guard games on graphs a team of mobile agents called guards tries to keep an intruder out of an assigned area by blocking all possible attacks in a graph model for this setting the guards and the intruder are located on the vertices of a graph and they move from node to node via connecting edges the area protected by the guards is an induced subgraph of the given graph we investigate the algorithmic aspects of the guarding problem which is to find the minimum number of guards sufficient to patrol the area we show that the guarding problem is pspace hard and provide a set of approximation algorithms all approximation algorithms are based on the study of a variant of the game where the intruder must reach the guarded area in a single step in order to win this variant of the game appears to be a 2 approximation for the guarding problem and for graphs without cycles of length 5 the minimum number of required guards in both games coincides we give a polynomial time algorithm for solving the one step guarding problem in graphs of bounded treewidth and complement this result by showing that the problem is w1 hard parameterized by the treewidth of the input graph we also show that the problem is fixed parameter tractable fpt parameterized by the treewidth and maximum degree of the input graph finally we turn our attention to a large class of sparse graphs including planar graphs and graphs of bounded genus namely apex minor free graphs we prove that the one step guarding problem is fpt and possess a ptas on apex minor free graphs

on the maximum weight minimal separator abstract given an undirected and connected graph g v e and two vertices s t v a vertex subset s that separates s and t is called an s t separator and an s t separator is called minimal if no proper subset of s separates s and t moreover we say that a set s is a minimal separator of g if s is a minimal s t separator for some s and t in this paper we consider finding a minimal s t separator with maximum weight on a vertex weighted graph we first prove that these problems are np hard on the other hand we give an o tw o tw time deterministic algorithm based on tree decompositions where o is the order notation omitting the polynomial factor of n moreover we improve the algorithm by using the rank based approach and the running time is o 38 2 tw finally we give an o 9 tw w 2 time randomized algorithm to determine whether there exists a minimal s t separator where w is its weight and tw is the treewidth of g

the complexity of mean payoff games on graphs abstract we study the complexity of finding the values and optimal strategies of mean payoff games on graphs a family of perfect information games introduced by ehrenfeucht and mycielski and considered by gurvich karzanov and khachiyan we describe a pseudo polynomial time algorithm for the solution of such games the decision problem for which is in np conp finally we describe a polynomial reduction from mean payoff games to the simple stochastic games studied by condon these games are also known to be in np conp but no polynomial or pseudo polynomial time algorithm is known for them

existential second order logic over graphs charting the tractability frontier fagin s theorem the first important result of descriptive complexity asserts that a property of graphs is in np if and only if it is definable by an existential second order formula in this article we study the complexity of evaluating existential second order formulas that belong to prefix classses of existential second order logic where a prefix class is the collection of all existential second order formulas in prenex normal form such that the second order and the first order quantifiers obey a certain quantifier pattern we completely characterize the computational complexity of prefix classes of existential second order logic in three different contexts 1 over directed graphs 2 over undirected graphs with self loops and 3 over undirected graphs without self loops our main result is that in each of these three contexts a dichotomy holds that is to say each prefix class of existential second order logic either contains sentences that can express np complete problems or each of its sentences expresses a polynomial time solvable problem although the boundary of the dichotomy coincides for the first two cases it changes as one moves to undirected graphs without self loops the key difference is that a certain prefix class based on the well known ackermann class of first order logic contains sentences that can express np complete problems over graphs of the first two types but becomes tractable over undirected graphs without self loops moreover establishing the dichotomy over undirected graphs without self loops turns out to be a technically challenging problem that requires the use of sophisticated machinery from graph theory and combinatorics including results about graphs of bounded tree width and ramsey s theorem

computations by fly automata beyond monadic second order logic parameterized algorithms based on automata infinite automata computing their transitions problems described in monadic second order logic counting and other problems not expressible in monadic second order logic the validity of a monadic second order ms expressible property can be checked in linear time on graphs of bounded tree width or clique width given with appropriate decompositions this result is proved by constructing from the ms sentence expressing the property and an integer that bounds the tree width or clique width of the input graph a finite automaton intended to run bottom up on the algebraic term representing a decomposition of the input graph as we cannot construct practically the transition tables of these automata because they are huge we use fly automata whose states and transitions are computed on the fly only when needed for a particular input furthermore we allow infinite sets of states and we equip automata with output functions thus they can check properties that are not ms expressible and compute values for example the number of p colorings of a graph we obtain xp and fpt graph algorithms parameterized by tree width or clique width we show how to construct easily such algorithms by combining predefined automata for basic functions and properties these combinations reflect the structure of the ms formula that specifies the property to check or the function to compute

generalizing constraint satisfaction on trees hybrid tractability and variable elimination the constraint satisfaction problem csp is a central generic problem in artificial intelligence considerable progress has been made in identifying properties which ensure tractability in such problems such as the property of being tree structured in this paper we introduce the broken triangle property which allows us to define a novel tractable class for this problem which significantly generalizes the class of problems with tree structure we show that the broken triangle property is conservative i e it is preserved under domain reduction and hence under arc consistency operations and that there is a polynomial time algorithm to determine an ordering of the variables for which the broken triangle property holds or to determine that no such ordering exists we also present a non conservative extension of the broken triangle property which is also sufficient to ensure tractability and can also be detected in polynomial time we show that both the broken triangle property and its extension can be used to eliminate variables and that both of these properties provide the basis for preprocessing procedures that yield unique closures orthogonal to value elimination by enforcement of consistency finally we also discuss the possibility of using the broken triangle property in variable ordering heuristics

a complexity dichotomy for matching cut in bipartite graphs of fixed diameter abstract in a graph a matching cut is an edge cut that is a matching matching cut is the problem of deciding whether or not a given graph has a matching cut which is known to be np complete even when restricted to bipartite graphs it has been proved that matching cut is polynomially solvable for graphs of diameter two in this paper we show that for any fixed integer d 3 matching cut is np complete in the class of graphs of diameter d this resolves an open problem posed by borowiecki and jesse jozefczyk 2008 6 we then show that for any fixed integer d 4 matching cut is np complete even when restricted to the class of bipartite graphs of diameter d complementing the hardness results we show that matching cut is polynomial time solvable in the class of bipartite graphs of diameter at most three and point out a new and simple polynomial time algorithm solving matching cut in graphs of diameter 2

n by n checkers is exptime complete the game of checkers can easily be generalized to be played on an n by n board and the complexity of deciding questions about positions regarded as a function of n this paper considers mainly the question of whether a particular player can force a win from a given position and also the question of what is the best move in a given position each of these problems is shown to be complete in exponential time this means that any algorithm to solve them must take time which rises exponentially with respect to some power of n and moreover that they are amongst the hardest problems with such a time bound for instance if there are any problems solvable in exponential time but not in polynomial space then these two problems are amongst them

alternation with restrictions on looping alternating turing machines with restrictions preventing them from returning to a previous configuration model games with rules enforcing such a restriction for instance the chinese version of go such restrictions do not affect the time complexity of problems for alternating turing machines but space s on a machine with the restriction is equivalent either to time or to space exponential in s on a normal alternating machine depending on the precise nature of the restriction

towards fixed parameter tractable algorithms for abstract argumentation abstract argumentation frameworks have received a lot of interest in recent years most computational problems in this area are intractable but several tractable fragments have been identified in particular dunne showed that many problems can be solved in linear time for argumentation frameworks of bounded tree width however these tractability results which were obtained via courcelle s theorem do not directly lead to efficient algorithms the goal of this paper is to turn the theoretical tractability results into efficient algorithms and to explore the potential of directed notions of tree width for defining larger tractable fragments as a by product we will sharpen some known complexity results

undirected edge geography abstract the game of edge geography is played by two players who alternately move a token on a graph from one vertex to an adjacent vertex erasing the edge in between the player who first has no legal move is the loser we show that the decision problem of determining whether a position in this game is a win for the first player is pspace complete further the problem remains pspace complete when restricted to planar graphs with maximum degree 3 however if the underlying graph is bipartite we provide 1 a linear algebraic characterization of the p and n positions yielding 2 a polynomial time algorithm for deciding whether any given position is p or n and also 3 a polynomial time algorithm to find winning moves

counting h colorings of partial k trees the problem of counting all h colorings of a graph g with n vertices is considered while the problem is in general p complete we give linear time algorithms that solve the main variants of this problem when the input graph g is a k tree or in the case where g is directed when the underlying graph of g is a k tree our algorithms remain polynomial even in the case where k o logn or in the case where the size of h is o n our results are easy to implement and imply the existence of polynomial time algorithms for a series of problems on partial k trees such as core checking and chromatic polynomial computation

algorithms for vertex partitioning problems on graphs with fixed clique width many vertex partitioning problems can be expressed within a general framework introduced by telle and proskurowski they showed that optimization problems in this framework can be solved in polynomial time on classes of graphs with bounded tree width in this paper we consider a very similar framework in relationship with more general classes of graphs we propose a polynomial time algorithm on classes of graphs with bounded clique width for all the optimization problems in our framework these classes of graphs are more general than the classes of graphs with bounded tree width in the sense that classes of graphs with bounded tree width have also bounded clique width but not necessarily the inverse our framework includes problems such as independent dominating set p dominating set induced bounded degree subgraph induced p regular subgraph perfect matching cut graph k coloring and graph list k coloring with cardinality constraints fixed k this paper thus provides a second distinct framework within which the optimization problems can be solved in polynomial time on classes of graphs with bounded clique width after a first framework called ms1 due to the work of courcelle makowsky and rotics for which they obtained a linear time algorithm

a comparison of compatible finite and inductive graph properties abstract in the theory of hyperedge replacement grammars and languages one encounters three types of graph properties that play an important role in proving decidability and structural results the three types are called compatible finite and inductive graph properties all three of them cover graph properties that are well behaved with respect to certain operations on hypergraphs in this paper we show that the three notions are essentially equivalent consequently three lines of investigation in the theory of hyperedge replacement so far separated merge into one

layout of graphs with bounded tree width a queue layout of a graph consists of a total order of the vertices and a partition of the edges into queues such that no two edges in the same queue are nested the minimum number of queues in a queue layout of a graph is its queue number a three dimensional straight line grid drawing of a graph represents the vertices by points in mathbb z 3 and the edges by noncrossing line segments this paper contributes three main results 1 it is proved that the minimum volume of a certain type of three dimensional drawing of a graph g is closely related to the queue number of g in particular if g is an n vertex member of a proper minor closed family of graphs such as a planar graph then g has a mathcal o 1 times mathcal o 1 times mathcal o n drawing if and only if g has a mathcal o 1 queue number 2 it is proved that the queue number is bounded by the tree width thus resolving an open problem due to ganley and heath discrete appl math 109 2001 pp 215 221 and disproving a conjecture of pemmaraju exploring the powers of stacks and queues via graph layouts ph d thesis virginia polytechnic institute and state university blacksburg va 1992 this result provides renewed hope for the positive resolution of a number of open problems in the theory of queue layouts 3 it is proved that graphs of bounded tree width have three dimensional drawings with mathcal o n volume this is the most general family of graphs known to admit three dimensional drawings with mathcal o n volume the proofs depend upon our results regarding track layouts and tree partitions of graphs which may be of independent interest

identification location domination and metric dimension on interval and permutation graphs i bounds we consider the problems of finding optimal identifying codes open locating dominating sets and resolving sets of an interval or a permutation graph in these problems one asks to find a subset of vertices normally called a solution set using which all vertices of the graph are distinguished the identification can be done by considering the neighborhood within the solution set or by employing the distances to the solution vertices normally the goal is to minimize the size of the solution set then here we study the case of interval graphs unit interval graphs bipartite permutation graphs and cographs for these classes of graphs we give tight lower bounds for the size of such solution sets depending on the order of the input graph while such lower bounds for the general class of graphs are in logarithmic order the improved bounds in these special classes are of the order of either quadratic root or linear in terms of number of vertices moreover the results for cographs lead to linear time algorithms to solve the considered problems on inputs that are cographs

size and treewidth bounds for conjunctive queries this article provides new worst case bounds for the size and treewith of the result q d of a conjunctive query q applied to a database d we derive bounds for the result size q d in terms of structural properties of q both in the absence and in the presence of keys and functional dependencies these bounds are based on a novel coloring of the query variables that associates a coloring number c q to each query q intuitively each color used represents some possible entropy of that variable using this coloring number we derive tight bounds for the size of q d in case i no functional dependencies or keys are specified and ii simple functional dependencies keys are given these results generalize recent size bounds for join queries obtained by atserias et al 2008 in the case of arbitrary compound functional dependencies we use tools from information theory to provide lower and upper bounds establishing a close connection between size bounds and a basic question in information theory our new coloring scheme also allows us to precisely characterize both in the absence of keys and with simple keys the treewidth preserving queries the queries for which the treewidth of the output relation is bounded by a function of the treewidth of the input database finally we give some results on the computational complexity of determining the size bounds and of deciding whether the treewidth is preserved

basic notions of universal algebra for language theory and graph grammars abstract this paper reviews the basic properties of the equational and recognizable subsets of general algebras these sets can be seen as generalizations of the context free and regular languages respectively this approach based on universal algebra facilitates the development of the theory of formal languages so as to include the description of sets of finite trees finite graphs finite hypergraphs tuples of words partially commutative words also called traces and other similar finite objects

bounded treewidth as a key to tractability of knowledge representation and reasoning several forms of reasoning in ai like abduction closed world reasoning circumscription and disjunctive logic programming are well known to be intractable in fact many of the relevant problems are on the second or third level of the polynomial hierarchy in this paper we show how the notion of treewidth can be fruitfully applied to this area in particular we show that all these problems become tractable actually even solvable in linear time if the treewidth of the involved formulae or programs is bounded by some constant clearly these theoretical tractability results as such do not immediately yield feasible algorithms however we have recently established a new method based on monadic datalog which allowed us to design an efficient algorithm for a related problem in the database area in this work we exploit the monadic datalog approach to construct new algorithms for logic based abduction

on the hardness of approximating minimization problems we prove results indicating that it is hard to compute efficiently good approximate solutions to the graph coloring set covering and other related minimization problems specifically there is an e 0 such that graph coloring cannot be approximated with ratio n e unless p np set covering cannot be approximated with ratio c log n for any c 1 4 unless np is contained in dtime n poly log n similar results follow for related problems such as clique cover fractional chromatic number dominating set and others

compatibility of unrooted phylogenetic trees is fpt a collection of t1 t2 tk of unrooted leaf labelled phylogenetic trees all with different leaf sets is said to be compatible if there exists a tree t such that each tree ti can be obtained from t by deleting leaves and contracting edges determining compatibility is np hard and the fastest algorithm to date has worst case complexity of around nk time n being the number of leaves here we present an o nf k algorithm proving that compatibility of unrooted phylogenetic trees is fixed parameter tractable fpt with respect to the number k of trees

the monadic second order logic of graphs xiv uniformly sparse graphs and edge set quantifications we consider the class usk of uniformly k sparse simple graphs i e the class of finite or countable simple graphs every finite subgraph of which has a number of edges bounded by k times the number of vertices we prove that for each k every monadic second order formula intended to express a graph property that uses variables denoting sets of edges can be effectively translated into a monadic second order formula where all set variables denote sets of vertices and that expresses the same property of the graphs in usk this result extends to the class of uniformly k sparse simple hypergraphs of rank at most m for any k and m it follows that every subclass of usk consisting of finite graphs of bounded clique width has bounded tree width clique width is a graph complexity measure similar to tree width and relevant to the construction of polynomial algorithms for np complete problems on special classes of graphs

trees grids and mso decidability from graphs to matroids monadic second order mso logic has proved to be a useful tool in many areas of application reaching flom decidability and complexity to picture processing correctness of programs and parallel processes to characterize the structural borderline between decidability and undecidability is a classical research problem here this problem is related to questions in computational complexity especially to the model checking problem for which many tools developed in the area of decidability have proved to be useful for more than two decades it was conjectured in d seese the structure of the models of decidable monadic theories of graphs ann pure appl logic 53 1991 169 195 that decidability of monadic theories of countable structures implies that the theory can be reduced via interpretability to a theory of trees it is one of the main goals of this article to prove a variant of this conjecture for matroids representable over a finite field matroids can be viewed as a wide generalization of graphs and they seem to capture some second order properties in a more suitable way than graphs themselves cf the recent development in matroid structure theory j f geelen a h m gerards g p whittle branch width and well quasi ordering in matroids and graphs j combin theory ser b 84 2002 270 290 j f geelen a h m gerards n robertson g p whittle excluding a planar graph from a gf q representable matroid manuscript 2003 more exactly we prove for every finite field f that any class of f representable matroids with a decidable mso theory must have uniformly bounded branch width moreover we show that bounding the branch width of all matroids in general is not sufficient to obtain a decidable mso theory our paper gives a rather detailed introduction to these different subjects and shows that a blend of ideas and methods from logic together with structural matroid theory can lead to new tools and algorithms and can shed light on some old open problems

algorithms for decision problems in argument systems under preferred semantics for dung s model of abstract argumentation under preferred semantics argumentation frameworks may have several distinct preferred extensions i e in informal terms sets of acceptable arguments thus the acceptance problem for a specific argument can consider deciding whether an argument is in at least one such extensions credulously accepted or in all such extensions skeptically accepted we start by presenting a new algorithm that enumerates all preferred extensions following this we build algorithms that decide the acceptance problem without requiring explicit enumeration of all extensions we analyze the performance of our algorithms by comparing these to existing ones and present experimental evidence that the new algorithms are more efficient with respect to the expected running time moreover we extend our techniques to solve decision problems in a widely studied development of dung s model namely value based argumentation frameworks vafs in this regard we examine analogous notions to the problem of enumerating preferred extensions and present algorithms that decide subjective respectively objective acceptance

a new approach to quantify power law cross correlation and its application to commodity markets abstract we proposed a new method detrended moving average cross correlation analysis dmca to detect the power law cross correlation between two correlated non stationary time series by combining detrended cross correlation analysis dcca and detrended moving average dma in order to compare the performance of dmca and dcca in the detection of cross correlation and to estimate the influence of periodic trend we generate two cross correlated time series x i and y i by a periodic two component fractionally autoregressive integrated moving average arfima process then we apply both methods to quantify the cross correlations of the generated series whose theoretical values are already known to us by comparing the results we obtained we find that the performance of this new approach is comparable to dcca with less calculating amounts our method can also reduce the impact of trends furthermore dmca for background and forward moving average case outperforms dcca in more accurate estimation when the analyzed times series are short in length to provide an example we also apply this new method to the time series of the real world data from brent and wti crude oil spot markets to investigate the complex cross market correlation between these commodity markets in all our method is another practical choice to detect the cross correlation between two short period non stationary time series and has potential application to real world problems

probabilistic hyperedge replacement grammars abstract in a probabilistic graph grammar each production has a probability attached to it this induces a probability assigned to each derivation tree and to each derived graph conditions for this probability function to be a probabilistic measure are discussed the statistical properties of the generated language are investigated we show how to compute the average size of an inductive function and the probability of an inductive graph predicate a relationship can be established between production probabilities and some statistical information of the generated language this way probabilities can be assigned to productions so that the generated graphs satisfy some statistical conditions

large induced subgraphs via triangulations and cmso we obtain an algorithmic metatheorem for the following optimization problem let varphi be a counting monadic second order logic cmso formula and t geq 0 be an integer for a given graph g v e the task is to maximize x subject to the following there is a set f subseteq v such that x subseteq f the subgraph g f induced by f is of treewidth at most t and the structure g f x models varphi i e g f x models varphi we give an algorithm solving this optimization problem on any n vertex graph g in time cal o pi g cdot n t 4 cdot f t varphi where pi g is the set of all potential maximal cliques in g and f is a function of t and varphi only pipelined with the known bounds on the number of potential maximal cliques in different graph classes there are a plethora of algorithmic consequences extending and subsuming many known results on polynomial time algorithms for graph classes we also show that all potential maximal cliques of g can be enumerated in time cal o 1 7347 n this implies the existence of an exact exponential algorithm of running time cal o 1 7347 n for many np hard problems related to finding maximum induced subgraphs with different properties

increasing the minimum degree of a graph by contractions abstract the degree contractibility problem is to test whether a given graph g can be modified to a graph of minimum degree at least d by using at most k contractions we prove the following three results first degree contractibility is np complete even when d 14 second it is fixed parameter tractable when parameterized by k and d third it is w 1 hard when parameterized by k we also study its variant where the input graph is weighted i e has some edge weighting and the contractions preserve these weights the weighted degree contractibility problem is to test if a weighted graph g can be contracted to a weighted graph of minimum weighted degree at least d by using at most k weighted contractions we show that this problem is np complete and that it is fixed parameter tractable when parameterized by k in addition we pinpoint a relationship with the problem of finding a minimal edge cut of maximum size in a graph and study the parameterized complexity of this problem and its variants

complexity of path forming games abstract for a number of two player games where players alternately choose the next vertex of a simple or an elementary path in a graph we consider the problem to determine whether for a given game instance there is a winning strategy for the first player we show several of these problems to be pspace complete in some special cases we obtain polynomial time algorithms based on graph rewriting or an intricate form of dynamic programming e g we show generalized geography and some other pspace complete problems to be linear time solvable on graphs with constant bounded treewidth

constant factor approximations of branch decomposition and largest grid minor of planar graphs in o n 1 time we give constant factor approximation algorithms for computing the optimal branch decompositions and largest grid minors of planar graphs for a planar graph g with n vertices let bw g be the branchwidth of g and gm g the largest integer g such that g has a gxg grid as a minor let c 1 be a fixed integer and a b arbitrary constants satisfying a c 1 and b 2c 1 we give an algorithm which constructs in o n 1 1 clogn time a branch decomposition of g with width at most abw g we also give an algorithm which constructs a gxg grid minor of g with g gm g b in o n 1 1 clogn time the constants hidden in the big o notations are proportional to c a c 1 and c b 2c 1 respectively

polynomial kernels for hitting forbidden minors under structural parameterizations abstract we investigate polynomial time preprocessing for the problem of hitting forbidden minors in a graph using the framework of kernelization for a fixed finite set of connected graphs f the f deletion problem is the following given a graph g and integer k is it possible to delete k vertices from g to ensure the resulting graph does not contain any graph from f as a minor earlier work by fomin lokshtanov misra and saurabh focs 12 showed that when f contains a planar graph an instance g k can be reduced in polynomial time to an equivalent one of size k o 1 in this work we focus on structural measures of the complexity of an instance with the aim of giving nontrivial preprocessing guarantees for instances whose solutions are large motivated by several impossibility results we parameterize the f deletion problem by the size of a vertex modulator whose removal results in a graph of constant treedepth we prove that for each set f of connected graphs and constant the f deletion problem parameterized by the size of a treedepth modulator has a polynomial kernel our kernelization is fully explicit and does not depend on protrusion reduction or well quasi ordering which are sources of algorithmic non constructivity in earlier works on f deletion our main technical contribution is to analyze how models of a forbidden minor in a graph g with modulator x interact with the various connected components of g x using the language of labeled minors we analyze the fragments of potential forbidden minor models that can remain after removing an optimal f deletion solution from a single connected component of g x by bounding the number of different types of behavior that can occur by a polynomial in x we obtain a polynomial kernel using a recursive preprocessing strategy our results extend earlier work for specific instances of f deletion such as vertex cover and feedback vertex set it also generalizes earlier preprocessing results for f deletion parameterized by a vertex cover which is a treedepth one modulator

intractability of clique width parameterizations we show that edge dominating set hamiltonian cycle and graph coloring are w 1 hard parameterized by clique width it was an open problem explicitly mentioned in several papers whether any of these problems is fixed parameter tractable when parameterized by the clique width that is solvable in time g k cdot n o 1 on n vertex graphs of clique width k where g is some function of k only our results imply that the running time o n f k of many clique width based algorithms is essentially the best we can hope for up to a widely believed assumption from parameterized complexity namely fpt neq w 1

the recognition of series parallel digraphs we present a linear time algorithm to recognize the class of vertex series parallel vsp digraphs our method is based on the relationship between vsp digraphs and the class of edge series paralle

estimating the proportion of immunes in a censored sample summary an estimator for the proportion of immunes in a population is proposed when a sample of censored failure times is available our suggestion is to use one minus the maximum observed value of the kaplan meier empirical distribution function this estimator is shown to be consistent and asymptotically normal under modest conditions on the censoring mechanism simulations suggest that the estimator is approximately normal for quite small sample sizes provided the immune proportion is not too close to zero a simple nonparametric statistic is proposed to test whether the assumptions of the analysis are likely to be valid

all structured programs have small tree width and good register allocation the register allocation problem for an imperative program is often modelled as the coloring problem of the interference graph of the control flow graph of the program the interference graph of a flow graph g is the intersection graph of some connected subgraphs of g these connected subgraphs represent the lives or life times of variables so the coloring problem models that two variables with overlapping life times should be in different registers for general programs with unrestricted gotos the interference graph can be any graph and hence we cannot in general color within a factor o n from optimality unless np p

a linear time algorithm for finding tree decompositions of small treewidth in this paper we give for constant k a linear time algorithm that given a graph g v e determines whether the treewidth of g is at most k and if so finds a tree decomposition of g with treewidth at most k a consequence is that every minor closed class of graphs that does not contain all planar graphs has a linear time recognition algorithm another consequence is that a similar result holds when we look instead for path decompositions with pathwidth at most some constant k

covariance and survivor function estimation using censored multivariate failure time data summary the covariance between counting process martingales is used to characterize the dependence between two failure time variates a representation of the bivariate survivor function is obtained in terms of the marginal survivor functions and this covariance function a closely related representation expresses the bivariate survivor function in terms of marginal survivor functions and a conditional covariance function leading to a new nonparametric survivor function estimator generalizations to higher dimensional failure time variates are also given simulation evaluations of the survivor function estimator are presented and generalizations to regression problems are outlined

treewidth distance on phylogenetic trees in this article we study the treewidth of the display graph an auxiliary graph structure obtained from the fusion of phylogenetic i e evolutionary trees at their leaves earlier work has shown that the treewidth of the display graph is bounded if the trees are in some formal sense topologically similar here we further expand upon this relationship we analyse a number of reduction rules commonly used in the phylogenetics literature to obtain fixed parameter tractable algorithms in some cases the subtree reduction the reduction rules behave similarly with respect to treewidth while others the cluster reduction behave very differently and the behaviour of the chain reduction is particularly intriguing because of its link with graph separators and forbidden minors we also show that the gap between treewidth and tree bisection and reconnect tbr distance can be infinitely large and that unlike for example planar graphs the treewidth of the display graph can be as much as linear in its number of vertices a number of other auxiliary results are given we conclude with a discussion and list a number of open problems

fugitive search games on graphs and related parameters abstract the goal of a fugitive search game on a graph is to trap a fugitive that hides on the vertices of the graph by systematically placing searchers on the vertices the fugitive is assumed to have complete knowledge of the graph and of the searchers moves but is restricted to move only along paths whose vertices are not guarded by searchers the search number of the graph is the least number of searchers necessary to trap the fugitive variants of the fugitive search game have been related to important graph parameters like treewidth and pathwidth in this paper we introduce a class of fugitive search games where the searchers do not see the fugitive and the fugitive can only move just before a searcher is placed on the vertex it occupies letting the fugitive s speed i e the maximum number of edges the fugitive can traverse at a single move vary we get different games we show that if the speed of the fugitive is unbounded then the search number minus 1 is equal to the treewidth of the graph while if the speed is 1 then the search number minus 1 is equal to a polynomially computable graph parameter which is called width or alternatively linkage and is studied in the context of the constraint satisfaction and boolean satisfiability problems we also show that in the above two cases the search number remains the same even if we consider only search strategies that at every step further restrict the fugitive s possible resorts this monotonicity property is usually expressed as recontamination does not help moreover we give an equivalent characterization of the search number for any given fugitive speed in terms of an elimination ordering of the vertices of the graph using this characterization we show that for any graph if the length of any chordless cycle is bounded by a constant s s 3 then the treewidth of the graph plus 1 is equal to the search number for fugitive speed s 2

the monadic second order logic of graphs i recognizable sets of finite graphs abstract the notion of a recognizable set of finite graphs is introduced every set of finite graphs that is definable in monadic second order logic is recognizable but not vice versa the monadic second order theory of a context free set of graphs is decidable

decidability of the finiteness of ranges of tree transductions abstract the finiteness of ranges of tree transductions is shown to be decidable for tby the composition closure of macro tree transductions furthermore tby definable sets and tby computable relations are considered which are obtained by viewing a tree as an expression that denotes an element of a given algebra a sufficient condition on the considered algebra is formulated under which the finiteness problem is decidable for tby definable sets and for the ranges of tby computable relations the obtained result applies in particular to the class of string languages that can be defined by tby transductions via the yield mapping this is a large class which is proved to form a substitution closed full afl

listing all potential maximal cliques of a graph a potential maximal clique of a graph is a vertex set that induces a maximal clique in some minimal triangulation of that graph it is known that if these objects can be listed in polynomial time for a class of graphs the treewidth and the minimum fill in are polynomially tractable for these graphs we show here that the potential maximal cliques of a graph can be generated in polynomial time in the number of minimal separators of the graph thus the treewidth and the minimum fill in are polynomially tractable for all classes of graphs with a polynomial number of minimal separators

three connected graphs whose maximum nullity is at most three for a graph g v e with vertex set v 1 2 n let s g be the set of all n n real valued symmetric matrices a which represent g the maximum nullity of a graph g denoted by m g is the largest possible nullity of any matrix a s g fiedler showed that a graph g has m g 1 if and only if g is a path johnson et al gave a characterization of all graphs g with m g 2 independently hogben and van der holst gave a characterization of all 2 connected graphs with m g 2 in this paper we show that k connected graphs g have m g k that k connected partial k graphs g have m g k and that for 3 connected graphs g m g 3 if and only if g is a partial 3 path

monadic second order evaluations on tree decomposable graphs abstract every graph generated by a hyperedge replacement graph grammar can be represented by a tree namely the derivation tree of the derivation sequence that produced it certain functions on graphs can be computed recursively on the derivation trees of these graphs by using monadic second order logic and semiring homomorphisms we describe in a single formalism a large class of such functions polynomial and even linear algorithms can be constructed for some of these functions we unify similar results obtained by takamizawa 1982 bern 1987 arnborg 1991 and habel 1989

some simple robust methods for the analysis of recurrent events nelson discussed a method of estimating the cumulative mean function for identically distributed processes of recurrent events we show that a similar approach can be used with more general models including regression the key idea is to use point estimates based on poisson models and to develop robust variance estimates that are valid more generally the methods are illustrated on reliability and warranty data

efficient solution to connectivity problems on hierarchically defined graphs using hierarchical definitions we can describe very large graphs in small spaces in this paper we discuss how such succinct graph descriptions can be used to speed up the solution of graph problems we present the bottom up method that solves graph problems without expanding the hierarchical description this allows solutions that are efficient in terms of the hierarchical graph description instead of the size of the expanded graph we exemplify the method by giving efficient solutions to connectivity problems on hierarchical graphs our results have applications in computer aided design for integrated circuit design and other engineering problems

the monadic second order logic of graphs xii planar graphs and planar maps we prove that we can specify by formulas of monadic second order logic the unique planar embedding of a 3 connected planar graph if the planar graph is not 3 connected but given with a linear order of its set of edges we can also define a planar embedding by monadic second order formulas we cannot do so in general without the ordering even for 2 connected planar graphs the planar embedding of a graph can be specified by a relational structure called a map which is a graph enriched with a circular ordering of the edges incident with each vertex this circular ordering called a rotation system represents a planar embedding of the neighbourhood of each vertex for each connected map one can define a linear order on its vertices by formulas of monadic second order logic hence we have for planar graphs some kind of equivalence between linear orderings and planar embeddings

kernel bounds for path and cycle problems connectivity problems like k path and k disjoint paths relate to many important milestones in parameterized complexity namely the graph minors project color coding and the recent development of techniques for obtaining kernelization lower bounds this work explores the existence of polynomial kernels for various path and cycle problems by considering nonstandard parameterizations we show polynomial kernels when the parameters are a given vertex cover a modulator to a cluster graph or a promised max leaf number we obtain lower bounds via cross composition e g for hamiltonian cycle and related problems when parameterized by a modulator to an outerplanar graph

boundary classes for graph problems involving non local properties abstract we continue the study of boundary classes for np hard problems and focus on seven np hard graph problems involving non local properties hamiltonian cycle hamiltonian cycle through specified edge hamiltonian path feedback vertex set connected vertex cover connected dominating set and graph vc con dimension our main result is the determination of the first boundary class for feedback vertex set we also determine boundary classes for hamiltonian cycle through specified edge and hamiltonian path and give some insights on the structure of some boundary classes for the remaining problems

a partial k arboretum of graphs with bounded treewidth the notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies this survey paper wants to give an overview of many classes of graphs that can be seen to have a uniform upper bound on the treewidth of graphs in the class also some mutual relations between such classes are discussed

deciding first order properties of locally tree decomposable structures we introduce the concept of a class of graphs or more generally relational structures being locally tree decomposable there are numerous examples of locally tree decomposable classes among them the class of planar graphs and all classes of bounded valence or of bounded tree width we also consider a slightly more general concept of a class of structures having bounded local tree width we show that for each property of structures that is definable in first order logic and for each locally tree decomposable class c of structures there is a linear time algorithm deciding whether a given structure a c has property for classes c of bounded local tree width we show that for every k 1 there is an algorithm solving the same problem in time o n1 1 k where n is the cardinality of the input structure

default logic and bounded treewidth abstract in this paper we study reiter s propositional default logic when the treewidth of a certain graph representation semi primal graph of the input theory is bounded we establish a dynamic programming algorithm on tree decompositions that decides whether a theory has a consistent stable extension cons our algorithm can even be used to enumerate all generating defaults enumsd that lead to stable extensions we show that our algorithm decides cons in linear time in the input theory and triple exponential time in the treewidth further our algorithm solves enumsd with a pre computation step that is linear in the input theory and triple exponential in the treewidth followed by a linear delay to output solutions finally we take the exponential time hypothesis eth into consideration and establish lower bounds of bounded treewidth algorithms for cons

an annotated bibliography on guaranteed graph searching graph searching encompasses a wide variety of combinatorial problems related to the problem of capturing a fugitive residing in a graph using the minimum number of searchers in this annotated bibliography we give an elementary classification of problems and results related to graph searching and provide a source of bibliographical references on this field

efficient algorithms for center problems in cactus networks efficient algorithms for solving the center problems in weighted cactus networks are presented in particular we have proposed the following algorithms for the weighted cactus networks of size n an o nlogn time algorithm to solve the 1 center problem and an o nlog 3n time algorithm to solve the weighted continuous 2 center problem we have also provided improved solutions to the general p center problems in cactus networks the developed ideas are then applied to solve the obnoxious 1 center problem in weighted cactus networks

exploring the random genesis of co occurrence networks using the network random generation models from gustedt 2009 we simulate and analyze several characteristics such as the number of components the degree sequence and the clustering coefficient of the generated networks this is done for a variety of distributions fixed value bernoulli poisson binomial that are used to control the parameters of generation process these parameters are in particular the size of newly appearing sets of objects the number of contexts in which new elements appear initially the number of objects that are shared with parent contexts and the time period inside which a context may serve as a parent context aging the results show that these models allow to fine tune the generation process such that the graphs adopt properties as they can be found in real world graphs

on the parameterized complexity of recognizing well covered r l graph an r ell partition of a graph g is a partition of its vertex set into r independent sets and ell cliques a graph is r ell if it admits an r ell partition a graph is well covered if every maximal independent set is also maximum a graph is r ell well covered if it is both r ell and well covered in this paper we consider two different decision problems in the r ell well covered graph problem r ell wcg for short we are given a graph g and the question is whether g is an r ell well covered graph in the well covered r ell graph problem wc r ell g for short we are given an r ell graph g together with an r ell partition of v g into r independent sets and ell cliques and the question is whether g is well covered we classify most of these problems into p conp complete np complete np hard or conp hard only the cases wc r 0 g for r ge 3 remain open in addition we consider the parameterized complexity of these problems for several choices of parameters such as the size alpha of a maximum independent set of the input graph its neighborhood diversity or the number ell of cliques in an r ell partition in particular we show that the parameterized problem of deciding whether a general graph is well covered parameterized by alpha can be reduced to the wc 0 ell g problem parameterized by ell and we prove that this latter problem is in xp but does not admit polynomial kernels unless mathsf conp subseteq mathsf np mathsf poly

query evaluation via tree decompositions a number of efficient methods for evaluating first order and monadic second order queries on finite relational structures are based on tree decompositions of structures or queries we systematically study these methods in the first part of the article we consider arbitrary formulas on tree like structures we generalize a theorem of courcelle 1990 by showing that on structures of bounded tree width a monadic second order formula with free first and second order variables can be evaluated in time linear in the structure size plus the size of the output in the second part we study tree like formulas on arbitrary structures we generalize the notions of acyclicity and bounded tree width from conjunctive queries to arbitrary first order formulas in a straightforward way and analyze the complexity of evaluating formulas of these fragments moreover we show that the acyclic and bounded tree width fragments have the same expressive power as the well known guarded fragment and the finite variable fragments of first order logic respectively

regression methods for poisson process data abstract this article is directed toward situations where individuals can experience repeated events and data on an individual consist of the number and occurrence times of events along with concomitant variables methods of regression analysis are presented based on poisson process and proportional intensity assumptions these include parametric and semi parametric approaches to model fitting model assessment and the treatment of random effects in addition insight is gained as to the central role of poisson and mixed poisson regression analysis of counts in these methods and as to the effects of unobserved heterogeneity on semi parametric analyses the methods in the article are based on the proportional intensity poisson process model for which an individual with given fixed covariate vector x has repeated events occur according to a nonhomogeneous poisson process with intensity function x t 0 t exp x estimation of and the baseline intensity 0 t are considered when 0 t is specifi

games on interval and permutation graph representations we describe combinatorial games on graphs in which two players antagonistically build a representation of a subgraph of a given graph we show that for a large class of these games determining whether a given instance is a winning position for the next player is pspace hard in contrast we give polynomial time algorithms for solving some versions of the games on trees

recurrence interval analysis of trading volumes we study the statistical properties of the recurrence intervals between successive trading volumes exceeding a certain threshold q the recurrence interval analysis is carried out for the 20 liquid chinese stocks covering a period from january 2000 to may 2009 and two chinese indices from january 2003 to april 2009 similar to the recurrence interval distribution of the price returns the tail of the recurrence interval distribution of the trading volumes follows a power law scaling and the results are verified by the goodness of fit tests using the kolmogorov smirnov ks statistic the weighted ks statistic and the cramer von mises criterion the measurements of the conditional probability distribution and the detrended fluctuation function show that both short term and long term memory effects exist in the recurrence intervals between trading volumes we further study the relationship between trading volumes and price returns based on the recurrence interval analysis method it is found that large trading volumes are more likely to occur following large price returns and the comovement between trading volumes and price returns is more pronounced for large trading volumes

dominating set is fixed parameter tractable in claw free graphs we show that the dominating set problem parameterized by solution size is fixed parameter tractable fpt in graphs that do not contain the claw k 1 3 the complete bipartite graph on four vertices where the two parts have one and three vertices respectively as an induced subgraph we present an algorithm that uses 2 o k 2 n o 1 time and polynomial space to decide whether a claw free graph on n vertices has a dominating set of size at most k note that this parameterization of dominating set is w 2 hard on the set of all graphs and thus is unlikely to have an fpt algorithm for graphs in general the most general class of graphs for which an fpt algorithm was previously known for this parameterization of dominating set is the class of k i j free graphs which exclude for some fixed i j n the complete bipartite graph k i j as a subgraph for i j 2 the class of claw free graphs and any class of k i j free graphs are not comparable with respect to set inclusion we thus extend the range of graphs over which this parameterization of dominating set is known to be fixed parameter tractable we also show that in some sense it is the presence of the claw that makes this parameterization of the dominating set problem hard more precisely we show that for any t 4 the dominating set problem parameterized by the solution size is w 2 hard in graphs that exclude the t claw k 1 t as an induced subgraph our arguments also imply that the related connected dominating set and dominating clique problems are w 2 hard in these graph classes finally we show that for any t n the clique problem parameterized by solution size which is w 1 hard on general graphs is fpt in t claw free graphs our results add to the small and growing collection of fpt results for graph classes defined by excluded subgraphs rather than by excluded minors

exact algorithms for treewidth and minimum fill in we show that the treewidth and the minimum fill in of an n vertex graph can be computed in time mathcal o 1 8899 n our results are based on combinatorial proofs that an n vertex graph has mathcal o 1 7087 n minimal separators and mathcal o 1 8135 n potential maximal cliques we also show that for the class of asteroidal triple free graphs the running time of our algorithms can be reduced to mathcal o 1 4142 n

recurrence duration statistics and time dependent intrinsic correlation analysis of trading volumes a study of chinese stock indices abstract the trading volume in stock markets is known as an important variable which reflects the liquidity of the financial markets and therefore is regarded to be greatly important for the measurement of market liquidity risk in this work a new concept called recurrence duration is introduced for study of daily trading volumes which is inspired by idea of the volatility duration that was proposed and studied in our previous work the recurrence duration is thought as the shortest passing time that the following days trading volume takes to exceed or go below the current trading volume which is time varying similar to the volatility duration distribution of the price returns the power law function could describe the empirical probability distribution of recurrence durations of trading volumes and their tail distributions can be fitted by two stretched exponential functions further the correlation relationships of trading volumes between chinese stock indices as well as the correlations of recurrence durations are investigated one approach employed is a recently proposed method time dependent intrinsic correlation tdic which is based on the empirical mode decomposition emd to decompose nonlinear and nonstationary signals into the intrinsic mode functions imfs the instantaneous periods of which are used then in determination of the sizes of sliding windows to compute the running correlation coefficients for the multiscale signals the empirical results reveal rich patterns of correlations for both trading volumes and recurrence durations at different scales for different modes another approach is the widely used dcca cross correlation coefficient by which the level of cross correlation is measured for both original series and imf modes of the stock indices

estimating the expected total number of events in a process we consider estimation of the cumulative mean function of a process recurring in time such as the numbers of arrests or migrations accrued by an individual as a function of their age we call this theage profile of a series of events in some situations we can expect a finite value for the total number of events experienced by an individual for example when the distribution of the interevent times is improper so that the process may cease at a finite time with positive probability we propose and analyze a new estimator constructed from kaplan meier km estimators of the interevent time distributions for such an age profile and compare it with the nelson aalen na estimator of the cumulative mean function of a process the km estimator is proved to be uniformly consistent for the age profile if and only if follow up in the sample is sufficient in a sense that is manifested in practice by the leveling off of the profiles at their right side ends and is asymptotically normally distributed around