frozen glass phase in the multi index matching problem the multi index matching is an np hard combinatorial optimization problem for two indices it reduces to the well understood bipartite matching problem that belongs to the polynomial complexity class we use the cavity method to solve the thermodynamics of the multi index system with random costs the phase diagram is much richer than for the case of the bipartite matching problem it shows a finite temperature phase transition to a completely frozen glass phase similar to what happens in the random energy model we derive the critical temperature the ground state energy density and properties of the energy landscape and compare the results to numerics based on exact analysis of small systems

a work time optimal algorithm for computing all string covers abstract in recent study of repetitive structures of strings generalized notions of periods have been introduced a typical regularity the period u of a given string x grasps the repetitiveness of x since x is a prefix of a string constructed by concatenations of u a substring w of x is called a cover of x if x can be constructed by concatenations and superpositions of w the notion cover is a generalization of periods in the sense that superpositions as well as concatenations are considered to define it whereas only concatenations are considered for periods we consider the all covers problem i e that of computing all the covers of a given string of length n we present an optimal o log log n time crcw pram algorithm for the all covers problem since there is an log log n lower bound on the time complexity of the all covers problem our algorithm is work time optimal

minimal critical exponent of quasiperiodic words abstract a quasiperiodic word is a finite or infinite word that can be obtained by concatenations or overlaps of a given finite word we proved that the least critical exponent of a quasiperiodic binary word is 7 3 for larger alphabets given any 0 we provide a construction of a ternary quasiperiodic word with critical exponent 2

period recovery of strings over the hamming and edit distances a string t of length m is periodic in p of length p if p is a substring of t and t i t i p t i t i p for all 0 i m p 1 0 i m p 1 and m 2p m 2 p the shortest such prefix p is called the period of t i e p t 0 p 1 p t 0 p 1 in this paper we investigate the period recovery problem given a string s of length n find the primitive period s p such that the distance between s and a string t that is periodic in p is below a threshold we consider the period recovery problem over both the hamming distance and the edit distance for the hamming distance case we present an o nlog n o n log n time algorithm where is given as n 2 p for 0 0 for the edit distance case n 3 75 p and 0 0 we provide an o n 4 3 o n 4 3 time algorithm

mixed formulation and locking in path following nonlinear analysis abstract the arc length riks strategy has rapidly become a standard tool for path following analysis of nonlinear structures due to its theoretical ability to surpass limit points the aim of this paper is to show that the failures in convergence that are occasionally experienced are not related to proper defects of the algorithm but come from a subtle locking effect intrinsic to the nonlinear nature of the problem as a consequence its sanitization has to be pursued within a reformulation of the structural model the use of a mixed stress displacement variant of the algorithm in particular appears very promising in this respect the topic is discussed with reference to the analysis of nonlinear frames using a mixed version of the nonlinear beam model discussed in 39 it is shown that with no extra computational cost and only a minor modification in coding with respect to a purely compatible formulation it is possible to achieve a noticeable improvement in convergence and a real gain in both computational time and overall robustness of the algorithm

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

optimization based stability analysis of structures under unilateral constraints this paper discusses an optimization based technique for determining the stability of a given equilibrium point of the unilaterally constrained structural system which is subjected to the static load we deal with the three problems in mechanics sharing the common mathematical properties i structures containing no compression cables ii frictionless contacts and iii elastic plastic trusses with non negative hardening it is shown that the stability of a given equilibrium point of these structures can be determined by solving a maximization problem of a convex function over a convex set on the basis of the difference of convex functions optimization we propose an algorithm to solve the stability determination problem at each iteration of which a second order cone programming problem is to be solved the problems presented are solved for various structures to determine the stability of given equilibrium points copyright 2008 john wiley sons ltd

the set of parameterized k covers problem the problem of the set of k covers is a distance measure for strings another well studied string comparison measure is that of parameterized matching we consider the problem of the set of parameterized k covers k spc which combines k cover measure with parameterized matching we prove that k spc is np complete we describe an approach to solve k spc this approach is based on constructing a logical model for k spc

covering problems for partial words and for indeterminate strings indeterminate strings are a subclass of non standard words having non deterministic nature in a classic string every position contains exactly one symbol we say it is a solid symbol while in an indeterminate string a position may contain a set of symbols possible at this position such sets are called non solid symbols the most important subclass of indeterminate strings are partial words where each non solid symbol is the whole alphabet in this case non solid symbols are also called don t care symbols we consider the problem of finding a shortest cover of an indeterminate string i e finding a shortest solid string whose occurrences cover the whole indeterminate string we show that this classical problem becomes np complete for indeterminate strings and even for partial words the proof of this fact is one of the main results of this paper our other main results focus on design of algorithms efficient with respect to certain parameters of the input so called fpt algorithms for the shortest cover problem for the indeterminate string covering problem we obtain an o nk2 2kk3 time algorithm where k is the number of non solid symbols while for the partial word covering problem we obtain a running time of o nk2 2o klog k additionally we prove that unless the exponential time hypothesis is false no 2o k no 1 time solution exists for either problem which shows that our algorithm for partial words is close to optimal we also present an algorithm for both problems parameterized both by k and the alphabet size with a simple implementation a preliminary version of this article was presented at the 25th international symposium on algorithms and computation isaac 2014 lncs vol 8889 pp 220 232 springer 2014 12

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

statistical mechanics of a simplified bipartite matching problem an analytical treatment we perform an analytical study of a simplified bipartite matching problem in which there exists a constant matching energy and both heterosexual and homosexual pairings are allowed we obtain the partition function in a closed analytical form and we calculate the corresponding thermodynamic functions of this model we conclude that the model is favored at high temperatures for which the probabilities of heterosexual and homosexual pairs tend to become equal in the limits of low and high temperatures the system is extensive however this property is lost in the general case there exists a relation between the matching energies for which the system becomes more stable under external thermal perturbations as the difference of energies between the two possible matches increases the system becomes more ordered while the maximum of entropy is achieved when these energies are equal in this limit there is a first order phase transition between two phases with constant entropy

an enumerative method for the solution of linear complementarity problems abstract in this paper an enumerative method for the solution of the linear complementarity problem lcp is presented this algorithm either finds all the solutions of any general lcp that is no assumption is made concerning the class of the matrix or it establishes that no such solution exists the method is extended to the second linear complementarity problem slcp a new problem which has been introduced for the solution of a general quadratic program

post buckling behaviour in variable stiffness cylindrical panels under compression loading with modal interaction effects abstract variable angle tow vat composite panels whereby fibre angle distributions vary continuously in plane have more scope for tuning structural properties than traditional straight fibre laminated composite materials currently the geometrically non linear response of such structures is typically modelled using path following methods implemented in commercial finite element analysis however the high computational cost given from both the incremental iterative procedure and fine mesh required for accurate modelling of the variable trajectory of fibre direction can be excessively time consuming driven by these shortcomings we use a fast multi modal koiter asymptotic method for investigating the nonlinear buckling behaviour of vat cylindrical panels in compression in doing so this paper provides new insight into the multi modal description and nonlinear buckling mode interactions which are responsible for the highly nonlinear behaviour of cylindrical panels in compression with a particular emphasis on the nonlinear components in the mathematical asymptotic description as such through an extensive parametric virtual testing programme we construct for each panel under investigation an asymptotic solution projecting the equilibrium equations in the subspace of its first 30 buckling modes then at several points of the resulting equilibrium path the percentage contribution of each of these modes to the solution is measured on the basis of the percentage obtained those modes which give the largest contribution to the solution are identified the main novelty of this work is that these results are used as a priori information for re projecting the equilibrium equations into a new modal subspace to which only the buckling modes with the largest participation belong moreover for the first time we observe that in a multi modal koiter inspired description the modal shapes giving the largest contribution to the asymptotic solution have the same degree of symmetry in this way for a generic panel under consideration we show that it is possible to obtain a more computationally efficient asymptotic description than current approaches finally the new computed equilibrium paths are compared to benchmark results using the commercial finite element software abaqus and the computational advantages given by using a priori information in the asymptotic expansion are commented upon

asymptotic post buckling fem analysis using corotational formulation finite element asymptotic post buckling analysis being based on fourth order expansions of the strain energy requires that nonlinear structural modeling be accurate to same order at least with respect to the rigid motions of the elements a corotational description is proposed here as a general tool to satisfy this requirement of objectivity by referring each element to a local frame which moves rotates with the element so filtering its rigid motion in this description nonlinearity of the problem derives essentially from the change of reference from the global fixed frame to the local one the strain energy being governed by their relative rotations in finite kinematics this noticeably complicates the algebra for obtaining exact expressions of its variations quite simple basic expressions for the first four corotational derivatives of the strain energy are provided allowing the set up of a fourth order accurate asymptotic analysis starting from standard finite elements based on linear or simplified nonlinear local modelings the formulation is implemented for the analysis of 3d beam assemblages and several numerical results are presented and discussed showing the effectiveness and robustness of the proposed approach in reproducing the nonlinear equilibrium path in both cases of monomodal and coupled multimodal buckling

a nonlinear beam finite element for the post buckling analysis of plane frames by koiter s perturbation approach abstract a nonlinear finite element of plane beam oriented to koiter s perturbation analysis of frames is presented the locking problem arising in the calculation of the post critical curvature is thoroughly examined and solved at the continuum level by means of a suitable definition of the kinematic settings the proposed strain measures are lagrangian and rationally founded geometrically exact the exact solutions of the critical problem have been chosen as shape functions of the finite element so obtaining an immediately convergent finite element in the calculation of the critical load and of the post critical slope

optimality of some algorithms to detect quasiperiodicities improving a 1993 algorithm of apostolico and ehrenfeucht independently iliopoulos and mouchard in 1999 and brodal and pedersen in 2000 provided o nlog n algorithms to determine all maximal quasiperiodicities of a word of length n we show here the optimality of this bound providing an infinite family of words w containing o w log w maximal quasiperiodicities we also show that this bound is not reached for the celebrated family of fibonacci words

imperfection sensitivity due to coupled local instability a non convex qp solution algorithm the paper deals with the collapse safety of slender elastic structures subjected to local buckling interaction using koiter s asymptotic approach the mechanical problem is reduced to the search for all the local minima of an indefinite quadratic form over the unit simplex an efficient recursive branch and cut algorithm is proposed for solving this non convex qp problem allowing a numerical procedure providing statistical information about the collapse load for a given distribution of random imperfections to be set up copyright 2006 john wiley sons ltd

koiter s analysis of thin walled structures by a finite element approach summary this paper refers to the analysis of the postbuckling behaviour of thin walled structures by means of an asymptotic approach based on a finite element implementation of koiter s non linear theory of instability the analysis has been accomplished by using the following assumptions i the structure is described as an assemblage of flat slender rectangular panels ii a non linear kirchhoff type plate theory is used to model each panel iii hc finite elements discretization is used iv linear and quadratic extrapolations are assumed for the fundamental and the postbuckling paths respectively v multimodal buckling is considered and vi imperfection sensitivity analysis is performed in both multimodal and monomodal form based on the steepest descent path criterion several numerical results are presented and discussed comparisons with numerical solution obtained by standard incremental codes are given which show the accuracy and reliability of the proposed approach

efficient on line repetition detection a repetition is a nonempty string of the form x q where q 2 given a string s character by character and the value of q the on line repetition detection problem is to detect and report the first repetition in s if it exists in an on line manner leung peng and ting first studied the problem for q 2 and gave an o mlog 2m time algorithm refer to h f leung z peng h f ting an efficient algorithm for online square detection theoretical computer science 363 1 2006 69 75 where m is the ending position of the first repetition in s in this paper we improve the above cited work by reducing the time complexity to o email protected where b is the number of distinct characters in the first m characters of s moreover we also solve the problem for q 3 with the same time complexity

storage capacity in symmetric binary perceptrons we study the problem of determining the capacity of the binary perceptron for two variants of the problem where the corresponding constraint is symmetric we call these variants the rectangle binary perceptron rpb and the u function binary perceptron ubp we show that unlike for the usual step function binary perceptron the critical capacity in these symmetric cases is given by the annealed computation in a large region of parameter space for all rectangular constraints and for narrow enough u function constraints k k we conclude that full step replica symmetry breaking would have to be evaluated in order to obtain the exact capacity in this case

collage of two dimensional words we consider a new operation on one dimensional resp two dimensional word languages obtained by piling up one on top of the other words of a given recognizable language resp two dimensional recognizable language on a previously empty one dimensional resp two dimensional array the resulting language is the set of words seen from above a position in the array is labeled by the topmost letter we show that in the one dimensional case the language is always recognizable this is no longer true in the two dimensional case which is shown by a counter example and we investigate in which particular cases the result may still hold

quasiperiodic sturmian words and morphisms we characterize all quasiperiodic sturmian words a sturmian word is not quasiperiodic if and only if it is a lyndon word moreover we study links between sturmian morphisms and quasiperiodicity

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

quasiperiodicity and string covering in this paper we study word regularities and in particular extensions of the notion of the word period quasiperiodicity covers and seeds we present overviews of algorithms for computing the quasiperiodicity the covers and the seeds of a given word we also present an overview of an algorithm that finds maximal word factors with the above regularities finally we show how fine and wilf s theorem fails if we try to extend it directly to quasiperiodicity as well as a new property on concatenation of periodic words

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

algorithms for detecting morphic images of a word we present efficient algorithms for two subcases of the general np complete problem an 80 which consists in matching patterns with variables matching an arbitrary one variable pattern with constants matching a two variable pattern

approximate periods of strings the study of approximately periodic strings is relevant to diverse applications such as molecular biology data compression and computer assisted music analysis here we study different forms of approximate periodicity under a variety of distance functions we consider three related problems for two of which we derive polynomial time algorithms we then show that the third problem is np complete

repetitive perhaps but certainly not boring in this paper some of the work done on repetitions in strings is surveyed especially that of an algorithmic nature several open problems are described and conjectures formulated about some of them

pairs of sat assignments in random boolean formulae we investigate geometrical properties of the random k satisfiability problem using the notion of x satisfiability a formula is x satisfiable is there exist two sat assignments differing in nx variables we show the existence of a sharp threshold for this property as a function of the clause density for large enough k we prove that there exists a region of clause density below the satisfiability threshold where the landscape of hamming distances between sat assignments experiences a gap pairs of sat assignments exist at small x and around x 12 but they do not exist at intermediate values of x this result is consistent with the clustering scenario which is at the heart of the recent heuristic analysis of satisfiability using statistical physics analysis the cavity method and its algorithmic counterpart the survey propagation algorithm our method uses elementary probabilistic arguments first and second moment methods and might be useful in other problems of computational and physical interest where similar phenomena appear

a note on the height of suffix trees consider a random word in which the individual symbols are drawn from a finite or infinite alphabet with symbol probabilities p i and let h n be the height of the suffix tree constructed from the first n suffixes of this word it is shown that h n is asymptotically close to 2 log n log 1 sum i p i 2 in many respects the difference is o log log n in probability and the ratio tends to one almost surely and in the mean

efficient seed computation revisited the notion of the cover is a generalization of a period of a string and there are linear time algorithms for finding the shortest cover the seed is a more complicated generalization of periodicity it is a cover of a superstring of a given string and the shortest seed problem is of much higher algorithmic difficulty the problem is not well understood no linear time algorithm is known in the paper we give linear time algorithms for some of its versions computing shortest left seed array longest left seed array and checking for seeds of a given length the algorithm for the last problem is used to compute the seed array of a string i e the shortest seeds for all the prefixes of the string in o n 2 time we describe also a simpler alternative algorithm computing efficiently the shortest seeds as a by product we obtain an o nlog n m time algorithm checking if the shortest seed has length at least m and finding the corresponding seed we also correct some important details missing in the previously known shortest seed algorithm iliopoulos et al 1996 14

entropy landscape of solutions in the binary perceptron problem the statistical picture of the solution space for a binary perceptron is studied the binary perceptron learns a random classification of input random patterns by a set of binary synaptic weights the learning of this network is difficult especially when the pattern constraint density is close to the capacity which is supposed to be intimately related to the structure of the solution space the geometrical organization is elucidated by the entropy landscape from a reference configuration and of solution pairs separated by a given hamming distance in the solution space we evaluate the entropy at the annealed level as well as replica symmetric level and the mean field result is confirmed by the numerical simulations on single instances using the proposed message passing algorithms from the first landscape a random configuration as a reference we see clearly how the solution space shrinks as more constraints are added from the second landscape of solution pairs we deduce the coexistence of clustering and freezing in the solution space

enhanced string covering a factor u of a string y is a cover of y if every letter of y lies within some occurrence of u in y thus every cover u is also a border both prefix and suffix of y if u is a cover of a superstring of y then u is a seed of y covers and seeds are two formalisations of quasiperiodicity and there exist linear time algorithms for computing all the covers and seeds of y a string y covered by u thus generalises the idea of a repetition that is a string composed of exact concatenations of u even though a string is coverable somewhat more frequently than it is a repetition still a string that can be covered by a single u is rare as a result seeking to find a more generally applicable and descriptive notion of cover many articles were written on the computation of a minimum k cover of y that is the minimum cardinality set of strings of length k that collectively cover y unfortunately this computation turns out to be np hard therefore in this article we propose new simple easily computed and widely applicable notions of string covering that provide an intuitive and useful characterisation of a string the enhanced cover the enhanced left cover and the enhanced left seed

efficient detection of quasiperiodicities in strings a string z is quasiperiodic if there is a second string w z such that the occurrences of w in z cover z entirely i e every position of z falls within some occurrence of w in z it is shown here that all maximal quasiperiodic substrings of a string x of n symbols can be detected in time o n log2 n

efficient algorithms for shortest partial seeds in words abstract a factor u of a word w is a cover of w if every position in w lies within some occurrence of u in w a factor u is a seed of w if it is a cover of a superstring of w covers and seeds extend the classical notions of periodicity we introduce a new notion of partial seed that is a factor covering as a seed at least positions in a given word we use the cover suffix tree recently introduced in the context of partial covers kociumaka et al 2015 13 an o n log n time algorithm constructing such a tree is known however it appears that partial seeds are more complicated than partial covers our algorithms require algebraic manipulations of special functions related to edges of the modified cover suffix tree and the border array we present a procedure for computing shortest partial seeds that works in o n time if the cover suffix tree is already given this is a full version which includes all the proofs of a paper that appeared at cpm 2014 1

quasiperiodic and lyndon episturmian words recently the second two authors characterized quasiperiodic sturmian words proving that a sturmian word is non quasiperiodic if and only if it is an infinite lyndon word here we extend this study to episturmian words a natural generalization of sturmian words by describing all the quasiperiods of an episturmian word which yields a characterization of quasiperiodic episturmian words in terms of their directive words even further we establish a complete characterization of all episturmian words that are lyndon words our main results show that unlike the sturmian case there is a much wider class of episturmian words that are non quasiperiodic besides those that are infinite lyndon words our key tools are morphisms and directive words in particular normalized directive words which we introduced in an earlier paper also of importance is the use of return words to characterize quasiperiodic episturmian words since such a method could be useful in other contexts

how to recognize the order of infinitesimal mechanisms a numerical approach structures presenting kinematical inderterminacy are usually called mechanisms this paper is entirely concerned with assemblies which reveal themselves to be mechanisms at a null value of the load among them a first distinction is made between infinitesimal and finite ones the former being characterized by one or several directions of lower but not zero stiffness whereas the latter show at least one finite admissible displacement for which none of the bars undergoes any elongation moreover there exists the possibility to make a further distinction among the infinitesimal mechanisms according to which is the order of the stiffness along the direction considered above the way of evaluating this order is to perform a local analysis of the strain energy of the assembly once the displacement field is parametrized in terms of a suitable parameter by means of a finite element technique this analysis can be easily performed through the numerical approach presented in this report

mode jumping and attractive paths in multimode elastic buckling this paper summarizes a part of the first author s ph d thesis completely devoted to multimode elastic buckling within an fem strategy the theoretical arguments unfold among critical points on radial paths the unique post critical paths variationally defined algebraic characterizations proposition demonstrations and so on by aiming to prove that the complexity of the phenomenon of multimode buckling secondary bifurcations post critical attractive paths can be theoretically explained 1997 by john wiley sons ltd

usefulness of the karp miller rosenberg algorithm in parallel computations on strings and arrays abstract the karp miller rosenberg 1972 algorithm was one of the first efficient almost linear sequential algorithms for finding repeated patterns and for string matching in the area of efficient sequential computations on strings it was soon superseded by more efficient and more sophisticated algorithms we show that the karp miller rosenberg algorithm kmr must be considered as a basic technique in parallel computations for many problems variations of kmr give the known most efficient parallel algorithms the representation of the set of basic factors subarrays of a string array produced by the algorithm is an extremely useful data structure in parallel algorithms on strings and arrays this gives also a general unifying framework for a large variety of problems we show that the following problems for strings and arrays can be solved by almost optimal parallel algorithms pattern matching longest repeated factor subarray longest common factor subarray maximal symmetric factor subarray also the following problems for strings can be solved within the same complexity bounds finding squares testing even palstars and compositions of k palindromes for k 2 3 4 computing lyndon factorization and building minimal pattern matching automata in the model without concurrent writes the parallel time is o log n 2 with n processors and in the model with concurrent writes the time for most of the problems is o log n with n processors for two problems related to the one dimensional case longest repeated factor and longest common factor there were designed parallel algorithms using suffix trees apostolico et al 1988 however our data structure is simpler and furthermore for the two dimensional case suffix trees do not work the complexity of our algorithms does not depend on the size of the alphabet except for the computation of pattern matching automata

string matching problems over free partially commutative monoids abstract this paper studies two string matching problems over free partially commutative monoids we analyze these two problems in detail and present two efficient polynomial time algorithms for solving them

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