fixed parameter algorithms for kemeny rankings the computation of kemeny rankings is central to many applications in the context of rank aggregation given a set of permutations votes over a set of candidates one searches for a consensus permutation that is closest to the given set of permutations unfortunately the problem is np hard we provide a broad study of the parameterized complexity for computing optimal kemeny rankings besides the three obvious parameters number of votes number of candidates and solution size called kemeny score we consider further structural parameterizations more specifically we show that the kemeny score and a corresponding kemeny ranking of an election can be computed efficiently whenever the average pairwise distance between two input votes is not too large in other words kemeny score is fixed parameter tractable with respect to the parameter average pairwise kendall tau distance d a we describe a fixed parameter algorithm with running time 16 d a email protected poly moreover we extend our studies to the parameters maximum range and average range of positions a candidate takes in the input votes whereas kemeny score remains fixed parameter tractable with respect to the parameter maximum range it becomes np complete in the case of an average range of two this excludes fixed parameter tractability with respect to the parameter average range unless p np finally we extend some of our results to votes with ties and incomplete votes where in both cases one no longer has permutations as input

approximation algorithms for np complete problems on planar graphs this paper describes a general technique that can be used to obtain approximation schemes for various np complete problems on planar graphs the strategy depends on decompos ing a planar graph into subgraphs of a form we call k outerplanar for fixed k the problems of interest are solvable optimally in linear time on k outerplanar graphs by dynamic programming for general planar graphs if the problem is a maximization problem such as maximum independent set this technique gives for each k a linear time algorithm that produces a solution whose size is at least k k 1 optimal if the problem is a minimization problem such as minimum vertex cover it gives for each k a linear time algorithm that produces a solution whose size is at most k 1 k optimal taking k c log log nl or k c log nl where n is the number of nodes and c is some constant we get polynomial time approximation algorithms whose solution sizes converge toward optimal as n increases the class of problems for which this approach provides approximation schemes includes maximum independent set maximum tile salvage partition into triangles maximum h matching minimum vertex cover minimum dominat ing set and minimum edge dominating set for these and certain other problems the proof of solvability on k outerplanar graphs also enlarges the class of planar gmphs for which the problems are known to be solvable in polynomial time

an algebraic theory of graph reduction we show how membership in classes of graphs definable in monadic second order logic and of bounded treewidth can be decided by finite sets of terminating reduction rules the method is constructive in the sense that we describe an algorithm which will produce from a formula in monadic second order logic and an integer k such that the class defined by the formula is of treewidth k a set of rewrite rules that reduces any member of the class to one of finitely many graphs in a number of steps bounded by the size of the graph this reduction system corresponds to an algorithm that runs in time linear in the size of the graph

minimum leaf out branching and related problems given a digraph d the minimum leaf out branching problem minlob is the problem of finding in d an out branching with the minimum possible number of leaves i e vertices of out degree 0 we prove that minlob is polynomial time solvable for acyclic digraphs in general minlob is np hard and we consider three parameterizations of minlob we prove that two of them are np complete for every value of the parameter but the third one is fixed parameter tractable fpt the fpt parameterization is as follows given a digraph d of order n and a positive integral parameter k check whether d contains an out branching with at most n k leaves and find such an out branching if it exists we find a problem kernel of order o k 2 and construct an algorithm of running time o 2 o k l o g k n 6 which is an additive fpt algorithm we also consider transformations from two related problems the minimum path covering and the maximum internal out tree problems into minlob which imply that some parameterizations of the two problems are fpt as well

adsorption of a binary mixture of monomers with nearest neighbour cooperative effects a model for the adsorption of a binary mixture on a one dimensional infinite lattice with nearest neighbour cooperative effects is considered the particles of the two species are both monomers but differ in the repulsive interaction experienced by them when trying to adsorb an exact expression for the coverage of the lattice is derived in the jamming limit it is a monotonic function of the ratio between the attempt frequencies of the two species varying between the values corresponding to each of the two single species this is in contrast with the results obtained in other models for the adsorption of particles of different sizes the structure of the jamming state is also investigated

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

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

the parameterized complexity of k edge induced subgraphs we prove that finding a k edge induced subgraph is fixed parameter tractable thereby answering an open problem of leizhen cai our algorithm is based on several combinatorial observations gauss famous eureka theorem and a generalization of the well known fpt algorithm for the model checking problem for first order logic on graphs with locally bounded tree width due to frick and grohe on the other hand we show that two natural counting versions of the problem are hard hence the k edge induced subgraph problem is one of the very few known examples in parameterized complexity that are easy for decision while hard for counting

on the dynamics of random sequential absorption the dynamics of random sequential absorption on d dimensional lattices is represented by a simple graphical expansion results for the entire filling process and in particular its saturation limit are easily obtained it is shown that the large d limit of the saturation density is ln 2d 2d the expression gives an accurate approximation for d or 3

representative sets and irrelevant vertices new tools for kernelization we continue the development of matroid based techniques for kernelization initiated by the present authors 47 we significantly extend the usefulness of matroid theory in kernelization by showing applications of a result on representative sets due to lovasz 51 and marx 53 as a first result we show how representative sets can be used to derive a polynomial kernel for the elusive almost 2 sat problem where the task is to remove at most k clauses to make a 2 cnf formula satisfiable solving a major open problem in kernelization this result also yields a new o log opt approximation for the problem improving on the o log n approximation of agarwal et al 3 and an implicit o log opt approximation due to even et al 24 we further apply the representative sets tool to the problem of finding irrelevant vertices in graph cut problems that is vertices that can be made undeletable without affecting the answer to the problem this gives the first significant progress towards a polynomial kernel for the multiway cut problem in particular we get a kernel of o ks 1 vertices for multiway cut instances with at most s terminals both these kernelization results have significant spin off effects producing the first polynomial kernels for a range of related problems more generally the irrelevant vertex results have implications for covering min cuts in graphs for a directed graph g v e and sets s t v let r be the size of a minimum s t vertex cut which may intersect s and t we can find a set z v of size o s t r that contains a minimum a b vertex cut for every a s b t similarly for an undirected graph g v e a set of terminals x v and a constant s we can find a set z v of size o x s 1 that contains a minimum multiway cut for every partition of x into at most s pairwise disjoint subsets both results are polynomial time we expect this to have further applications in particular we get direct reduction rule based kernelizations for all problems above in contrast to the indirect compression based kernel previously given for odd cycle transversal 47 all our results are randomized with failure probabilities that can be made exponentially small in n due to needing a representation of a matroid to apply the representative sets tool

on the kernelization of split graph problems abstract a split graph is a graph whose vertices can be partitioned into a clique and an independent set we study numerous problems on split graphs namely the k vertex disjoint paths k cycle k path and k l stable set problems in the k vertex disjoint paths problem we are given a graph and k terminal pairs of vertices and are asked whether there is a set of k vertex disjoint paths linking these terminal pairs respectively in the k cycle k path problem we are given a graph and are asked whether there is a path cycle of length k the k l stable set problem takes a graph and an integer k as input and asks whether the graph has a subset of k vertices such that the distance between every two vertices in the subset is at least l 1 it is known that all the above problems are np complete on split graphs we derive a 4 k vertex kernel for the k vertex disjoint paths problem and an o k 2 vertex kernel for both the k path problem and the k cycle problem concerning the k l stable set problem for l 1 or l 3 the problem is polynomial time solvable on split graphs for l 2 we prove that the k l stable set problem is w 1 complete on split graphs with respect to k however if the given split graph contains no k 1 r as an induced subgraph and every vertex in the independent set of the split graph has degree at most d we derive a linear vertex kernel for the k 2 stable set problem where both r and d are constants

scaling behavior near jamming in random sequential adsorption for the random sequential adsorption model we introduce the availability as a new variable corresponding to the number of available locations in which an adsorbate can be accommodated we investigate the relation of the availability to the coverage of the adsorbent surface over time power law scaling between the two is obtained both through numerical simulations and analytical techniques for both one and two dimensional rsa as well as in the case of competitive random sequential adsorption in one dimension

the parameterized complexity of editing graphs for bounded degeneracy we examine the parameterized complexity of the problem of editing a graph to obtain an r degenerate graph we show that for the editing operations vertex deletion and edge deletion both separately and combined the problem is w p complete and remains w p complete even if the input graph is already r 1 degenerate or has maximum degree 2r 1 for all r 2 we also demonstrate fixed parameter tractability for several clique based problems when the input graph has bounded degeneracy

on finding short resolution refutations and small unsatisfiable subsets we consider the parameterized problems of whether a given set of clauses can be refuted within k resolution steps and whether a given set of clauses contains an unsatisfiable subset of size at most k we show that both problems are complete for the class w 1 the first level of the w hierarchy of fixed parameter intractable problems our results remain true if restricted to 3 sat instances and or to various restricted versions of resolution including tree like resolution input resolution and read once resolution applying a metatheorem of frick and grohe we show that restricted to classes of sets of clauses of locally bounded treewidth the considered problems are fixed parameter tractable for example the problems are fixed parameter tractable for planar cnf formulas

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

a linear kernel for a planar connected dominating set we provide polynomial time data reduction rules for connected dominating set on planar graphs and analyze these to obtain a linear kernel for the planar connected dominating set problem to obtain the desired kernel we introduce a method that we call reduce or refine our kernelization algorithm analyzes the input graph and either finds an appropriate reduction rule that can be applied or zooms in on a region of the graph which is more amenable to reduction we find this method of independent interest and believe that it will be useful for obtaining linear kernels for other problems on planar graphs

preservation under extensions on well behaved finite structures a class of relational structures is said to have the extension preservation property if every first order sentence that is preserved under extensions on the class is equivalent to an existential sentence the class of all finite structures does not have the extension preservation property we study the property on classes of finite structures that are better behaved we show that the property holds for classes of acyclic structures structures of bounded degree and more generally structures that are wide in a sense that we will make precise we also show that the preservation property holds for the class of structures of treewidth at most k for any k in contrast we show that the property fails for the class of planar graphs

another paraconsistent algebraic semantics for lukasiewicz pavelka logic abstract as recently proved in a previous work of turunen tsoukias and ozturk starting from an evidence pair a b on the real unit square and associated with a propositional statement we can construct evidence matrices expressed in terms of four values t f k u that respectively represent the logical valuations true false contradiction both true and false and unknown neither true nor false regarding the statement the components of the evidence pair a b are to be understood as evidence for and against respectively moreover the set of all evidence matrices can be equipped with an injective mv algebra structure thus the set of evidence matrices can play the role of truth values of a lukasiewicz pavelka fuzzy logic a rich and applicable mathematical foundation for fuzzy reasoning and in such a way that the obtained new logic is paraconsistent in this paper we show that a similar result can be also obtained when the evidence pair a b is given on the real unit triangle since the real unit triangle does not admit a natural mv structure we introduce some mathematical results to show how this shortcoming can be overcome and another injective mv algebra structure in the corresponding set of evidence matrices is obtained also we derive several formulas to explicitly calculate the evidence matrices for the operations associated to the usual connectives

the many facets of upper domination this paper studies upper domination i e the problem of computing the maximum cardinality of a minimal dominating set in a graph with respect to classical and parameterised complexity as well as approximability

on the complexity of connection games in this paper we study three connection games among the most widely played havannah twixt and slither we show that determining the outcome of an arbitrary input position is pspace complete in all three cases our reductions are based on the popular graph problem generalized geography and on hex itself we also consider the complexity of generalizations of hex parameterized by the length of the solution and establish that while short generalized hex is w1 hard short hex is fpt finally we prove that the ultra weak solution to the empty starting position in hex cannot be fully adapted to any of these three games the games of havannah twixt and slither are pspace complete the game of slither does not admit draws on finite planar grid boards short generalized hex is w1 hard and short hex is fixed parameter tractable

graph editing problems with extended regularity constraints graph editing problems offer an interesting perspective on sub and supergraph identification problems for a large variety of target properties they have also attracted significant attention in recent years particularly in the area of parameterized complexity as the problems have rich parameter ecologies in this paper we examine generalisations of the notion of editing a graph to obtain a regular subgraph in particular we extend the notion of regularity to include two variants of edge regularity along with the unifying constraint of strong regularity we present a number of results with the central observation that these problems retain the general complexity profile of their regularity based inspiration when the number of edits k and the maximum degree r are taken together as a combined parameter the problems are tractable i e in fpt but are otherwise intractable we also examine variants of the basic editing to obtain a regular subgraph problem from the perspective of parameterizing by the treewidth of the input graph in this case the treewidth of the input graph essentially becomes a limiting parameter on the natural k r parameterization

parallel algorithms with optimal speedup for bounded treewidth we describe the first parallel algorithm with optimal speedup for constructing minimum width tree decompositions of graphs of bounded treewidth on n vertex input graphs the algorithm works in o log n 2 time using o n operations on the erew pram we also give faster parallel algorithms with optimal speedup for the problem of deciding whether the treewidth of an input graph is bounded by a given constant and for a variety of problems on graphs of bounded treewidth including all decision problems expressible in monadic second order logic on n vertex input graphs the algorithms use o n operations together with o log n log n time on the erew pram or o log n time on the crcw pram

augmenting tractable fragments of abstract argumentation we present a new approach to the efficient solution of important computational problems that arise in the context of abstract argumentation our approach makes known algorithms defined for restricted fragments generally applicable at a computational cost that scales with the distance from the fragment thus in a certain sense we gradually augment tractable fragments surprisingly it turns out that some tractable fragments admit such an augmentation and that others do not more specifically we show that the problems of credulous and skeptical acceptance are fixed parameter tractable when parameterized by the distance from the fragment of acyclic argumentation frameworks for most semantics other tractable fragments such as the fragments of symmetrical and bipartite frameworks seem to prohibit an augmentation the acceptance problems are already intractable for frameworks at distance 1 from the fragments for our study we use a broad setting and consider several different semantics for the algorithmic results we utilize recent advances in fixed parameter tractability

on parameterized independent feedback vertex set we investigate a generalization of the classical feedback vertex set fvs problem from the point of view of parameterized algorithms independent feedback vertex set ifvs is the independent variant of the fvs problem and is defined as follows given a graph g and an integer k decide whether there exists email protected v g f k such that g v g f is a forest and g f is an independent set the parameter is k note that the similarly parameterized version of the fvs problem where there is no restriction on the graph g f has been extensively studied in the literature the connected variant cfvs where g f is required to be connected has received some attention as well the fvs problem easily reduces to the ifvs problem in a manner that preserves the solution size and so any algorithmic result for ifvs directly carries over to fvs we show that ifvs can be solved in o 5 kn o 1 time where n is the number of vertices in the input graph g and obtain a cubic o k 3 kernel for the problem note the contrast with the cfvs problem which does not admit a polynomial kernel unless email protected np poly

fixed parameter tractability and completeness i basic results for many fixed parameter problems that are trivially soluable in polynomial time such as k dominating set essentially no better algorithm is presently known than the one which tries all possible solutions other problems such as k feedback vertex set exhibit fixed parameter tractability for each fixed k the problem is soluable in time bounded by a polynomial of degree c where c is a constant independent of k we establish the main results of a completeness program which addresses the apparent fixed parameter intractability of many parameterized problems in particular we define a hierarchy of classes of parameterized problems fpt subseteq w 1 subseteq w 2 subseteq cdots subseteq w sat subseteq w p and identify natural complete problems for w t for t geq 2 in other papers we have shown many problems complete for w 1 dominating set is shown to be complete for w 2 and thus is not fixed parameter tractable unless independent set clique irredundant set and many other natural problems in w 2 are also fixed parameter tractable we also give a compendium of currently known hardness results as an appendix

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

parameterized algorithms for feedback set problems and their duals in tournaments the parameterized feedback vertex arc set problem is to find whether there are k vertices arcs in a given graph whose removal makes the graph acyclic the parameterized complexity of this problem in general directed graphs is a long standing open problem we investigate the problems on tournaments a well studied class of directed graphs we consider both weighted and unweighted versions we also address the parametric dual problems which are also natural optimization problems we show that they are fixed parameter tractable not just in tournaments but in oriented directed graphs where there is at most one directed arc between a pair of vertices more specifically the dual problem we show fixed parameter tractable are given an oriented directed graph is there a subset of k vertices arcs that forms an acyclic directed subgraph of the graph our main results include an o 2 4143 kn 1 algorithm for weighted feedback vertex set problem and an o 2 415 kn algorithm for weighted feedback arc set problem in tournaments an o e2k k kk2 min m ig n n2 algorithm for the dual of feedback vertex set problem maximum vertex induced acyclic graph in oriented directed graphs and an o 4kk m algorithm for the dual of feedback arc set problem maximum arcinduced acyclic graph in general directed graphs we also show that the dual of feedback vertex set is w 1 hard in general directed graphs and the feedback arc set problem is fixed parameter tractable in dense directed graphs our results are the first non trivial results for these problems

meta kernelization in a parameterized problem every instance i comes with a positive integer k the problem is said to admit a polynomial kernel if in polynomial time one can reduce the size of the instance i to a polynomial in k while preserving the answer in this work we give two meta theorems on kernelization the first theorem says that all problems expressible in counting monadic second order logic and satisfying a coverability property admit a polynomial kernel on graphs of bounded genus our second result is that all problems that have finite integer index and satisfy a weaker coverability property admit a linear kernel on graphs of bounded genus these theorems unify and extend all previously known kernelization results for planar graph problems

kernels for packing and covering problems abstract we show how the notion of combinatorial duality related to the well known notion of duality from linear programming may be used for translating kernel results obtained for packing problems into kernel results for covering problems we exemplify this approach by having a closer look at the problems of packing a graph with vertex disjoint trees or vertex disjoint stars with r edges the case r 2 has been studied in several other papers by establishing a general notion of a crown we show how linear size vertex kernels can be efficiently achieved for the mentioned problems

paraconsistent semantics for pavelka style fuzzy sentential logic the root of this work is on the one hand in belnap s four valued paraconsistent logic and on the other hand on pavelka s papers further developed by turunen we do not introduce a new non classical logic but based on a related study of perny and tsoukias we introduce paraconsistent semantics of pavelka style fuzzy sentential logic restricted to lukasiewicz t norm our approach and the approach of perny and tsoukias partly overlap the main difference lies in the interpretation of the logical connectives implication and negation the essential mathematical tool proved in this paper is a one one correspondence between evidence couples and evidence matrices that holds in all injective mv algebras evidence couples associate to each atomic formula p two values a and b that can be interpreted as the degrees of pros and cons for p respectively four values t f k u interpreted as the degrees of the truth falsehood contradiction and unknownness of p respectively can then be calculated by means of a and b and finally the degrees of the truth falsehood contradiction and unknownness of any well formed formula a are available the obtained logic is pavelka style fuzzy sentential logic in such an approach truth and falsehood are not each others complements moreover we solve some open problems presented by perny and tsoukias

combinatorics for smaller kernels the differential of a graph let g v e be a graph of order n and let b d be the set of vertices in v d that have a neighbor in the vertex set d the differential of d is defined as d b d d and the differential of a graph g written g is equal to max d d v if g is connected and n 3 g n 5 is known this immediately leads to a linear vertex kernel result in the terminology of parameterized complexity for the problem of deciding whether g k taking k as the parameter we then establish a new combinatorial result which establishes that g n 4 if g is a connected graph of order n 6 and if g contains no induced path of five vertices whose midpoint is a cut vertex and whose endpoints have degree one this technical combinatorial theorem can be used to derive an even smaller linear vertex kernel for general graphs also we show that the related maximization problem allows for a polynomial time factor 14 approximation algorithm

on parameterized exponential time complexity in this paper we study the notion of parameterized exponential time complexity we show that a parameterized problem can be solved in parameterized 2 o f k p n time if and only if it is solvable in time o 2 d f k q n for any constant d 0 where p and q are polynomials we then illustrate how this equivalence can be used to show that special instances of parameterized np hard problems are as difficult as the general instances for example we show that the planar dominating set problem on degree 3 graphs can be solved in 2 o k p n parameterized time if and only if the general planar dominating set problem can apart from their complexity theoretic implications our results have some interesting algorithmic implications as well

fixed parameter algorithms for cochromatic number and disjoint rectangle stabbing via iterative localization given a permutation p of 1 n and a positive integer k can p be partitioned into at most k subsequences each of which is either increasing or decreasing we give an algorithm with running time 2 o k 2 l o g k n o 1 that solves this problem thereby showing that it is fixed parameter tractable this np complete problem is equivalent to deciding whether the cochromatic number of a given permutation graph on n vertices is at most k our algorithm solves in fact a more general problem within the mentioned running time it decides whether the cochromatic number of a given perfect graph on n vertices is at most k to obtain our result we use a combination of two well known techniques within parameterized algorithms iterative compression and greedy localization consequently we name this combination iterative localization we further demonstrate the power of this combination by giving an algorithm with running time 2 o k 2 l o g k nlogn that decides whether a given set of n non overlapping axis parallel rectangles can be stabbed by at most k of a given set of horizontal and vertical lines

jamming coverage in competitive random sequential adsorption of a binary mixture we propose a generalized car parking problem where cars of two different sizes are sequentially parked on a line with a given probability q the free parameter q interpolates between the classical car parking problem of only one car size and the competitive random sequential adsorption crsa of a binary mixture we give an exact solution to the crsa rate equations and find that the final coverage the jamming limit of the line is always larger for a binary mixture than for the unisized case the analytical results are in good agreement with our direct numerical simulations of the problem

kernels for below upper bound parameterizations of the hitting set and directed dominating set problems in the hitting set problem we are given a collection f of subsets of a ground set v and an integer p and asked whether v has a p element subset that intersects each set in f we consider two parameterizations of hitting set below tight upper bounds p m k and p n k in both cases k is the parameter we prove that the first parameterization is fixed parameter tractable but has no polynomial kernel unless conp np poly the second parameterization is w 1 complete but the introduction of an additional parameter the degeneracy of the hypergraph h v f makes the problem not only fixed parameter tractable but also one with a linear kernel here the degeneracy of h v f is the minimum integer d such that for each x v the hypergraph with vertex set v x and edge set containing all edges of f without vertices in x has a vertex of degree at most d in nonblocker directed nonblocker we are given an undirected graph a directed graph g on n vertices and an integer k and asked whether g has a set x of n k vertices such that for each vertex y x there is an edge arc from a vertex in x to y nonblocker can be viewed as a special case of directed nonblocker replace an undirected graph by a symmetric digraph dehne et al proc sofsem 2006 proved that nonblocker has a linear order kernel we obtain a linear order kernel for directed nonblocker

kinetics of random sequential parking on a line we study the kinetics of irreversible random sequential parking of intervals of different sizes on an infinite line for the simplest fixed length parking distribution the model reduces to the known car parking problem and we present an alternate solution to this problem we also consider the general homogeneous case when the parking distribution varies asx 1 atx 1 with the lengthx of the filling interval we develop a scaling theory describing such mixture deposition processes and show that the scaled hole size distribution with xtz a scaling variable decays with the scaled mass as exp const 1 as we determine scaling exponentsz and and find that at large times the coverage t has a power law form 1 t t v with nonuniversal exponent 2 1 depending on the homogeneity index

deciding first order properties of nowhere dense graphs nowhere dense graph classes introduced by neset il and ossona de mendez 2010 2011 form a large variety of classes of sparse graphs including the class of planar graphs actually all classes with excluded minors and also bounded degree graphs and graph classes of bounded expansion we show that deciding properties of graphs definable in first order logic is fixed parameter tractable on nowhere dense graph classes parameterized by the length of the input formula at least for graph classes closed under taking subgraphs this result is optimal it was known before that for all classes c of graphs closed under taking subgraphs if deciding first order properties of graphs in c is fixed parameter tractable then c must be nowhere dense under a reasonable complexity theoretic assumption as a by product we give an algorithmic construction of sparse neighborhood covers for nowhere dense graphs this extends and improves previous constructions of neighborhood covers for graph classes with excluded minors at the same time our construction is considerably simpler than those our proofs are based on a new game theoretic characterization of nowhere dense graphs that allows for a recursive version of locality based algorithms on these classes on the logical side we prove a rank preserving version of gaifman s locality theorem

testing first order properties for subclasses of sparse graphs we present a linear time algorithm for deciding first order fo properties in classes of graphs with bounded expansion a notion recently introduced by neset il and ossona de mendez this generalizes several results from the literature because many natural classes of graphs have bounded expansion graphs of bounded tree width all proper minor closed classes of graphs graphs of bounded degree graphs with no subgraph isomorphic to a subdivision of a fixed graph and graphs that can be drawn in a fixed surface in such a way that each edge crosses at most a constant number of other edges we deduce that there is an almost linear time algorithm for deciding fo properties in classes of graphs with locally bounded expansion more generally we design a dynamic data structure for graphs belonging to a fixed class of graphs of bounded expansion after a linear time initialization the data structure allows us to test an fo property in constant time and the data structure can be updated in constant time after addition deletion of an edge provided the list of possible edges to be added is known in advance and their simultaneous addition results in a graph in the class all our results also hold for relational structures and are based on the seminal result of neset il and ossona de mendez on the existence of low tree depth colorings

feedback vertex sets on restricted bipartite graphs a feedback vertex set fvs in a graph is a subset of vertices whose complement induces a forest finding a minimum fvs is np complete on bipartite graphs but tractable on convex bipartite graphs and on chordal bipartite graphs a bipartite graph is called tree convex if a tree is defined on one part of the vertices such that for every vertex in the other part its neighborhood induces a subtree when the tree is a path a triad or a star the bipartite graph is called convex bipartite triad convex bipartite or star convex bipartite respectively we show that 1 fvs is tractable on triad convex bipartite graphs 2 fvs is np complete on star convex bipartite graphs and on tree convex bipartite graphs where the maximum degree of vertices on the tree is at most three

on the small cycle transversal of planar graphs we consider the problem of finding a k edge transversal set that intersects all simple cycles of length at most s in a planar graph where s 3 is a constant this problem referred to as small cycle transversal is known to be np complete we present a polynomial time algorithm that computes a kernel of size 36s 3k for small cycle transversal in order to achieve this kernel we extend the region decomposition technique of alber et al 2004 1 by considering a unique region decomposition that is defined by shortest paths our kernel size is a significant improvement in terms of s over the kernel size obtained under the meta kernelization framework by bodlaender et al 2009 7

markov chain of distances between parked cars we describe the distribution of distances between parked cars as a solution of certain markov processes and show that its solution is obtained with the help of a distributional fixed point equation under certain conditions the process is solved explicitly the resulting probability density is compared with the actual parking data measured in the city

parametric duality and kernelization lower bounds and upper bounds on kernel size determining whether a parameterized problem is kernelizable and has a small kernel size has recently become one of the most interesting topics of research in the area of parameterized complexity and algorithms theoretically it has been proved that a parameterized problem is kernelizable if and only if it is fixed parameter tractable practically applying a data reduction algorithm to reduce an instance of a parameterized problem to an equivalent smaller instance i e a kernel has led to very efficient algorithms and now goes hand in hand with the design of practical algorithms for solving mathcal np hard problems well known examples of such parameterized problems include the vertex cover problem which is kernelizable to a kernel of size bounded by 2k and the planar dominating set problem which is kernelizable to a kernel of size bounded by 335k in this paper we develop new techniques to derive upper and lower bounds on the kernel size for certain parameterized problems in terms of our lower bound results we show for example that unless mathcal p mathcal np planar vertex cover does not have a problem kernel of size smaller than 4k 3 and planar independent set and planar dominating set do not have kernels of size smaller than 2k in terms of our upper bound results we further reduce the upper bound on the kernel size for the planar dominating set problem to 67 k improving significantly the 335 k previous upper bound given by alber fellows and niedermeier j acm 51 2004 pp 363 384 this latter result is obtained by introducing a new set of reduction and coloring rules which allows the derivation of nice combinatorial properties in the kernelized graph leading to a tighter bound on the size of the kernel the paper also shows how this improved upper bound yields a simple and competitive algorithm for the planar dominating set problem

random sequential addition a distribution function approach random sequential addition rsa of hard objects is an irreversible process defined by three rules objects are introduced on a surface or ad dimensional volume randomly and sequentially two objects cannot overlap and once inserted an object is clamped in its position the configurations generated by an rsa can be characterized in the macroscopic limit by a unique set of distribution functions and a density we show that these nonequilibrium rsa configurations can be described in a manner which in many respects parallels the usual statistical mechanical treatment of equilibrium configurations kirkwood salsburg like hierarchies for the distribution functions zero separation theorems diagrammatic expansions and approximate equations for the pair distribution function approximate descriptions valid for low to intermediate densities can be combined with exact results already derived for higher densities close to the jamming limit of the process similarities and differences between the equilibrium and the rsaconfigurations are emphasized finally the potential application of rsa processes to the study of glassy phases is discussed

highly acyclic groups hypergraph covers and the guarded fragment we construct finite groups whose cayley graphs have large girth even with respect to a discounted distance measure that contracts arbitrarily long sequences of edges from the same color class subgroup and only counts transitions between color classes cosets these groups are shown to be useful in the construction of finite bisimilar hypergraph covers that avoid any small cyclic configurations we present two applications to the finite model theory of the guarded fragment a strengthening of the known finite model property for gf and the characterization of gf as the guarded bisimulation invariant fragment of first order logic in the sense of finite model theory

gap size distribution functions of a random sequential adsorption model of segments on a line we performed extensive simulations accompanied by a detailed study of a two segment size random sequential model on the line we followed the kinetics towards the jamming state but we paid particular attention to the characterization of the jamming state structure in particular we studied the effect of the size ratio on the mean gap size the gap size dispersion gap size skewness and gap size kurtosis at the jamming state we also analyzed the above quantities for the four possible segment to segment gap types we ranged the values of the size ratio from one to twenty in the limit of a size ratio of one one recovers the classical car parking problem we observed that at low size ratios the jamming state is constituted by short streaks of small and large segments while at high values of the size ratio the jamming state structure is formed by long streaks of small segments separated by a single large segment this view of the jamming state structure as a function of the size ratio is supported by the various measured quantities the present work can help provide insight for example on how to minimize the interparticle distance or minimize fluctuations around the mean particle to particle distance

variable domain fuzzy sets part i representation abstract despite the fact that fuzzy sets can generally have different domains standard definitions of fuzzy set operations assume a common reference set for all their operands the usual way to satisfy this precondition is to assign zero membership to elements outside the domain of each operand in part i of this two part paper we point out several issues with this method and argue that keeping track of the original domains is necessary to ensure the intended behavior of numerous fuzzy set operations we discuss several ways of representing fuzzy sets with variable domains preparing the grounds for the apparatus of variable domain fuzzy set theory described in part ii of the paper

random packing of lines in a lattice cube a study is made of the random sequential packing of complete lines in a cube of integer lattice points with side n for n 15 exact packing fractions are computed it is found that if line occupation attempts arrive as a spatial poisson process the packing has two distinct phases initially where large numbers of potential adsorption sites are blocked and subsequently where no further blocking occurs so that filling is exponential in time it is shown that the ratio of the durations of the blocking to the nonblocking phases falls to zero as n in this limit the packing fraction at time t is t 3 4 1 e t the rapid switch between phases in large systems creates a dramatic fall in the packing rate at the start of the process this becomes a discontinuity as n and is a consequence of the high aspect ratio of the packing objects it provides a physical explanation for the diverging coefficients in expansions of t about t 0 for objects with diverging aspect ratio after considering the three dimensional case the analysis is extended to d dimensional cubes for which it is conjectured that d 2d 1 in the limit n

fractal dimension and degree of order in sequential deposition of mixture we present a number models describing the sequential deposition of a mixture of particles whose size distribution is determined by the power law p x sim alpha x alpha 1 x leq l we explicitly obtain the scaling function in the case of random sequential adsorption rsa and show that the pattern created in the long time limit becomes scale invariant this pattern can be described by an unique exponent the fractal dimension in addition we introduce an external tuning parameter beta to describe the correlated sequential deposition of a mixture of particles where the degree of correlation is determined by beta while beta 0 corresponds to random sequential deposition of mixture we show that the fractal dimension of the resulting pattern increases as beta increases and reaches a constant non zero value in the limit beta to infty when the pattern becomes perfectly ordered or non random fractals

on preservation under homomorphisms and unions of conjunctive queries unions of conjunctive queries also known as select project join union queries are the most frequently asked queries in relational database systems these queries are definable by existential positive first order formulas and are preserved under homomorphisms a classical result of mathematical logic asserts that the existential positive formulas are the only first order formulas up to logical equivalence that are preserved under homomorphisms on all structures finite and infinite the question of whether the homomorphism preservation theorem holds for the class of all finite structures resisted solution for a long time it was eventually shown that unlike other classical preservation theorems the homomorphism preservation theorem does hold in the finite in this article we show that the homomorphism preservation theorem holds also for several restricted classes of finite structures of interest in graph theory and database theory specifically we show that this result holds for all classes of finite structures of bounded degree all classes of finite structures of bounded treewidth and more generally all classes of finite structures whose cores exclude at least one minor

reduction algorithms for graphs of small treewidth this paper presents a number of new ideas and results on graph reduction applied to graphs of bounded treewidth s arnborg b courcelle a proskurowski and d seese j assoc comput mach 40 1134 1164 1993 have shown that many decision problems on graphs can be solved in linear time on graphs of bounded treewidth using a finite set of reduction rules these algorithms can be used to solve problems on graphs of bounded treewidth without the need to obtain a tree decomposition of the input graph first we show that the reduction method can be extended to solve the construction variants of many decision problems on graphs of bounded treewidth including all problems definable in monadic second order logic we also show that a variant of these reduction algorithms can be used to solve constructive optimization problems in o n time for example optimization and construction variants of independent set and hamiltonian completion number can be solved in this way on graphs of small treewidth additionally we show that the results of h l bodlaender and t hagerup siam j comput 27 1725 1746 1998 can be applied to our reduction algorithms which results in parallel reduction algorithms that use o n operations and o log n log n time on an erew pram or o log n time on a crcw pram

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

analytic model for the ballistic adsorption of polydisperse mixtures we study the ballistic adsorption of a polydisperse mixture of spheres onto a line within a mean field approximation the problem can be analytically solved by means of a kinetic equation for the gap distribution in the mean field approach the adsorbed substrate is replaced by a set of effective particles having the same size equal to the average diameter of the spheres in the original mixture the analytic solution in the case of binary mixtures agrees quantitatively with direct monte carlo simulations of the model and qualitatively with previous simulations of a related model in d 2

neutrosophic logics prospects and problems neutrosophy has been introduced some years ago by florentin smarandache as a new branch of philosophy dealing with the origin nature and scope of neutralities as well as their interactions with different ideational spectra a variety of new theories have been developed on the basic principles of neutrosophy among them is neutrosophic logics a family of many valued systems that can be regarded as a generalization of fuzzy logics in this paper we present a critical introduction to neutrosophic logics focusing on the problem of defining suitable neutrosophic propositional connectives and discussing the relationship between neutrosophic logics and other well known frameworks for reasoning with uncertainty and vagueness such as intuitionistic and interval valued fuzzy systems and belnap s logic

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

finding large degree anonymous subgraphs is hard a graph is said to be k anonymous for an integer k if for every vertex in the graph there are at least k 1 other vertices with the same degree we examine the computational complexity of making a given undirected graph k anonymous either through at most s vertex deletions or through at most s edge deletions the corresponding problem variants are denoted by anonym v del and anonym e del we present a variety of hardness results most of them hold for both problems the two variants are intractable from the parameterized as well as from the approximation point of view in particular we show that both variants remain np hard on very restricted graph classes like trees even if k 2 we further prove that both variants are w1 hard with respect to the combined parameter solutions size s and anonymity level k with respect to approximability we obtain hardness results showing that neither variant can be approximated in polynomial time within a factor better than n 1 2 unless p np furthermore for the optimization variants where the solution size s is given and the task is to maximize the anonymity level k this inapproximability result even holds if we allow a running time of f s n o 1 for any computable function f on the positive side we classify both problem variants as fixed parameter tractable with respect to the combined parameter solution size s and maximum degree

noetherianity up to conjugation of locally diagonal inverse limits abstract we prove that the inverse limit of the sequence dual to a sequence of lie algebras is noetherian up to the action of the direct limit of the corresponding sequence of classical algebraic groups when the sequence of groups consists of diagonal embeddings we also classify all conjugation stable closed subsets of the space of n n matrices

on the treewidth of dynamic graphs dynamic graph theory is a novel growing area that deals with graphs that change over time and is of great utility in modeling modern wireless mobile and dynamic environments as a graph evolves possibly arbitrarily it is challenging to identify the graph properties that can be preserved over time and understand their respective computability in this paper we are concerned with the treewidth of dynamic graphs we focus on metatheorems which allow the generation of a series of results based on general properties of classes of structures in graph theory two major metatheorems on treewidth provide complexity classifications by employing structural graph measures and finite model theory courcelle s theorem gives a general tractability result for problems expressible in monadic second order logic on graphs of bounded treewidth and frick and grohe demonstrate a similar result for first order logic and graphs of bounded local treewidth we extend these theorems by showing that dynamic graphs of bounded local treewidth where the length of time over which the graph evolves and is observed is finite and bounded can be modeled in such a way that the local treewidth of the underlying graph is maintained we show the application of these results to problems in dynamic graph theory and dynamic extensions to static problems in addition we demonstrate that certain widely used dynamic graph classes have bounded local treewidth

a 13k kernel for planar feedback vertex set via region decomposition we show a kernel of at most 13k vertices for the feedback vertex set problem restricted to planar graphs i e a polynomial time algorithm that transforms an input instance g k to an equivalent instance with at most 13k vertices to this end we introduce a few new reduction rules however our main contribution is an application of the region decomposition technique in the analysis of the kernel size we show that our analysis is tight up to a constant additive term

on the random filling of rd by non overlapping d dimensional cubes abstract we compute the time dependent coverage in the random sequential adsorption of aligned d dimensional cubes in r d using time series expansions the seventh order series in 2 3 and 4 dimensions is resummed in order to predict the coverage at jamming the result is in agreement with monte carlo simulations a simple argument based on a property of the pertubative expansion valid at arbitrary orders allows us to analytically derive some generalizations of the palasti approximation

faster approximation schemes and parameterized algorithms on odd h minor free graphs we improve the running time of the general algorithmic technique known as baker s approach 1994 1 on h minor free graphs from o n f h to o f h n o 1 the numerous applications include e g a 2 approximation for coloring and ptases for various problems such as dominating set and max cut where we obtain similar improvements on classes of odd minor free graphs which have gained significant attention in recent time we obtain a similar acceleration for a variant of the structural decomposition theorem proved by demaine et al 2010 20 we use these algorithms to derive faster 2 approximations furthermore we present the first ptases and subexponential fpt algorithms for independent set and vertex cover on these graph classes using a novel dynamic programming technique we also introduce a technique to derive nearly subexponential parameterized algorithms on h minor free graphs our technique applies in particular to problems such as steiner tree directed subgraph with a property directed longest path and connected independent dominating set on some or all proper minor closed graph classes we obtain as a corollary that all problems with a minor monotone subexponential kernel and amenable to our technique can be solved in subexponential fpt time onh minor free graphs this results in a general methodology for subexponential parameterized algorithms outside the framework of bidimensionality

polynomial time data reduction for dominating set dealing with the np complete dominating set problem on graphs we demonstrate the power of data reduction by preprocessing from a theoretical as well as a practical side in particular we prove that dominating set restricted to planar graphs has a so called problem kernel of linear size achieved by two simple and easy to implement reduction rules moreover having implemented our reduction rules first experiments indicate the impressive practical potential of these rules thus this work seems to open up a new and prospective way how to cope with one of the most important problems in graph theory and combinatorial optimization

fixed parameter tractability and completeness ii on completeness for w 1 abstract for many fixed parameter problems that are trivially solvable in polynomial time such as k dominating set essentially no better algorithm is presently known than the one which tries all possible solutions other problems such as feedback vertex set exhibit fixed parameter tractability for each fixed k the problem is solvable in time bounded by a polynomial of degree c where c is a constant independent of k in a previous paper the w hierarchy of parameterized problems was defined and complete problems were identified for the classes w t for t 2 our main result shows that independent set is complete for w 1

on the random sequential adsorption of d dimensional cubes the jamming coverage d for the random sequential adsorption of aligned d dimensional cubes in rd is studied through a one gap distribution function heuristic arguments generally used to describe the large time kinetics are found to imply that this distribution is rather independent of the space dimension this is shown to give a quantitative explanation of the so called palasti approximation d 1d

excluded grid minors and efficient polynomial time approximation schemes two of the most widely used approaches to obtain polynomial time approximation schemes ptass on planar graphs are the lipton tarjan separator based approach and baker s approach in 2005 demaine and hajiaghayi strengthened both approaches using bidimensionality and obtained efficient polynomial time approximation schemes eptass for several problems including c onnected d ominating s et and f eedback v ertex s et in this work we unify the two strengthened approaches to combine the best of both worlds we develop a framework allowing the design of eptas on classes of graphs with the subquadratic grid minor sqgm property roughly speaking a class of graphs has the sqgm property if for every graph g from the class the fact that g contains no t t grid as a minor guarantees that the treewidth of g is subquadratic in t for example the class of planar graphs and more generally classes of graphs excluding some fixed graph as a minor have the sqgm property at the heart of our framework is a decomposition lemma stating that for most bidimensional problems on a graph class g with the sqgm property there is a polynomial time algorithm that given a graph g e g as input and an e 0 outputs a vertex set x of size e opt such that the treewidth of g x is f e here opt is the objective function value of the problem in question and f is a function depending only on e this allows us to obtain eptass on apex minor free graphs for all problems covered by the previous framework as well as for a wide range of packing problems partial covering problems and problems that are neither closed under taking minors nor contractions to the best of our knowledge for many of these problems including c ycle p acking f p acking f d eletion m ax l eaf s panning t ree or p artial r d ominating s et no eptass even on planar graphs were previously known we also prove novel excluded grid theorems in unit disk and map graphs without large cliques using these theorems we show that these classes of graphs have the sqgm property based on the developed framework we design eptass and subexponential time parameterized algorithms for various classes of problems on unit disk and map graphs

multicommodity max flow min cut theorems and their use in designing approximation algorithms in this paper we establish max flow min cut theorems for several important classes of multicommodity flow problems in particular we show that for any n node multicommodity flow problem with uniform demands the max flow for the problem is within an o log n factor of the upper bound implied by the min cut the result which is existentially optimal establishes an important analogue of the famous 1 commodity max flow min cut theorem for problems with multiple commodities the result also has substantial applications to the field of approximation algorithms for example we use the flow result to design the first polynomial time polylog n times optimal approximation algorithms for well known np hard optimization problems such as graph partitioning min cut linear arrangement crossing number vlsi layout and minimum feedback arc set applications of the flow results to path routing problems network reconfiguration communication in distributed networks scientific computing and rapidly mixing markov chains are also described in the paper categories and subject descriptors f 2 2 analysis of algorithms and problem complexity

competitive random sequential adsorption of point and fixed sized particles analytical results we study the kinetics of competitive random sequential adsorption rsa of particles of binary mixture of points and fixed sized particles within the mean field approach the present work is a generalization of the random car parking problem in the sense that it considers the case when either a car of fixed size is parked with probability q or the parking space is partitioned into two smaller spaces with probability 1 q at each time event this allows an interesting interplay between the classical rsa problem at one extreme q 1 and the kinetics of fragmentation processes at the other extreme q 0 we present exact analytical results for coverage for a whole range of q values and physical explanations are given for different aspects of the problem in addition a comprehensive account of the scaling theory emphasizing dimensional analysis is presented and the exact expression for the scaling function and exponents are obtained

recursive approach to random sequential adsorption we present a generalization of renyi s a renyi trans math stat prob 4 205 1963 classical solution to the one dimensional random sequential adsorption rsa problem to the case where particle sizes are drawn from an arbitrary distribution a process known as competitive rsa we formulate the process using recursive relations and without explicitly solving the equations we extract limiting behavior which leads to exact analytic expressions for the final coverage our analysis is confirmed by computer simulations

nth nearest neighbor distribution functions of an interacting fluid from the pair correlation function a hierarchical approach the paper presents a general formalism for the nth nearest neighbor distribution nnd of identical interacting particles in a fluid confined in a nu dimensional space the nth nnd functions w n r for n 1 2 3 em leader in a fluid are obtained hierarchically in terms of the pair correlation function and w n 1 r alone the radial distribution function rdf profiles obtained from the molecular dynamics md simulation of lennard jones lj fluid is used to illustrate the results it is demonstrated that the collective structural information contained in the maxima and minima of the rdf profiles being resolved in terms of individual nnd functions may provide more insights about the microscopic neighborhood structure around a reference particle in a fluid representative comparison between the results obtained from the formalism and the md simulation data shows good agreement apart from the quantities such as nth nnd functions and nth nearest neighbor distances the average neighbor population number is defined these quantities are evaluated for the lj model system and interesting density dependence of the microscopic neighborhood shell structures are discussed in terms of them the relevance of the nnd functions in various phenomena is also pointed out

improved linear problem kernel for planar connected dominating set in this paper we study the planar connected dominating set problem which given a planar graph g v e and a non negative integer k asks for a subset email protected v with d k such that d forms a dominating set of g and induces a connected graph answering an open question posed at the 2nd workshop on kernelization worker 2010 we provide a kernelization algorithm for this problem leading to a problem kernel with at most 130k vertices improving the previously best upper bound on the kernel size to this end we incorporate a vertex coloring technique with data reduction rules and introduce a type distinction of regions into the region decomposition framework which allows a refined analysis of the region size

a 9k kernel for nonseparating independent set in planar graphs we study kernelization a kind of efficient preprocessing for np hard problems on planar graphs we focus on the planar maximum nonseparating independent set problem where given a planar graph and an integer k one has to find an independent set of size k whose removal leaves the graph connected our main result is a kernel of size at most 9k vertices for this problem a direct consequence of this result is that planar connected vertex cover has no kernel with at most 9 email protected k vertices for any e 0 assuming p np as a by product we show extremal graph theory results which might be of independent interest we prove that graphs that contain no separator consisting of only degree two vertices contain a a spanning tree with at least n 4 leaves and b a nonseparating independent set of size at least n 9 also equivalently a connected vertex cover of size at most 89n the result a is a generalization of a theorem of kleitman and west 12 who showed the same bound for graphs of minimum degree three finally we show that every n vertex outerplanar graph contains an independent set i and a collection of vertex disjoint cycles c such that 9 i 4n 3 c

universal amplitude ratios of the renormalization group two dimensional tricritical ising model the scaling form of the free energy near a critical point allows for the definition of various thermodynamical amplitudes and the determination of their dependence on the microscopic nonuniversal scales universal quantities can be obtained by considering special combinations of the amplitudes together with the critical exponents they characterize the universality classes and may be useful quantities for their experimental identification we compute the universal amplitude ratios for the tricritical ising model in two dimensions by using several theoretical methods from perturbed conformal field theory and scattering integrable quantum field theory the theoretical approaches are further supported and integrated by results coming from a numerical determination of the energy eigenvalues and eigenvectors of off critical systems in an infinite cylinder

a fixed parameter algorithm for the directed feedback vertex set problem the parameterized feedback vertex set problem on directed graphs i e the dfvs problem is defined as follows given a directed graph g and a parameter k either construct a feedback vertex set of at most k vertices in g or report that no such a set exists it has been a well known open problem in parameterized computation and complexity whether the dfvs problem is fixed parameter tractable that is whether the problem can be solved in time f k no 1 for some function f in this article we develop new algorithmic techniques that result in an algorithm with running time 4k ke no 1 for the dfvs problem therefore we resolve this open problem

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

hardness of subgraph and supergraph problems in c tournaments problems like the directed feedback vertex set problem have much better algorithms in tournaments when compared to general graphs this motivates us to study a natural generalization of tournaments named c tournaments and see if the structural properties of these graphs are helpful in obtaining similar algorithms c tournaments are simple digraphs which have directed paths of length at most c 1 between all pairs of vertices we study the complexity of feedback vertex set and r dominating set in c tournaments we also present hardness results on some graph editing problems involving c tournaments

a more effective linear kernelization for cluster editing in the np hard cluster editing problem we have as input an undirected graph g and an integer k 0 the question is whether we can transform g by inserting and deleting at most k edges into a cluster graph that is a union of disjoint cliques we first confirm a conjecture by michael fellows iwpec 2006 that there is a polynomial time kernelization for cluster editing that leads to a problem kernel with at most 6k vertices more precisely we present a cubic time algorithm that given a graph g and an integer k 0 finds a graph g and an integer k k such that g can be transformed into a cluster graph by at most k edge modifications iff g can be transformed into a cluster graph by at most k edge modifications and the problem kernel g has at most 6k vertices so far only a problem kernel of 24k vertices was known second we show that this bound for the number of vertices of g can be further improved to 4k vertices finally we consider the variant of cluster editing where the number of cliques that the cluster graph can contain is stipulated to be a constant d 0 we present a simple kernelization for this variant leaving a problem kernel of at most d 2 k d vertices

random sequential adsorption series expansion and monte carlo simulation abstract random sequential adsorption is an irreversible surface deposition of extended objects in systems with continuous degrees of freedom coverage follows a power law t j ct where the exponent depends on the geometric shape symmetry of the objects lattice models give typically exponential saturation to jamming coverage we discuss how such function t can be computed by series expansions and analyzed with pade approximations we consider the applications of efficient monte carlo computer simulation method event driven method to random sequential adsorptions with high precision and at very long time scale

fixed parameter tractability definability and model checking in this article we study parameterized complexity theory from the perspective of logic or more specifically descriptive complexity theory we propose to consider parameterized model checking problems for various fragments of first order logic as generic parameterized problems and show how this approach can be useful in studying both fixed parameter tractability and intractability for example we establish the equivalence between the model checking for existential first order logic the homomorphism problem for relational structures and the substructure isomorphism problem our main tractability result shows that model checking for first order formulas is fixed parameter tractable when restricted to a class of input structures with an excluded minor on the intractability side for every t ge 0 we prove an equivalence between model checking for first order formulas with t quantifier alternations and the parameterized halting problem for alternating turing machines with t alternations we discuss the close connection between this alternation hierarchy and downey and fellows w hierarchy on a more abstract level we consider two forms of definability called fagin definability and slicewise definability that are appropriate for describing parameterized problems we give a characterization of the class fpt of all fixed parameter tractable problems in terms of slicewise definability in finite variable least fixed point logic which is reminiscent of the immerman vardi theorem characterizing the class ptime in terms of definability in least fixed point logic