Results 11  20
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48
Towards fixedparameter tractable algorithms for argumentation
 In Proc. KR’10
, 2010
"... 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 o ..."
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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 treewidth. 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 treewidth for defining larger tractable fragments.
Exact algorithms and applications for Treelike Weighted Set Cover
 JOURNAL OF DISCRETE ALGORITHMS
, 2006
"... We introduce an NPcomplete special case of the Weighted Set Cover problem and show its fixedparameter tractability with respect to the maximum subset size, a parameter that appears to be small in relevant applications. More precisely, in this practically relevant variant we require that the given ..."
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We introduce an NPcomplete special case of the Weighted Set Cover problem and show its fixedparameter tractability with respect to the maximum subset size, a parameter that appears to be small in relevant applications. More precisely, in this practically relevant variant we require that the given collection C of subsets of a some base set S should be “treelike.” That is, the subsets in C can be organized in a tree T such that every subset onetoone corresponds to a tree node and, for each element s of S, the nodes corresponding to the subsets containing s induce a subtree of T. This is equivalent to the problem of finding a minimum edge cover in an edgeweighted acyclic hypergraph. Our main result is an algorithm running in O(3 k ·mn) time where k denotes the maximum subset size, n: = S, and m: = C. The algorithm also implies a fixedparameter tractability result for the NPcomplete Multicut in Trees problem, complementing previous approximation results. Our results find applications in computational biology in phylogenomics and for saving memory in tree decomposition based graph algorithms.
AnswerSet Programming with Bounded Treewidth
, 2009
"... In this paper, we present a novel approach to the evaluation of propositional answerset programs. In particular, for programs with bounded treewidth, our algorithm is capable of (i) computing the number of answer sets in linear time and (ii) enumerating all answer sets with linear delay. Our algori ..."
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Cited by 8 (6 self)
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In this paper, we present a novel approach to the evaluation of propositional answerset programs. In particular, for programs with bounded treewidth, our algorithm is capable of (i) computing the number of answer sets in linear time and (ii) enumerating all answer sets with linear delay. Our algorithm relies on dynamic programming. Therefore, our approach significantly differs from standard ASP systems which implement techniques stemming from SAT or CSP, and thus usually do not exploit fixed parameter properties of the programs. We provide first experimental results which underline that, for programs with low treewidth, even a prototypical implementation is competitive compared to stateoftheart systems.
Algorithmic analysis of Parity games
, 2006
"... Parity games are discrete infinite games of two players with complete information. There are two main motivations to study parity games. Firstly the problem of deciding a winner in a parity game is polynomially equivalent to the modal µcalculus model checking, and therefore is very important in the ..."
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Cited by 5 (1 self)
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Parity games are discrete infinite games of two players with complete information. There are two main motivations to study parity games. Firstly the problem of deciding a winner in a parity game is polynomially equivalent to the modal µcalculus model checking, and therefore is very important in the field of computer aided verification. Secondly it is the intriguing status of parity games from the point of view of complexity theory. Solving parity games is one of the few natural problems in the class NP∩coNP (even in UP∩coUP), and there is no known polynomial time algorithm, despite the substantial amount of effort to find one. In this thesis we add to the body of work on parity games. We start by presenting parity games and explaining the concepts behind them, giving a survey of known algorithms, and show their relationship to other problems. In the second part of the thesis we want to answer the following question: Are there classes of graphs on which we can solve parity games in polyno
Exact and approximation algorithms for densest ksubgraph
, 2012
"... The densest ksubgraph problem is a generalization of the maximum clique problem, in which we are given a graph G and a positive integer k, and we search among the subsets of k vertices of G one inducing a maximum number of edges. In this paper, we present algorithms for finding exact solutions of d ..."
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The densest ksubgraph problem is a generalization of the maximum clique problem, in which we are given a graph G and a positive integer k, and we search among the subsets of k vertices of G one inducing a maximum number of edges. In this paper, we present algorithms for finding exact solutions of densest ksubgraph improving the standard exponential time complexity of O ∗ (2 n) and using polynomial space. Two FPT algorithms are also proposed; the first considers as parameter the treewidth of the input graph and uses exponential space, while the second is parameterized by the size of the minimum vertex cover and uses polynomial space. Finally, we propose several approximation algorithms running in moderately exponential or parameterized time.
Improved approximation for 3dimensional matching via bounded pathwidth local search
 In 54th IEEE Annual Symposium on Foundations of Computer Science (FOCS
, 2013
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The Space Complexity of kTree Isomorphism
 In In Proceedings of ISAAC
, 2007
"... Abstract. We show that isomorphism testing of ktrees is in the class StUSPACE(log n) (strongly unambiguous logspace). This bound follows from a deterministic logspace algorithm that accesses a strongly unambiguous logspace oracle for canonizing ktrees. Further we give a logspace canonization algor ..."
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Abstract. We show that isomorphism testing of ktrees is in the class StUSPACE(log n) (strongly unambiguous logspace). This bound follows from a deterministic logspace algorithm that accesses a strongly unambiguous logspace oracle for canonizing ktrees. Further we give a logspace canonization algorithm for kpaths. 1
Fast evaluation of interlace polynomials on graphs of bounded treewidth
, 2009
"... We consider the multivariate interlace polynomial introduced by Courcelle (2008), which generalizes several interlace polynomials defined by Arratia, Bollobás, and Sorkin (2004) and by Aigner and van der Holst (2004). We present an algorithm to evaluate the multivariate interlace polynomial of a gra ..."
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Cited by 4 (1 self)
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We consider the multivariate interlace polynomial introduced by Courcelle (2008), which generalizes several interlace polynomials defined by Arratia, Bollobás, and Sorkin (2004) and by Aigner and van der Holst (2004). We present an algorithm to evaluate the multivariate interlace polynomial of a graph with n vertices given a tree decomposition of the graph of width k. The best previously known result (Courcelle 2008) employs a general logical framework and leads to an algorithm with running time f(k) · n, where f(k) is doubly exponential in k. Analyzing the GF(2)rank of adjacency matrices in the context of tree decompositions, we give a faster and more direct algorithm. Our algorithm uses 2 3k2 +O(k) · n arithmetic operations and can be efficiently implemented in parallel. 1
Counting and enumeration problems with bounded treewidth
 In Logic for Programming, Artificial Intelligence and Reasoning. 15th International Conference, LPAR16
"... Abstract. By Courcelle’s Theorem we know that any property of finite structures definable in monadic secondorder logic (MSO) becomes tractable over structures with bounded treewidth. This result was extended to counting problems by Arnborg et al. and to enumeration problems by Flum et al. Despite ..."
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Abstract. By Courcelle’s Theorem we know that any property of finite structures definable in monadic secondorder logic (MSO) becomes tractable over structures with bounded treewidth. This result was extended to counting problems by Arnborg et al. and to enumeration problems by Flum et al. Despite the undisputed importance of these results for proving fixedparameter tractability, they do not directly yield implementable algorithms. Recently, Gottlob et al. presented a new approach using monadic datalog to close the gap between theoretical tractability and practical computability for MSOdefinable decision problems. In the current work we show how counting and enumeration problems can be tackled by an appropriate extension of the datalog approach. 1
Representative Sets of Product Families
"... A subfamily F ′ of a set family F is said to qrepresent F if for every A ∈ F and B of size q such that A ∩ B = ∅ there exists a set A ′ ∈ F ′ such that A ′ ∩ B = ∅. In a recent paper [SODA 2014] three of the authors gave an algorithm that given as input a family F of sets of size p together with ..."
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A subfamily F ′ of a set family F is said to qrepresent F if for every A ∈ F and B of size q such that A ∩ B = ∅ there exists a set A ′ ∈ F ′ such that A ′ ∩ B = ∅. In a recent paper [SODA 2014] three of the authors gave an algorithm that given as input a family F of sets of size p together with an integer q, efficiently computes a qrepresentative family F ′ of F of size approximately () p+q p, and demonstrated several applications of this algorithm. In this paper, we consider the efficient computation of qrepresentative sets for product families F. A family F is a product family if there exist families A and B such that F = {A ∪ B: A ∈ A, B ∈ B, A ∩ B = ∅}. Our main technical contribution is an algorithm which given A, B and q computes a qrepresentative family F ′ of F. The running time of our algorithm is sublinear in F  for many choices of A, B and q which occur naturally in several dynamic programming algorithms. We also give an algorithm for the computation of qrepresentative sets for product families F in the more general setting where qrepresentation also involves independence in a matroid in addition to disjointness. This algorithm considerably outperforms the naive approach where one first computes F from A and B, and then computes the qrepresentative family F ′ from F. We give two applications of our new algorithms for computing qrepresentative sets for product families. The first is a 3.8408knO(1) deterministic algorithm for the Multilinear Monomial Detection (kMlD) problem. The second is a significant improvement of deterministic dynamic programming algorithms for “connectivity problems ” on graphs of bounded treewidth.