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Computational properties of argument systems satisfying graphtheoretic constraints
 Artificial Intelligence
, 2007
"... One difficulty that arises in abstract argument systems is that many natural questions regarding argument acceptability are, in general, computationally intractable having been classified as complete for classes such as NP, coNP, and ¢¡ £. In consequence, a number of researchers have considered me ..."
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Cited by 34 (9 self)
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One difficulty that arises in abstract argument systems is that many natural questions regarding argument acceptability are, in general, computationally intractable having been classified as complete for classes such as NP, coNP, and ¢¡ £. In consequence, a number of researchers have considered methods for specialising the structure of such systems so as to identify classes for which efficient decision processes exist. In this paper the effect of a number of graphtheoretic restrictions is considered: ¤partite systems (¤¦¥¨ § ) in which the set of arguments may be partitioned into ¤ sets each of which is conflictfree; systems in which the numbers of attacks originating from and made upon any argument are bounded; planar systems; and, finally, those of ¤bounded treewidth. For the class of bipartite graphs, it is shown that determining the acceptability status of a specific argument can be accomplished in polynomialtime under both credulous and sceptical semantics. In addition we establish the existence of polynomial time methods for systems having bounded treewidth when deciding the following: whether a given (set of) arguments is credulously accepted; if the system has a nonempty preferred extension; has a stable extension; is coherent;
Pathwidth and ThreeDimensional StraightLine Grid Drawings of Graphs
"... We prove that every nvertex graph G with pathwidth pw(G) has a threedimensional straightline grid drawing with O(pw(G) n) volume. Thus for ..."
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Cited by 26 (15 self)
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We prove that every nvertex graph G with pathwidth pw(G) has a threedimensional straightline grid drawing with O(pw(G) n) volume. Thus for
Fast robber in planar graphs
, 2008
"... In the cops and robber game, two players play alternately by moving their tokens along the edges of a graph. The first one plays with the cops and the second one with one robber. The cops aim at capturing the robber, while the robber tries to infinitely evade the cops. The main problem consists in m ..."
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Cited by 5 (2 self)
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In the cops and robber game, two players play alternately by moving their tokens along the edges of a graph. The first one plays with the cops and the second one with one robber. The cops aim at capturing the robber, while the robber tries to infinitely evade the cops. The main problem consists in minimizing the number of cops used to capture the robber in a graph. This minimum number is called the copnumber of the graph. If the cops and the robber have the same velocity, g cops are sufficient to capture one robber in any graph with genus g (Schröder, 2001). In the particular case of a grid, 2 cops are sufficient. We investigate the game in which the robber is slightly faster than the cops. In this setting, we prove that the copnumber of planar graphs becomes unbounded. More precisely, we prove that Ω ( √ log n) cops are necessary to capture a fast robber in the n × n squaregrid. This proof consists in designing an elegant evasionstrategy for the robber. Then, it is interesting to ask whether a high value of the copnumber of a planar graph H is related to a large grid G somehow contained in H. We prove that it is not the case when the notion of containment is related to the classical transformations of edge removal, vertex removal, and edge contraction. For instance, we prove that there are graphs with copnumber at most 2 and that are subdivisions of arbitrary large grid. On the positive side, we prove that, if H planar contains a large grid as an induced subgraph, then H has large copnumber. Note that, generally, the copnumber of a graph H is not closed by taking induced subgraphs G, even if H is planar and G is an distancehereditary inducedsubgraph.
Complexity and approximation results for the connected vertex cover problem
"... We study a variation of the vertex cover problem where it is required that the graph induced by the vertex cover is connected. We prove that this problem is polynomial in chordal graphs, has a PTAS in planar graphs, is APXhard in bipartite graphs and is 5/3approximable in any class of graphs wher ..."
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Cited by 5 (0 self)
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We study a variation of the vertex cover problem where it is required that the graph induced by the vertex cover is connected. We prove that this problem is polynomial in chordal graphs, has a PTAS in planar graphs, is APXhard in bipartite graphs and is 5/3approximable in any class of graphs where the vertex cover problem is polynomial (in particular in bipartite graphs).
www.cs.uu.nl PreProcessing Rules for Triangulation of Probabilistic Networks £
"... The currently most efficient algorithm for inference with a probabilistic network builds upon a triangulation of a network’s graph. In this paper, we show that preprocessing can help in finding good triangulations for probabilistic networks, that is, triangulations with a minimal maximum clique siz ..."
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The currently most efficient algorithm for inference with a probabilistic network builds upon a triangulation of a network’s graph. In this paper, we show that preprocessing can help in finding good triangulations for probabilistic networks, that is, triangulations with a minimal maximum clique size. We provide a set of rules for stepwise reducing a graph, without losing optimality. This reduction allows us to solve the triangulation problem on a smaller graph. From the smaller graph’s triangulation, a triangulation of the original graph is obtained by reversing the reduction steps. Our experimental results show that the graphs of some wellknown reallife probabilistic networks can be triangulated optimally just by preprocessing; for other networks, huge reductions in their graph’s size are obtained. 1
1 Fachbereich Mathematik
"... We survey operations on (possibly infinite) relational structures that are compatible with logical theories in the sense that, if we apply the operation to given structures then we can compute the theory of the resulting structure from the theories of the arguments (the logics under consideration fo ..."
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We survey operations on (possibly infinite) relational structures that are compatible with logical theories in the sense that, if we apply the operation to given structures then we can compute the theory of the resulting structure from the theories of the arguments (the logics under consideration for the result and the arguments might differ). Besides general compatibility results for these operations we also present several results on restricted classes of structures, and their use for obtaining classes of infinite structures with decidable theories. 1