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53
PartitionBased Logical Reasoning for FirstOrder and Propositional Theories
 Artificial Intelligence
, 2000
"... In this paper we provide algorithms for reasoning with partitions of related logical axioms in propositional and firstorder logic (FOL). We also provide a greedy algorithm that automatically decomposes a set of logical axioms into partitions. Our motivation is twofold. First, we are concerned with ..."
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Cited by 61 (9 self)
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In this paper we provide algorithms for reasoning with partitions of related logical axioms in propositional and firstorder logic (FOL). We also provide a greedy algorithm that automatically decomposes a set of logical axioms into partitions. Our motivation is twofold. First, we are concerned with how to reason e#ectively with multiple knowledge bases that have overlap in content. Second, we are concerned with improving the e#ciency of reasoning over a set of logical axioms by partitioning the set with respect to some detectable structure, and reasoning over individual partitions. Many of the reasoning procedures we present are based on the idea of passing messages between partitions. We present algorithms for reasoning using forward messagepassing and using backward messagepassing with partitions of logical axioms. Associated with each partition is a reasoning procedure. We characterize a class of reasoning procedures that ensures completeness and soundness of our messagepassing ...
Mdpop: Faithful distributed implementation of efficient social choice problems
 In AAMAS’06  Autonomous Agents and Multiagent Systems
, 2006
"... In the efficient social choice problem, the goal is to assign values, subject to side constraints, to a set of variables to maximize the total utility across a population of agents, where each agent has private information about its utility function. In this paper we model the social choice problem ..."
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Cited by 48 (17 self)
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In the efficient social choice problem, the goal is to assign values, subject to side constraints, to a set of variables to maximize the total utility across a population of agents, where each agent has private information about its utility function. In this paper we model the social choice problem as a distributed constraint optimization problem (DCOP), in which each agent can communicate with other agents that share an interest in one or more variables. Whereas existing DCOP algorithms can be easily manipulated by an agent, either by misreporting private information or deviating from the algorithm, we introduce MDPOP, the first DCOP algorithm that provides a faithful distributed implementation for efficient social choice. This provides a concrete example of how the methods of mechanism design can be unified with those of distributed optimization. Faithfulness ensures that no agent can benefit by unilaterally deviating from any aspect of the protocol, neither informationrevelation, computation, nor communication, and whatever the private information of other agents. We allow for payments by agents to a central bank, which is the only central authority that we require. To achieve faithfulness, we carefully integrate the VickreyClarkeGroves (VCG) mechanism with the DPOP algorithm, such that each agent is only asked to perform computation, report
Object Location Using Path Separators
, 2006
"... We study a novel separator property called kpath separable. Roughly speaking, a kpath separable graph can be recursively separated into smaller components by sequentially removing k shortest paths. Our main result is that every minor free weighted graph is kpath separable. We then show that kpat ..."
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Cited by 43 (11 self)
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We study a novel separator property called kpath separable. Roughly speaking, a kpath separable graph can be recursively separated into smaller components by sequentially removing k shortest paths. Our main result is that every minor free weighted graph is kpath separable. We then show that kpath separable graphs can be used to solve several object location problems: (1) a smallworldization with an average polylogarithmic number of hops; (2) an (1 + ε)approximate distance labeling scheme with O(log n) space labels; (3) a stretch(1 + ε) compact routing scheme with tables of polylogarithmic space; (4) an (1+ε)approximate distance oracle with O(n log n) space and O(log n) query time. Our results generalizes to much wider classes of weighted graphs, namely to boundeddimension isometric sparable graphs.
Fast Mucalculus Model Checking when Treewidth is Bounded
, 2003
"... We show that the model checking problem for calculus on graphs of bounded treewidth can be solved in time linear in the size of the system. The result is presented by rst showing a related result: the winner in a parity game on a graph of bounded treewidth can be decided in polynomial time. ..."
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Cited by 24 (2 self)
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We show that the model checking problem for calculus on graphs of bounded treewidth can be solved in time linear in the size of the system. The result is presented by rst showing a related result: the winner in a parity game on a graph of bounded treewidth can be decided in polynomial time. The given algorithm is then modi ed to obtain a new algorithm for calculus model checking. One possible use of this algorithm may be software veri cation, since control ow graphs of programs written in highlevel languages are usually of bounded treewidth.
Approximation algorithms for treewidth
, 2002
"... Abstract. This paper presents algorithms whose input is an undirected graph, and whose output is a tree decomposition of width that approximates the optimal, the treewidth of that graph. The algorithms differ in their computation time and their approximation guarantees. The first algorithm works in ..."
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Cited by 17 (0 self)
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Abstract. This paper presents algorithms whose input is an undirected graph, and whose output is a tree decomposition of width that approximates the optimal, the treewidth of that graph. The algorithms differ in their computation time and their approximation guarantees. The first algorithm works in polynomialtime and finds a factorO(log OP T), where OP T is the treewidth of the graph. This is the first polynomialtime algorithm that approximates the optimal by a factor that does not depend on n, the number of nodes in the input graph. As a result, we get an algorithm for finding pathwidth within a factor of O(log OP T · log n) from the optimal. We also present algorithms that approximate the treewidth of a graph by constant factors of 3.66, 4, and 4.5, respectively and take time that is exponential in the treewidth. These are more efficient than previously known algorithms by an exponential factor, and are of practical interest. Finding triangulations of minimum treewidth for graphs is central to many problems in computer science. Realworld problems in artificial intelligence, VLSI design and databases are efficiently solvable if we have an efficient approximation algorithm for them. Many of those applications rely on weighted graphs. We extend our results to weighted graphs and weighted treewidth, showing similar approximation results for this more general notion. We report on experimental results confirming the effectiveness of our algorithms for large
I/Oefficient algorithms for graphs of bounded treewidth
 In Proceedings of the 12th Annual ACMSIAM Symposium on Discrete Algorithms (SODA’2001
, 2001
"... We present an algorithm that takes O(sort(N)) I/Os 1 to compute a tree decomposition of width at most k, for any graph G of treewidth at most k and size N. Given such a tree decomposition, we use a dynamic programming framework to solve a wide variety of problems on G in O(N/(DB)) I/Os, including th ..."
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Cited by 16 (5 self)
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We present an algorithm that takes O(sort(N)) I/Os 1 to compute a tree decomposition of width at most k, for any graph G of treewidth at most k and size N. Given such a tree decomposition, we use a dynamic programming framework to solve a wide variety of problems on G in O(N/(DB)) I/Os, including the singlesource shortest path problem and a number of problems that are NPhard on general graphs. The tree decomposition can also be used to obtain an optimal separator decomposition of G. We use such a decomposition to perform depthfirst search in G in O(N/(DB)) I/Os. As important tools that are used in the tree decomposition algorithm, we introduce flippable DAGs and present an algorithm that computes a perfect elimination ordering of a ktree in O(sort(N)) I/Os. The second contribution of our paper, which is of independent interest, is a general and simple framework for obtaining I/Oefficient algorithms for a number of graph problems that can be solved using greedy algorithms in internal memory. We apply this framework in order to obtain an improved algorithm for finding a maximal matching and the first deterministic I/Oefficient algorithm for finding a maximal independent set of an arbitrary graph. Both algorithms take O(sort(V +E)) I/Os. The maximal matching algorithm is used in the tree decomposition algorithm.
Improved algorithms and complexity results for power domination
 in graphs, Lecture Notes Comp. Sci. 3623
, 2005
"... Abstract. The Power Dominating Set problem is a variant of the classical domination problem in graphs: Given an undirected graph G = (V, E), find a minimum P ⊆ V such that all vertices in V are “observed” by vertices in P. Herein, a vertex observes itself and all its neighbors, and if an observed ve ..."
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Cited by 15 (2 self)
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Abstract. The Power Dominating Set problem is a variant of the classical domination problem in graphs: Given an undirected graph G = (V, E), find a minimum P ⊆ V such that all vertices in V are “observed” by vertices in P. Herein, a vertex observes itself and all its neighbors, and if an observed vertex has all but one of its neighbors observed, then the remaining neighbor becomes observed as well. We show that Power Dominating Set can be solved by “boundedtreewidth dynamic programs.” Moreover, we simplify and extend several NPcompleteness results, particularly showing that Power Dominating Set remains NPcomplete for planar graphs, for circle graphs, and for split graphs. Specifically, our improved reductions imply that Power Dominating Set parameterized by P  is W[2]hard and cannot be better approximated than Dominating Set. 1
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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Cited by 14 (8 self)
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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.
The parameterized complexity of the induced matching problem in planar graphs
 In Proceedings of the 2007 International Frontiers of Algorithmics Workshop, Lecture Notes in Comput. Sci
, 2007
"... Given a graph G and an integer k ≥ 0, the NPcomplete Induced Matching problem asks whether there exists an edge subset M of size at least k such that M is a matching and no two edges of M are joined by an edge of G. The complexity of this problem on general graphs as well as on many restricted grap ..."
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Cited by 14 (1 self)
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Given a graph G and an integer k ≥ 0, the NPcomplete Induced Matching problem asks whether there exists an edge subset M of size at least k such that M is a matching and no two edges of M are joined by an edge of G. The complexity of this problem on general graphs as well as on many restricted graph classes has been studied intensively. However, other than the fact that the problem is W[1]hard on general graphs little is known about the parameterized complexity of the problem in restricted graph classes. In this work, we provide firsttime fixedparameter tractability results for planar graphs, boundeddegree graphs, graphs with girth at least six, bipartite graphs, line graphs, and graphs of bounded treewidth. In particular, we give a linearsize problem kernel for planar graphs.