on finding the adams consensus tree abstract this article presents a fast algorithm for finding the adams consensus tree of a set of conflicting phylogenetic trees with identical leaf labels its worst case running time is o k n log n where k is the number of input trees and n is the size of the leaf label set in comparison the original algorithm of adams has a worst case running time of o k n 2 to achieve subquadratic running time the centroid path decomposition technique is applied in a novel way that traverses the input trees by following a centroid path in each of them in unison for k 2 an even faster algorithm running in o n log n log log n time is provided which relies on an extension of the wavelet tree based technique of bose et al for orthogonal range counting on a grid our extended wavelet tree data structure also supports truncated range maximum minimum queries efficiently

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

a model for describing and composing direction relations between overlapping and contained regions current models of direction relations are not designed to describe direction information inside the minimum bounding rectangle mbr of a reference region thus the direction relations between overlapping and contained regions cannot be effectively described and derived to resolve this problem a new model of direction relations namely interior boundary direction relations is proposed in this study to describe direction concepts relative to the interior or boundary of a region such as east part of a region west border of a region a line goes through east part of a region and etc by combining the interior and exterior direction relations three types of compositions of direction relations are investigated 1 composing two interior direction relations which can be used to derive the interior or exterior direction relations between two regions with the same parent region 2 composing an interior direction relation with an exterior direction relation and 3 composing an interior with an exterior direction relation the results indicate that the new interior boundary direction relations and its compositions with exterior direction relations are powerful in describing and deriving direction relations between overlapped and contained regions

dynamic 3 sided planar range queries with expected doubly logarithmic time the priority search tree is the classic solution for the problem of dynamic 2 dimensional searching for the orthogonal query range of the form a b x c 3 sided rectangle it supports all operations in logarithmic worst case complexity in both main and external memory in this work we show that the update and query complexities can be improved to expected doubly logarithmic when the input coordinates are being continuously drawn from specific probability distributions we present three pairs of linear space solutions for the problem i e a ram and a corresponding i o model variant 1 first we improve the update complexity to doubly logarithmic expected with high probability under the most general assumption that both the x and y coordinates of the input points are continuously being drawn from a distribution whose density function is unknown but fixed 2 next we improve both the query complexity to doubly logarithmic expected with high probability and the update complexity to doubly logarithmic amortized expected by assuming that only the x coordinates are being drawn from a class of smooth distributions and that the deleted points are selected uniformly at random among the currently stored points in fact the y coordinates are allowed to be arbitrarily distributed 3 finally we improve both the query and the update complexity to doubly logarithmic expected with high probability by moreover assuming the y coordinates to be continuously drawn from a more restricted class of realistic distributions all data structures are deterministic and their complexity s expectation is with respect to the assumed distributions they comprise combinations of known data structures and of two new data structures introduced here namely the weight balanced exponential tree and the external modified priority search tree

a scalable approach to computing representative lowest common ancestor in directed acyclic graphs lca computation for vertex pairs in trees can be achieved in constant time after linear time preprocessing however extension of these techniques to compute lca for vertex pairs in dags has been not possible due to the non tree edges in a dag in this paper we present an algorithm for computing the lca for vertex pairs in a dag which treats the dag s spanning tree and its non tree edges separately our approach enables us to tap the efficiency of existing lca algorithms for trees furthermore our algorithm decomposes the dag into a set of component trees called clusters which significantly reduces the preprocessing necessary to incorporate non tree edges in the lca computation our algorithm seamlessly interpolates the performance graph between the best reported algorithms for trees and the best reported algorithms for dags depending on the incidence of non tree edges in the dag using the proposed techniques it is possible to achieve near linear preprocessing and constant query time for sparse dags

recursive voids for identifying a nonconvex boundary of a set of points in the plane we introduce a method that identifies the boundary of a nonconvex shape of a set of points in the plane the boundary of the shape is explored through finding empty regions recursively within a shell that encapsulates all of the points our algorithm is output sensitive and runs in linear o n time determined by the output parameter which is proportional to the length of the nonconvex boundary measured by a threshold unit distance the recursive nature of our algorithm allows a tree structure that characterizes the empty regions and by complementarity the nonconvex shape itself we use a distance measure based on lowest common ancestor of a pair of nodes in this tree and define the complexity of a shape as the average of the distances between all pairs we present computational results on data size threshold shape complexity and noise on a set of different nonconvex shapes

order preserving indexing kubica et al 33 and kim et al 29 introduced order preserving pattern matching for a given text the goal is to find its factors having the same shape as a given pattern known results include a linear time algorithm for this problem in case of polynomially bounded alphabet and a generalization to multiple patterns we propose an index that enables order preserving pattern matching queries in time proportional to pattern length the index can be constructed in o n log log n expected time or in o n log 2 log n log log log n worst case time it is an incomplete order preserving suffix tree which may miss a single edge label at each branching node for most applications such incomplete suffix trees provide the same functional power as the complete ones we show a number of their applications including computation of longest common factors longest previously occurring factors and squares in a string in the order preserving setting we also give an o n log n time algorithm constructing complete order preserving suffix trees

continuous time identification of periodically parameter varying state space models this paper presents a new frequency domain identification technique to estimate multivariate linear parameter varying lpv continuous time state space models where a periodic variation of the parameters is assumed or imposed the main goal is to obtain an lpv state space model suitable for control from a single parameter varying experiment although most lpv controller synthesis tools require continuous time state space models the identification of such models is new the proposed identification method designs a periodic input signal taking the periodicity of the parameter variation into account we show that when an integer number of periods is observed for both the input and the scheduling the state space model representation has a specific sparse structure in the frequency domain which is exploited to speed up the estimation procedure a weighted non linear least squares algorithm then minimizes the output error two initialization methods are explored to generate starting values the first approach uses a linear time invariant lti approximation the second estimates a linear time variant ltv input output differential equation from which a corresponding state space realization is computed

delaunay triangulations in o sort n time and more we present several results about delaunay triangulations dts and convex hulls in transdichotomous and hereditary settings i the dt of a planar point set can be computed in expected time o sort n on a word ram where sort n is the time to sort n numbers we assume that the word ram supports the shuffle operation in constant time ii if we know the ordering of a planar point set in x and in y direction its dt can be found by a randomized algebraic computation tree of expected linear depth iii given a universe u of points in the plane we construct a data structure d for delaunay queries for any p s u d can find the dt of p in expected time o vpv log log vuv iv given a universe u of points in 3 space in general convex position there is a data structure d for convex hull queries for any p s u d can find the convex hull of p in expected time o vpv log log vuv 2 v given a convex polytope in 3 space with n vertices which are colored with g 2 colors we can split it into the convex hulls of the individual color classes in expected time o n log log n 2 the results i iii generalize to higher dimensions where the expected running time now also depends on the complexity of the resulting dt we need a wide range of techniques most prominently we describe a reduction from dts to nearest neighbor graphs that relies on a new variant of randomized incremental constructions using dependent sampling

efficient algorithms for two generalized 2 median problems and the group median problem on trees the p median problem on a tree t is to find a set s of p vertices on that minimizes the sum of distances from t s vertices to s in this paper we study two generalizations of the 2 median problem which are obtained by imposing constraints on the two vertices selected as a 2 median one is to limit their distance while the other is to limit their eccentricity previously both the best upper bounds of these two generalizations were o n2 a tamir d perez brito j a moreno perez a polynomial algorithm for the p centdian problem on a tree networks 32 1998 255 262 b f wang s c ku k h shi cost optimal parallel algorithms for the tree bisector problem and applications ieee transactions on parallel and distributed systems 12 9 2001 888 898 in this paper we solve both in o nlogn time we also study cases when linear time algorithms exist for the two generalizations for example we solve both in linear time when edge lengths and vertex weights are all polynomially bounded integers furthermore we consider the relaxation of the two generalized problems by allowing 2 medians on any position of edges instead of just on vertices and we give o nlogn time algorithms for them a problem named the tree marker problem arises several times in our approaches to the two generalized 2 median problems and we give an o nlogn time algorithm for this problem we also use this algorithm to speedup an algorithm of gupta and punnen s k gupta a p punnen group center and group median of a tree european journal of operational research 65 1993 400 406 for the group median problem improving the running time from o kn to o n klogn where k is the number of groups in the input

fast algorithms for finding nearest common ancestors we consider the following problem given a collection of rooted trees answer on line queries of the form what is the nearest common ancester of vertices x and y we show that any pointer machine that solves this problem requires omega log log n time per query in the worst case where n is the total number of vertices in the trees on the other hand we present an algorithm for a random access machine with uniform cost measure and a bound of omega log n on the number of bits per word that requires o 1 time per query and o n preprocessing time assuming that the collection of trees is static for a version of the problem in which the trees can change between queries we obtain an almost linear time and linear space algorithm

string matching with weighted errors abstract in the approximate string matching problem differences are allowed between the pattern string p and each of its occurrences in the text string t and one is interested in finding all the occurrences of p in t with at most k differences we consider here weighted differences errors between p and t and develop fast sequential and parallel algorithms in particular we allow the following types of errors mismatch whose weight depends on the mismatching characters extra character with constant weight missing character with constant weight and transposition of two consecutive characters with constant weight a set of theoretical results allows to extend known algorithms to solve this problem with o kn sequential time and o k log m parallel time on a 4pram model with max n k 1 mp2 processors where k is the maximum sum of the error weights n is the length of t and m is the length of p

on line planarity testing the on line planarity testing problem consists of performing the following operations on a planar graph g i testing if a new edge can be added to g so that the resulting graph is itself planar ii adding vertices and edges such that planarity is preserved an efficient technique for on line planarity testing of a graph is presented that uses o n space and supports tests and insertions of vertices and edges in o log n time where n is the current number of vertices of g the bounds for tests and vertex insertions are worst case and the bound for edge insertions is amortized we also present other applications of this technique to dynamic algorithms for planar graphs

a convex characterization of gain scheduled h sub spl infin controllers an important class of linear time varying systems consists of plants where the state space matrices are fixed functions of some time varying physical parameters spl theta small gain techniques can be applied to such systems to derive robust time invariant controllers yet this approach is often overly conservative when the parameters spl theta undergo large variations during system operation in general higher performance can be achieved by control laws that incorporate available measurements of spl theta and therefore adjust to the current plant dynamics this paper discusses extensions of h sub spl infin synthesis techniques to allow for controller dependence on time varying but measured parameters when this dependence is linear fractional the existence of such gain scheduled h sub spl infin controllers is fully characterized in terms of linear matrix inequalities the underlying synthesis problem is therefore a convex program for which efficient optimization techniques are available the formalism and derivation techniques developed here apply to both the continuous and discrete time problems existence conditions for robust time invariant controllers are recovered as a special case and extensions to gain scheduling in the face of parametric uncertainty are discussed in particular simple heuristics are proposed to compute such controllers

algorithms for finding the weight constrained k longest paths in a tree and the length constrained k maximum sum segments of a sequence in this work we obtain the following new results given a tree t v e with a length function e r and a weight function w e r a positive integer k and an interval l u the weight constrainedklongest paths problem is to find the k longest paths among all paths in t with weights in the interval l u we show that the weight constrainedklongest paths problem has a lower bound w vlogv k in the algebraic computation tree model and give an o vlogv k time algorithm for it given a sequence a a 1 a 2 a n of numbers and an interval l u we define the sum and length of a segment a i j to be a i a i 1 a j and j i 1 respectively the length constrainedkmaximum sum segments problem is to find the k maximum sum segments among all segments of a with lengths in the interval l u we show that the length constrainedkmaximum sum segments problem can be solved in o n k time

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

exact algorithms for computing the tree edit distance between unordered trees this paper presents a fixed parameter algorithm for the tree edit distance problem for unordered trees under the unit cost model that works in o 2 62 email protected poly n time and o n 2 space where the parameter k is the maximum bound of the edit distance and n is the maximum size of input trees this paper also presents polynomial time algorithms for the case where the maximum degree of the largest common subtree is bounded by a constant

traveling salesman problem heuristics leading methods implementations and latest advances heuristics for the traveling salesman problem tsp have made remarkable advances in recent years we survey the leading methods and the special components responsible for their successful implementa tions together with an experimental analysis of computational tests on a challenging and diverse set of symmetric and asymmetric tsp benchmark problems the foremost algorithms are represented by two families deriving from the lin kernighan lk method and the stem and cycle s c method we show how these families can be conveniently viewed within a common ejection chain framework which sheds light on their similarities and differences and gives clues about the nature of potential enhance ments to today s best methods that may provide additional gains in solving large and difficult tsps

an algorithm to determine the directional relationship between arbitrarily shaped polygons in the plane abstract the directional relationship between two polygons e g left above beside east north is an important spatial property and can also be used as a selection criterion for retrieving objects from a spatial database if the database is large this could help significantly in speeding search by reducing the size of the necessary search space this paper builds upon past work to develop a model for determining the directional relationship in 2 d space between two simply connected polygons of arbitrary shape size and distance from each other the model is based on visual interpretation and is data structure independent the model is also stated in algorithmic terms and is found to have a computational complexity of o n where n is the total number of vertices or cells used to represent the two polygons

from gene trees to species trees this paper studies various algorithmic issues in reconstructing a species tree from gene trees under the duplication and the mutation cost model this is a fundamental problem in computational molecular biology our main results are as follows a linear time algorithm is presented for computing all the losses in duplications associated with the least common ancestor mapping from a gene tree to a species tree this answers a problem raised recently by eulenstein mirkin and vingron j comput bio 5 1998 pp 135 148 the complexity of finding an optimal species tree from gene trees is studied the problem is proved to be np hard for the duplication cost and for the mutation cost further the concept of reconciled trees was introduced by goodman et al and formalized by page for visualizing the relationship between gene and species trees we show that constructing an optimal reconciled tree for gene trees is also np hard finally we consider a general reconstruction problem and show it to be np hard even for the well known nearest neighbor interchange distance a new and efficiently computable metric is defined based on the duplication cost we show that the problem of finding an optimal species tree from gene trees is np hard under this new metric but it can be approximated within factor 2 in polynomial time using this approximation result we propose a heuristic method for finding a species tree from gene trees with uniquely labeled leaves under the duplication cost our experimental tests demonstrate that when the number of species is larger than 15 and gene trees are close to each other our heuristic method is significantly better than the existing program in page s genetree 1 0 that starts the search from a random tree

bounded hairpin completion hairpin completion is a formal operation inspired from biochemistry here we consider a restricted variant of hairpin completion called bounded hairpin completion applied to a word encoding a single stranded molecule x such that either a suffix or a prefix of x is complementary to a subword of x hairpin completion produces a new word z which is a prolongation of x to the right or to the left by annealing although this operation is a purely mathematical one and the biological reality is just a source of inspiration it seems rather unrealistic to impose no restriction on the length of the prefix or suffix added by the hairpin completion the restriction considered here concerns the length of all prefixes and suffixes that are added to the current word by hairpin completion they cannot be longer than a given constant closure properties of some classes of formal languages under the non iterated and iterated bounded hairpin completion are investigated we consider the bounded hairpin completion distance between two words and generalize this distance to languages and discuss algorithms for computing them finally also the inverse operation namely bounded hairpin reduction as well as the set of all primitive bounded hairpin roots of a regular language are considered

query point visibility constrained shortest paths in simple polygons in this paper we study the problem of finding the shortest path between two points inside a simple polygon such that there is at least one point on the path from which a query point is visible we provide an algorithm which preprocesses the input in o n 2 nk time and space and provides logarithmic query time the input polygon has n vertices and k is a parameter dependent on the input polygon which is o n 2 in the worst case but is much smaller for most polygons the preprocessing algorithm sweeps an angular interval around every reflex vertex of the polygon to store the optimal contact points between the shortest paths and the windows separating the visibility polygons of the query points from the source and the destination

indexing weighted sequences neat and efficient in a weighted sequence for every position of the sequence and every letter of the alphabet a probability of occurrence of this letter at this position is specified weighted sequences are commonly used to represent imprecise or uncertain data for example in molecular biology where they are known under the name of position weight matrices given a probability threshold 1 z we say that a string p of length m occurs in a weighted sequence x at position i if the product of probabilities of the letters of p at positions i i m 1 in x is at least 1 z in this article we consider an indexing variant of the problem in which we are to pre process a weighted sequence to answer multiple pattern matching queries we present an o nz time construction of an o nz sized index for a weighted sequence of length n that answers pattern matching queries in the optimal o m occ time where occ is the number of occurrences reported the cornerstone of our data structure is a novel construction of a family of z strings that carries the information about all the strings that occur in the weighted sequence with a sufficient probability we thus improve the most efficient previously known index by amir et al theor comput sci 2008 with size and construction time o nz2 log z preserving optimal query time on the way we develop a new more straightforward index for the so called property matching problem we provide an open source implementation of our data structure and present experimental results using both synthetic and real data our construction allows us also to obtain a significant improvement over the complexities of the approximate variant of the weighted index presented by biswas et al at edbt 2016 and an improvement of the space complexity of their general index we also present applications of our index

on the construction of classes of suffix trees for square matrices we provide a uniform framework for the study of index data structures for a two dimensional matrixtext1 n 1 n whose entries are drawn from an ordered alphabet an index fortextcan be informally seen as the two dimensional analog of the suffix tree for a string it allows on line searches and statistics to be performed ontextby representing compactly the n3 square submatrices oftextin optimalo n2 space we identify 4n 1families of indices fortext each containing ni 1 2i 1 isomorphic data structures we also develop techniques leading to a single algorithm that efficiently builds any index in any family ino n2logn time ando n2 space such an algorithm improves in various respects the algorithms for the construction of the pat tree and the lsuffix tree the framework and the algorithm easily generalize tod 2 dimensions moreover as part of our algorithm we provide new algorithmic tools that yield a space efficient implementation of the naming scheme of r karpet al in proceedings fourth symposium on theory of computing pp 125 136 for strings and matrices

on the complexity of finding a largest common subtree of bounded degree the largest common subtree problem is to find a bijective mapping between subsets of nodes of two input rooted trees of maximum cardinality or weight that preserves labels and ancestry relationship the problem is known to be np hard for unordered trees in this paper we consider a restricted unordered case in which the maximum outdegree of a common subtree is bounded by a constant d we present an o nd time algorithm where n is the maximum size of two input trees which improves a previous o n2d time algorithm we also present an o h222h1d2h d1poly n time algorithm where h is the maximum height of two input trees

enumeration of bc subtrees of trees a bc tree block cutpoint tree is a tree with at least two vertices where the distance between any two leaves is even motivated from the study of the core of a graph bc trees form an interes

tree contractions and evolutionary trees an evolutionary tree is a rooted tree where each internal vertex has at least two children and where the leaves are labeled with distinct symbols representing species evolutionary trees are useful for modeling the evolutionary history of species an agreement subtree of two evolutionary trees is an evolutionary tree which is also a topological subtree of the two given trees we give an algorithm to determine the largest possible number of leaves in any agreement subtree of two trees t1 and t2 with n leaves each if the maximum degree d of these trees is bounded by a constant the time complexity is o n log2n and is within a log n factor of optimal for general d this algorithm runs in o nd2 log d log2 n time or alternatively in o nd sqrt d log 3 n time

novel transformation techniques using q heaps with applications to computational geometry using the notions of q heaps and fusion trees developed by fredman and willard we develop general transformation techniques to reduce a number of computational geometry problems to their special versions in partially ranked spaces in particular we develop a fast fractional cascading technique which uses linear space and enables sublogarithmic iterative search on catalog trees in the case when the degree of each node is bounded by o log epsilon n for some constant epsilon 0 where n is the total size of all the lists stored in the tree we apply the fast fractional cascading technique in combination with the other techniques to derive the first linear space sublogarithmic time algorithms for two fundamental geometric retrieval problems orthogonal segment intersection and rectangular point enclosure

implementing the dantzig fulkerson johnson algorithm for large traveling salesman problems dantzig fulkerson and johnson 1954 introduced the cutting plane method as a means of attacking the traveling salesman problem this method has been applied to broad classes of problems in combinatorial optimization and integer programming in this paper we discuss an implementation of dantzig et al s method that is suitable for tsp instances having 1 000 000 or more cities our aim is to use the study of the tsp as a step towards understanding the applicability and limits of the general cutting plane method in large scale applications

inferring evolutionary trees with strong combinatorial evidence we consider the problem of inferring the evolutionary tree of a set of n species we propose a quartet reconstruction method which specifically produces trees whose edges have strong combinatorial evidence let q be a set of resolved quartets defined on the studied species the method computes the unique maximum subset q of q which is equivalent to a tree and outputs the corresponding tree as an estimate of the species phylogeny we use a characterization of the subset q due to bandelt and dress adv appl math 7 1986 309 343 to provide an o n4 incremental algorithm for this variant of the np hard quartet consistency problem moreover when chosing the resolution of the quartets by the four point method fpm and considering the cavender farris model of evolution we show that the convergence rate of the q method is at worst polynomial when the maximum evolutive distance between two species is bounded we complete these theoretical results by an experimental study on real and simulated data sets the results show that i as expected the strong combinatorial constraints it imposes on each edge leads the q method to propose very few incorrect edges ii more surprisingly the method infers trees with a relatively high degree of resolution

linear time algorithms for two disjoint paths problems on directed acyclic graphs we present an algorithm that given two vertices s 1 and s 2 of a directed acyclic graph constructs in linear time a data structure using linear space that for each pair u v of two vertices u and v in constant time can output a tuple s 1 t 1 s 2 t 2 with t 1 t 2 u v such that there are two disjoint paths p 1 from s 1 to t 1 and p 2 from s 2 to t 2 if such a tuple exists the data structure is simpler than such a data structure for general directed graphs that can be obtained from results of georgiadis and tarjan disjoint can mean vertex as well as edge disjoint as an application and main result we show that the data structure can be used to solve the 2 disjoint paths problem on directed acyclic graphs optimally i e in linear time

fast parallel and serial multidimensional approximate array matching abstract consider the multidimensional array matching problem where differences between characters of the pattern and characters of the text are permitted a difference may be due to a mismatch between a text and pattern character superfluous text character or superfluous pattern character given a d dimensional array of size nd text and a d dimensional array of size md pattern we present the following algorithms for a given k find all occurrences of the pattern in the text with at most k differences our serial algorithm runs in time o nd dk k2 and the parallel algorithm runs in time o d dlog n k k2 using nd processors if superfluous characters are not allowed and the only permitted errors are mismatches we solve the problem serially in time o nddk and in parallel in time o d dlogn k using nd processors we present an alternate algorithm for the mismatches problem which runs serially in time o 2dndlog2 m and in parallel in time o d log n using nd processors this algorithm is more efficient for large k we also give an efficient solution to the close match problem here a mismatch weight function f 0 1 is assigned the weight function gives weight to the mismatches some mismatches being worse than others we present a serial algorithm for finding all appearances of the pattern in the text with a bounded total error in time o 2dnd log2 m our parallel algorithm is again of time complexity o d log n using nd processors

fast comparison of evolutionary trees abstract constructing evolutionary trees for species sets is a fundamental problem in biology unfortunately there is no single agreed upon method for this task and many methods are in use current practice dictates that trees be constructed using different methods and that the resulting trees then be compared for consensus it has become necessary to automate this process as the number of species under consideration has grown we study the unrooted maximum agreement subtree problem umast and its rooted variant rmast the umast problem is as follows given a set a and two trees t 0 and t 1 leaf labeled by the elements of a find a maximum cardinality subset b of a such that the restrictions of t 0 and t 1 to b are topologically isomorphic our main result is an o n 2 o 1 time algorithm for the umast problem we also derive an o n 2 time algorithm for the rmast problem the previous best algorithm for both these problems has running time o n 4 5 o 1

a decomposition theorem and two algorithms for reticulation visible networks in studies of molecular evolution phylogenetic trees are rooted binary trees whereas phylogenetic networks are rooted acyclic digraphs edges are directed away from the root and leaves are uniquely labeled with taxa in phylogenetic networks for the purpose of validating evolutionary models biologists check whether or not a phylogenetic tree resp cluster is contained in a phylogenetic network on the same taxa these tree and cluster containment problems are known to be np complete a phylogenetic network is reticulation visible if every reticulation node separates the root of the network from at least a leaf we answer an open problem by proving that the tree containment problem is solvable in quadratic time for reticulation visible networks the key tool used in our answer is a powerful decomposition theorem it also allows us to design a linear time algorithm for the cluster containment problem for networks of this type and to prove that every galled network with n leaves has 2 n 1 reticulation nodes at most

improved algorithms for the range next value problem and applications the range next value problem problem rnv is a recent interesting variant of the range search problems where the query is for the immediate next or equal value of a given number within a given interval of an array problem rnv was introduced and studied very recently by crochemore et al maxime crochemore costas s iliopoulos m sohel rahman finding patterns in given intervals in antonin kucera ludek kucera eds mfcs 22 in lecture notes in computer science vol 4708 springer 2007 pp 645 656 in this paper we present improved algorithms for problem rnv and algorithms for extended versions of the rnv problem we also show how this problem can be used to achieve optimal query time for a number of interesting variants of the classic pattern matching problems

inferring a tree from lowest common ancestors with an application to the optimization of relational expressions we present an algorithm for constructing a tree to satisfy a set of lineage constraints on common ancestors we then apply this algorithm to synthesize a relational algebra expression from a simple tableau a problem arising in the theory of relational databases

on parameter estimation using nonparametric noise models fitting multidimensional parametric models in frequency domain using nonparametric noise models is considered in this paper a nonparametric estimate of the noise statistics is obtained from a finite number of independent data sets the estimated noise model is then substituted for the the true noise covariance matrix in the maximum likelihood loss function to obtain suboptimal parameter estimates the goal here is to present an analysis of the resulting estimates sufficient conditions for consistency are derived and an asymptotic accuracy analysis is carried out the first and second order statistics of the cost function at the global minimum point are also explored which can be used for model validation the analytical findings are validated using numerical simulation results

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

an algebraic view of the relation between largest common subtrees and smallest common supertrees the relationship between two important problems in tree pattern matching the largest common subtree and the smallest common supertree problems is established by means of simple constructions which allow one to obtain a largest common subtree of two trees from a smallest common supertree of them and vice versa these constructions are the same for isomorphic homeomorphic topological and minor embeddings they take only time linear in the size of the trees and they turn out to have a clear algebraic meaning

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

compact oracles for reachability and approximate distances in planar digraphs it is shown that a planar digraph can be preprocessed in near linear time producing a near linear space oracle that can answer reachability queries in constant time the oracle can be distributed as an o log n space label for each vertex and then we can determine if one vertex can reach another considering their two labels only the approach generalizes to give a near linear space approximate distances oracle for a weighted planar digraph with weights drawn from 0 n it approximates distances within a factor 1 e in o log log nn 1 e time our scheme can be extended to find and route along correspondingly short dipaths

approximate periodicity finding an approximate period in a given string s of length n is defined as follows let s be a periodic string closest to s under some distance metric find the smallest period of s this period is called an approximate period of s under the given metric let the distance between the input string s and a closest periodic string under the hamming distance s be k we develop algorithms that construct an approximate period of s under the hamming distance in time o n k log log n and under the swap distance in time o n 2 finally we show an o n log n algorithm for finite alphabets and an o n log 3 n algorithm for infinite alphabets that approximate the minimum number of mismatches between the input string and a closest periodic string under the hamming distance

fuzzy semantics for direction relations between composite regions this paper proposes a model that combines qualitative spatial reasoning with fuzzy semantic typing to derive direction relations between two composite regions in a spatial configuration it extends goyal and egenhofer s direction relation model initially proposed for simple regions towards composite regions a fuzzy semantics typing qualifies the overall direction relations of two composite regions we introduce flexible fuzzy measures that allow for both a qualitative and metric study of direction relation similarities

l1 shortest path queries in simple polygons abstract let p be a simple polygon of n vertices we consider two point l 1 shortest path queries in p we build a data structure of o n size in o n time such that given any two query points s and t the length of an l 1 shortest path from s to t in p can be computed in o log n time or in o 1 time if both s and t are vertices of p and an actual shortest path can be output in additional linear time in the number of edges of the path to achieve the result we propose a mountain decomposition of simple polygons which may be interesting in its own right most importantly our approach is much simpler than the previous work on this problem

on pointers versus addresses summary what is the cost of random access to memory we address this fnndamental problem by studying the simulation of random addressing by a machine which lacks it a pointer machine the model we define allows the use of a data type of our choice a ram program of time i and space s can be simulated in o t log a time using a tree however this is not an obvious lower bound since a high level data type may allow us to encode the data in a more economic way our major contribution is the formalization of incompressibility for general data types the definition extends a similar property 01 strings that underlies the theory of kolmogorov complexity the main theorem states that for all incompressible data types an q t log s lower bound holds incompressibility trivially holds for strings but is harder to prove for a powerlul data type we prove incompressibility for the real numbers with a set of primitives which includes all functions which are continuously differentiable except on a countable closed set this may be the richest set of operations considered in a lower bound proof the prooi relies on the implicit functions theorem and baire s category theorem we also show that the integers with arithmetic x and lz zj any boolean operations and left shift are incompressible the inclusion of right shift reverses the situation and we obtain an o tq s upper bound where s is a functional inverse of ackermann s function

gain scheduling control of lft systems using parameter dependent lyapunov functions in this paper we propose a new control design approach for linear fractional transformation lft systems using parameter dependent lyapunov functions instead of assuming parameter dependency in lft fashion we consider general parameter dependent controllers to achieve better closed loop performance using full block multipliers new lpv synthesis conditions have been derived in terms of finite number of linear matrix inequalities lmis both continuous and discrete time cases are discussed a ship steering example has been used to demonstrate advantages and benefits of the proposed approach

improved algorithms for constructing consensus trees a consensus tree is a single phylogenetic tree that summarizes the branching structure in a given set of conflicting phylogenetic trees many different types of consensus trees have been proposed in the literature three of the most well known and widely used ones are the majority rule consensus tree the loose consensus tree and the greedy consensus tree this article presents new deterministic algorithms for constructing them that are faster than all the previously known ones given k phylogenetic trees with n leaves each and with identical leaf label sets our algorithms run in o nk time majority rule consensus tree o nk time loose consensus tree and o n2k time greedy consensus tree our algorithms for the majority rule consensus and the loose consensus trees are optimal since the input size is nk experimental results show that the algorithms are fast in practice

two dimensional periodicity in rectangular arrays string matching is rich with a variety of algorithmic tools in contrast multidimensional matching has had a rather sparse set of techniques this paper presents a new algorithmic technique for two dimensional matching periodicity analysis its strength appears to lie in the fact that it is inherently two dimensional periodicity in strings has been used to solve string matching problems multidimensional periodicity however is not as simple as it is in strings and was not formally studied or used in pattern matching in this paper we define and analyze two dimensional periodicity in rectangular arrays one definition of string periodicity is that a periodic string can self overlap in a particular way an analogous concept is true in two dimensions the self overlap vectors of a rectangle generate a regular pattern of locations where the rectangle may originate based on this regularity we define four categories of periodic arrays nonperiodic lattice periodic line periodic and radiant periodic and prove theorems about the properties of the classes we give serial and parallel algorithms that find all locations where an overlap originates in addition our algorithms find a witness proving that the array does not self overlap in any other location the serial algorithm runs in time o m2 linear time when the alphabet size is finite and in o m2log m otherwise the parallel algorithm runs in time o log m using o m2 crcw processors

tight bounds on the solutions of multidimensional divide and conquer maximin recurrences abstract in this paper upper bounds are presented for the solution of the following multidimensional divide and conquer maximin recurrence g n max n 1 n 2 n p n n 1 n 2 n p 1 i 1 p g n i smin 1 i p k f n i where p 2 1 k f is an arbitrary nondecreasing function and smin 1 i p k f n i denotes the sum of the smallest k numbers among f n 1 f n 2 and f n p all the presented upper bounds are at most log 2 k p times the exact solution of g n the derivation of the upper bounds is based on properties of partition trees for k 1 and k p 1 we obtain respectively two of the recurrences previously studied by alonso et al siam j discrete math 8 1995 428 447 in both of these two cases our results improve theirs

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

the suffix tree of a tree and minimizing sequential transducers abstract this paper gives a linear time algorithm for the construction of the suffix tree of a tree which was introduced by kosaraju as a natural generalization of the suffix tree of a string the suffix tree of a tree is used to obtain an efficient algorithm for the minimization of sequential transducers

fast algorithms for computing tree lcs the lcs of two rooted ordered and labeled trees f and g is the largest forest that can be obtained from both trees by deleting nodes we present algorithms for computing tree lcs which exploit the sparsity inherent to the tree lcs problem assuming g is smaller than f our first algorithm runs in time o email protected height f height g lglg g where r is the number of pairs email protected f email protected g such that v and w have the same label our second algorithm runs in time o email protected lglg g where l is the size of the lcs of f and g for this algorithm we present a novel three dimensional alignment graph our third algorithm is intended for the constrained variant of the problem in which only nodes with zero or one children can be deleted for this case we obtain an o rhlglg g time algorithm where h height f height g

generalized substring compression in substring compression one is given a text to preprocess so that upon request a compressed substring is returned generalized substring compression is the same with the following twist the queries contain an additional context substring or a collection of context substrings and the answers are the substring in compressed format where the context substring is used to make the compression more efficient we focus our attention on generalized substring compression and present the first non trivial correct algorithm for this problem inherent to our algorithm is a new method for finding the bounded longest common prefix of substrings which may be of independent interest in addition we propose an efficient algorithm for substring compression which makes use of range successor queries we present several tradeoffs for both problems for compressing the substring s i j possibly with the substring s email protected as a context the best query times we achieve are o c and o clog j ic for substring compression query and generalized substring compression query respectively where c is the number of phrases encoded a preliminary version of this paper has been presented in 21

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

efficient retrieval of approximate palindromes in a run length encoded string in this paper we study the palindrome retrieval problem with the input string compressed into run length encoded form given a run length encoded string rle t we show how to preprocess rle t to support subsequent queries of the longest palindrome centered at any specified position and having any specified number of mismatches between its arms we present two algorithms for the problem both taking time and space polynomial in the compressed string size let n denote the number of runs of rle t and let k denote the number of mismatches the first algorithm devised for small k identifies the desired palindrome in o logn min k n time with o nlogn preprocessing time while the second algorithm achieves o log 2n query time independent of k after o n 2logn time preprocessing

a new linear convex hull algorithm for simple polygons corresp a new optimal algorithm for computing the convex hull of a simple polygon in the plane along with a proof of correctness is presented the main novelty of the proposed algorithm is its use of existing concepts such as the unimodality of the area of a triangle inscribed in a convex polygon and sldansky s scan the combination of these concepts gives us new insight into the problem

a new way to represent the relative position between areal objects the fuzzy qualitative evaluation of directional spatial relationships such as to the right of to the south of between areal objects often relies on the computation of a histogram of angles which is considered to provide a good representation of the relative position of an object with regard to another in this paper the notion of the histogram of forces is introduced it generalizes and may supersede the histogram of angles the objects 2d entities are handled as longitudinal sections 1d entities not as points od entities it is thus possible to fully benefit from the power of integral calculus and so ensure rapid processing of raster data as well as of vector data explicitly considering both angular and metric information

incremental string comparison the problem of comparing two sequences a and b to determine their longest common subsequence lcs or the edit distance between them has been much studied in this paper we consider the following incremental version of these problems given an appropriate encoding of a comparison between a and b can one incrementally compute the answer for a and bb and the answer for a and bb with equal efficiency where b is an additional symbol our main result is a theorem exposing a surprising relationship between the dynamic programming solutions for two such adjacent problems given a threshold k on the number of differences to be permitted in an alignment the theorem leads directly to an o k algorithm for incrementally computing a new solution from an old one as contrasts the o k2 time required to compute a solution from scratch we further show with a series of applications that this algorithm is indeed more powerful than its nonincremental counterpart we show this by solving the applications with greater asymptotic efficiency than heretofore possible for example we obtain o nk algorithms for the longest prefix approximate match problem the approximate overlap problem and cyclic string comparison

qualitative spatial reasoning from the observer s point of view towards a generalization of symbolic projection abstract qualitative spatial reasoning is normally concerned with various methods for reasoning in images that in many cases are symbolic like for instance maps the goal is to identify complex object relations by means of methods operating on a high abstraction level several approaches to spatial reasoning have been proposed and one such method is symbolic projection which is a qualitative reasoning technique the method that will be discussed here is an extension of symbolic projection that specifically is concerned with the observer s point of view in other words the work presented here is concerned with qualitative spatial reasoning for determination of among other things directions distances and other object relations seen from the observer s perspective i e the projections are in the majority of cases concerned with a singular point furthermore it will also be demonstrated that the slope projections introduced in this paper are a generalization of the original approach of symbolic projection

improved data structures for fully dynamic biconnectivity we present fully dynamic algorithms for maintaining the biconnected components in general and plane graphs a fully dynamic algorithm maintains a graph during a sequence of insertions and deletions of edges or isolated vertices let m be the number of edges and n be the number of vertices in a graph the time per operation of the best deterministic algorithms is o sqrt n in general graphs and o log n in plane graphs for fully dynamic connectivity and o min m2 3 n in general graphs and o sqrt n in plane graphs for fully dynamic biconnectivity we improve the later running times to o sqrt m log n in general graphs and o log 2 n in plane graphs our algorithm for general graphs can also find the biconnected components of all vertices in time o n

building species trees from larger parts of phylogenomic databases gene trees are leaf labeled trees inferred from molecular sequences because of gene duplication events arising in genomes some species host several copies of the same gene hence individual gene trees usually have several leaves labeled with identical species names dealing with such multi labeled gene trees mul trees is a substantial problem in phylogenomics e g current supertree methods do not handle mul trees which restricts studies aimed at building the tree of life to a very small core of mono copy genes we propose to tackle this problem by mainly transforming a collection of mul trees into a collection of trees each containing single copies of labels to achieve that aim we provide several fast algorithmic building stones and describe how they fit in a general framework to build a species tree first we propose to separately preprocess each mul tree in order to remove its redundant parts with respect to speciation events for this purpose we present a tree isomorphism algorithm for mul trees to reduce redundant parts of these trees second we show how the speciation signal contained in a mul tree can be represented by a linear set of triplets when this set is topologically coherent compatible we show that it can be used to produce a single copy gene tree to replace the mul tree while preserving the information it contains on speciation events as an alternative approach we propose to extract from each mul tree a maximum size subtree that is free of duplication events the algorithms are finally applied in a supertree analysis of hogenom a database of homologous genes from fully sequenced genomes

computing the maximum agreement of phylogenetic networks we introduce the maximum agreement phylogenetic subnetwork problem masn for finding branching structure shared by a set of phylogenetic networks we prove that the problem is np hard even if restricted to three phylogenetic networks and give an o n2 time algorithm for the special case of two level 1 phylogenetic networks where n is the number of leaves in the input networks and where n is called a level f phylogenetic network if every biconnected component in the underlying undirected graph induces a subgraph of n containing at most f nodes with indegree 2 we also show how to extend our technique to yield a polynomial time algorithm for any two level f phylogenetic networks n1 n2 satisfying f o log n more precisely its running time is o v n1 v n2 2f1 f2 where v ni and fi denote the set of nodes in ni and the level of ni respectively for i 1 2

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

brief paper robust stability of time varying polytopic systems via parameter dependent homogeneous lyapunov functions this paper deals with robust stability analysis of linear state space systems affected by time varying uncertainties with bounded variation rate a new class of parameter dependent lyapunov functions is introduced whose main feature is that the dependence on the uncertain parameters and the state variables are both expressed as polynomial homogeneous forms this class of lyapunov functions generalizes those successfully employed in the special cases of unbounded variation rates and time invariant perturbations the main result of the paper is a sufficient condition to determine the sought lyapunov function which amounts to solving an lmi feasibility problem derived via a suitable parameterization of polynomial homogeneous forms moreover lower bounds on the maximum variation rate for which robust stability of the system is preserved are shown to be computable in terms of generalized eigenvalue problems numerical examples are provided to illustrate how the proposed approach compares with other techniques available in the literature

an o n log n algorithm for the maximum agreement subtree problem for binary trees the maximum agreement subtree problem is the following given two rooted trees whose leaves are drawn from the same set of items e g species find the largest subset of these items so that the portions of the two trees restricted to these items are isomorphic we consider the case which occurs frequently in practice i e the case when the trees are binary and give an o nlog n time algorithm for this problem

minimal state space realisation of continuous time linear time variant input output models abstractin the linear time invariant lti framework the transformation from an input output equation into state space representation is well understood several canonical forms exist that realise the same dynamic behaviour if the coefficients become time varying however the lti transformation no longer holds we prove by induction that there exists a closed form expression for the observability canonical state space model using binomial coefficients

preemptive ensemble motion planning on a tree consider the problem of finding a minimum cost tour to transport a set of objects between the vertices of a tree by a vehicle that travels along the edges of the tree the vehicle can carry only one object at a time and it starts and finishes at the same vertex of the tree it is shown that if objects can be dropped at intermediate vertices along its route and picked up later then the problem can be solved in polynomial time two efficient algorithms are presented for this problem the first algorithm runs in o k qn time where n is the number of vertices in the tree k is the number of objects to be moved and q leq min k n is the number of nontrivial connected components in a related directed graph the second algorithm runs in o k n log n time

the 2 radius and 2 radiian problems on trees in this paper we consider two facility location problems on tree networks one is the 2 radius problem whose goal is to partition the vertex set of the given network into two non empty subsets such that the sum of the radii of these two induced subgraphs is minimum the other is the 2 radiian problem whose goal is to partition the network into two non empty subsets such that the sum of the centdian values of these two induced subgraphs is minimum we propose an o n time algorithm for the 2 radius problem on trees and an o nlogn time algorithm for the 2 radiian problem on trees where n is the number of vertices in the given tree

random access to grammar compressed strings and trees grammar based compression where one replaces a long string by a small context free grammar that generates the string is a simple and powerful paradigm that captures sometimes with slight reduction in efficiency many of the popular compression schemes including the lempel ziv family run length encoding byte pair encoding sequitur and re pair in this paper we present a novel grammar representation that allows efficient random access to any character or substring without decompressing the string let s be a string of length n compressed into a context free grammar mathcal s of size n we present two representations of mathcal s achieving o log n random access time and either o n cdot alpha k n construction time and space on the pointer machine model or o n construction time and space on the ram here alpha k n is the inverse of the k th row of ackermann s function our representations also efficiently support decompression of any substring in s we can decompres

maximum agreement subtree in a set of evolutionary trees metrics and efficient algorithms the maximum agreement subtree approach is one method of reconciling different evolutionary trees for the same set of species an agreement subtree enables choosing a subset of the species for whom the restricted subtree is equivalent under a suitable definition in all given evolutionary trees recently dynamic programming ideas were used to provide polynomial time algorithms for finding a maximum homeomorphic agreement subtree of two trees generalizing these methods to sets of more than two trees yields algorithms that are exponential in the number of trees unfortunately it turns out that in reality one is usually presented with more than two trees sometimes as many as thousands of trees in this paper we prove that the maximum homeomorphic agreement subtree problem is cal np complete for three trees with unbounded degrees we then show an approximation algorithm of time o kn5 for choosing the species that are not in a maximum agreement subtree of a set of k trees our approximation is guaranteed to provide a set that is no more than 4 times the optimum solution while the set of evolutionary trees may be large in practice the trees usually have very small degrees typically no larger than three we develop a new method for finding a maximum agreement subtree of k trees of which one has degree bounded by d this new method enables us to find a maximum agreement subtree in time o knd 1 n2d

approximating the stretch factor of euclidean graphs there are several results available in the literature dealing with efficient construction of t spanners for a given set s of n points in ir d t spanners are euclidean graphs in which distances between vertices in g are at most t times the euclidean distances between them in other words distances in g are stretched by a factor of at most t we consider the interesting dual problem given a euclidean graph g whose vertex set corresponds to the set s compute the stretch factor of g i e the maximum ratio between distances in g and the corresponding euclidean distances it can trivially be solved by solving the all pairs shortest path problem however if an approximation to the stretch factor is sufficient then we show it can be efficiently computed by making only o n approximate shortest path queries in the graph g we apply this surprising result to obtain efficient algorithms for approximating the stretch factor of euclidean graphs such as paths cycles trees planar graphs and general graphs the main idea behind the algorithm is to use callahan and kosaraju s well separated pair decomposition

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

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

an efficient algorithm for sequence comparison with block reversals given two sequences x and y that are strings over some alphabet set we consider the distance d x y between them defined to be minimum number of character replacements and block substring reversals needed to transform x to y or vice versa the operations are required to be disjoint this is the simplest sequence comparison problem we know of that allows natural block edit operations block reversals arise naturally in genomic sequence comparison they are also of interest in matching music data we present an algorithm for exactly computing the distance d x y it takes time o x log2 x and hence is near linear trivial approach takes quadratic time

on gradient based search for multivariable system estimates this paper addresses the design of gradient based search algorithms for multivariable system estimation in particular the paper here considers so called ldquofull parametrizationrdquo approaches and establishes that the recently developed ldquodata driven local coordinaterdquo methods can be seen as a special case within a broader class of techniques that are designed to deal with rank deficient jacobians this informs the design of a new algorithm that via a strategy of dynamic jacobian rank determination is illustrated to offer enhanced performance

swapping a failing edge of a shortest paths tree by minimizing the average stretch factor we consider a two edge connected undirected graph g v e with n nodes and m non negatively real weighted edges and a single source shortest paths tree spt t of g rooted at an arbitrary node r if an edge in t is temporarily removed it makes sense to reconnect the nodes disconnected from the root by adding a single non tree edge called a swap edge instead of rebuilding a new optimal spt from scratch in the past several optimality criteria have been considered to select a best possible swap edge in this paper we focus on the most prominent one that is the minimization of the average distance between the root and the disconnected nodes to this respect we present an o mlog2n time and o m space algorithm to find a best swap edge for every edge of t thus improving for m o n2 log2n the previously known o n2 time and space complexity algorithm

verification and sensitivity analysis of minimum spanning trees in linear time komlos has devised a way to use a linear number of binary comparisons to test whether a given spanning tree of a graph with edge costs is a minimum spanning tree the total computational work required by his method is much larger than linear however this paper describes a linear time algorithm for verifying a minimum spanning tree this algorithm combines the result of komlos with a preprocessing and table look up method for small subproblems and with a previously known almost linear time algorithm additionally an optimal deterministic algorithm and a linear time randomized algorithm for sensitivity analysis of minimum spanning trees are presented