph dawg of blumer et al jacm 1987 our second algorithm which is based on the ac automaton supports insertions in o m log u f u o time for the semi dynamic setting and supports both insertions and deletions in o m u f u o time for the dynamic setting where u f and u o respectively denote the numbers of states in which the failure function and the output function need to be updated this algorithm performs pattern matching in o n log occ time for both settings our algorithm achieves optimal update time for ac automaton based methods over constant size alphabets since any algorithm which explicitly maintains the ac automaton requires m u f u o update time

the structure of hemispaces in rn abstract we study hemispaces i e convex sets with convex complements in r n we give several geometric characterizations of hemispaces and several ways of representing them with the aid of linear operators and lexicographical order we obtain a metric affine classification of hemispaces in terms of their rank and type and a decomposition theorem we also give some characterizations of affine transformations which preserve a hemispace

online parameterized dictionary matching with one gap abstract we study the online parameterized dictionary matching with one gap problem pdmog which is the following preprocess a dictionary d of d patterns where each pattern contains a special gap symbol that can match any string so that given a text t arriving online a character at a time we can report all the patterns from d that parameterized match to suffixes of the text that has arrived so far before the next character arrives two equal length strings are a parameterized match if there exists a bijection on the alphabets such that one string matches the other under the bijection the gap symbols are associated with bounds determining the possible lengths of matching strings online dictionary matching with one gap dmog captures the difficulty in a bottleneck procedure for cyber security as many digital signatures of viruses manifest themselves as patterns with a single gap parameterized match captures possible encryption of the patterns we also define the strict pdmog problem in which subpatterns of the same dictionary pattern should be parameterized matched via the same bijection this captures situations where subpatterns of a dictionary pattern are encoded simultaneously we study this problem for special case called alphabet saturated dictionairy where every subpattern contains all characters of the dictionary alphabet we use the following parameters to describe our results d is the total size of the dictionary not including the gaps plsc is the longest parameterized suffix chain of subpatterns in d op is the number of parameterized patterns occurrences in t and are the minimum left and maximum right gap borders in the non uniformly bounded dictionary case g d is the degeneracy of the graph g d representing dictionary d this graph is classified as sparse or dense according the value of the g d and plsc parameters we obtain o d preprocessing time space and o g d plsc plsc max m o p query time per text character algorithm for online pdmog with sparse graph dictionaries o d d preprocessing time space and o plsc d plsc max m o p query time per text character algorithm for online pdmog with dense graph dictionaries o d preprocessing time space and o g d plsc o p query time per text character algorithm for strict pdmog with alphabet saturated dictionaries these results are parallel to the ones obtained for the dictionary with one gap dmog problem almost matching the lower bounds achieved for this problem 7 while the parameter g d can be as large as d and much lager if the dictionary has non uniform gap boundaries and the parameter plsc could theoretically be as large as d in many practical situations these parameters are actually small the strength of our work is in achieving results that explore and exploit small values for these parameters thus supplying algorithms that are suitable for some practical cyber security needs

characterization of tropical hemispaces by p r decompositions abstract we consider tropical hemispaces defined as tropically convex sets whose complements are also tropically convex and tropical semispaces defined as maximal tropically convex sets not containing a given point we introduce the concept of p r decomposition this yields to our knowledge a new kind of representation of tropically convex sets extending the classical idea of representing convex sets by means of extreme points and rays we characterize tropical hemispaces as tropically convex sets that admit a p r decomposition of certain kind in this characterization with each tropical hemispace we associate a matrix with coefficients in the completed tropical semifield satisfying an extended rank one condition our proof techniques are based on homogenization lifting a convex set to a cone and the relation between tropical hemispaces and semispaces

the smallest automaton recognizing the subwords of a text let a partial deterministic finite automaton be a dfa in which each state need not have a transition edge for each letter of the alphabet we demonstrate that the smallest partial dfa for the set of all subwords of a given word w iwl 2 has at most 21w 2 states and 3 wl 4 transition edges independently of the alphabet size we give an algorithm to build this smallest partial dfa from the input w on line in linear time

closed convex sets of minkowski type abstract in this paper we provide several characterizations of minkowski sets i e closed possibly unbounded convex sets which are representable as the convex hulls of their sets of extreme points the equality between the relative boundary of a closed convex set containing no lines and its pareto like associated set ensures the minkowski property of the set in two dimensions this equality characterizes the minkowski sets containing no lines

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

motif patterns in 2d motif patterns consisting of sequences of intermixed solid and don t care characters have been introduced and studied in connection with pattern discovery problems of computational biology and other domains in order to alleviate the exponential growth of such motifs notions of maximal saturation and irredundancy have been formulated whereby more or less compact subsets of the set of all motifs can be extracted that are capable of expressing all others by suitable combinations in this paper we introduce the notion of maximal irredundant motifs in a two dimensional array and develop initial properties and a combinatorial argument that poses a linear bound on the total number of such motifs the remainder of the paper presents approaches to the discovery of irredundant motifs both by offline and incremental algorithms

special factors and the combinatorics of suffix and factor automata the suffix automaton resp factor automaton of a finite word w is the minimal deterministic automaton recognizing the set of suffixes resp factors of w we study the relationships between the structure of the suffix and factor automata and classical combinatorial parameters related to the special factors of w we derive formulae for the number of states of these automata we also characterize the languages l s a and l f a of words having respectively suffix automaton and factor automaton with the minimal possible number of states

motzkin decomposition of closed convex sets via truncation this work has been supported by the micinn of spain grants mtm2011 29064 c03 01 02 by the barcelona graduate school of economics by the government of catalonia by conacyt of mexico grant 55681 and by cnpq of brazil grant 301280 86 the first author is partner investigator in the australian research council discovery project dp120100467 the third author is affiliated tomove markets organizations and votes in economics

on φ convexity of convex functions abstract we construct a non trivial set of extended real valued functions on r n containing all affine functions such that an extended real valued function f on r n is convex if and only if it is convex in the sense of dolecki and kurcyusz i e the pointwise supremum of some subset of also we prove a new sandwich theorem finally we characterize the set of all extended real valued functions on r n which are simultaneously convex and concave and we show that it contains properly the above set hence a function f on r n is convex if and only if it is the pointwise supremum of a set of simultaneously convex and concave functions

multiple matching of rectangular patterns we describe the first worst case efficient algorithm for simultaneously matching multiple rectangular patterns of varying sizes and aspect ratios in a rectangular text efficient means significantly more efficient asymptotically than applying known algorithms that handle one height or width or aspect ratio at a time for each height our algorithm features an interesting use of multidimensional range searching as well as new adaptations of several known techniques for two dimensional string matching we also extend our algorithm to a dynamic setting where the set of patterns can change over time

compatible preorders and linear operators on rn abstract we characterize the total preorders on rn which are compatible with the vector space structure in terms of linear operators and the lexicographical order in particular we obtain that the lexicographical order is up to a linear isometry the unique compatible total order on rn we also study compatible total extensions of compatible preorders and give some szpilrajn type results for compatible preorders and compatible orders

dynamic nested brackets we consider the problem of maintaining a string of n brackets or under the operation reverse i that changes the ith bracket from to or vice versa and returns yes if and only if the resulting string is properly balanced we show that this problem can be solved on the ram in time o logn log log n per operation using linear space and preprocessing moreover we show that this is optimal in the sense that every data structure supporting reverse no matter its space and preprocessing complexity needs time log n log log n per operation in the cell probe model

normal forms of quasiperiodic strings here we consider the problem of computing normal forms of quasiperiodic strings a string x is quasiperiodic if it can be constructed by concatenation and superpositions of one of its proper factor cover the notion of quasiperiodicity is a generalization of periodicity in the sense that superpositions as well as concatenations are allowed to define it it is shown here that given a quasiperiodic string x there exists a unique factorization of x into roots of its shortest cover and how we can efficiently build such a factorization in linear time these forms can be used for example to test whether or not a string v covers xk for some integer k where v covers x

characteristic sturmian words are extremal for the critical factorization theorem we prove that characteristic sturmian words are extremal for the critical factorization theorem cft in the following sense if p x n denotes the local period of an infinite word x at point n we prove that x is a characteristic sturmian word if and only if p x n is smaller than or equal to n 1 for all n 1 and it is equal to n 1 for infinitely many integers n this result is extremal with respect to the cft since a consequence of the cft is that for any infinite recurrent word x either the function p x is bounded and in such a case x is periodic or p x n n 1 for infinitely many integers n as a byproduct of the techniques used in the paper we extend a result of harju and nowotka 2002 in 18 stating that any finite fibonacci word f n n 5 has only one critical point indeed we determine the exact number of critical points in any finite standard sturmian word