An edge dominating set D of graph G = (V,E) is a set of edges such that every edge not in D is adjacent to at least one edge in D. We develop polynomial time algorithms for finding a minimum edge dominating set for a ...
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An edge dominating set D of graph G = (V,E) is a set of edges such that every edge not in D is adjacent to at least one edge in D. We develop polynomial time algorithms for finding a minimum edge dominating set for a cotriangulated graph and a bipartite permutation graph.
We present an improved optimal parallel algorithm with time complexity O(log(3) n) for computing a maximal matching in a graph. The improvement is made on the recent result of Kelsen which requires O(log(4) n) time fo...
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We present an improved optimal parallel algorithm with time complexity O(log(3) n) for computing a maximal matching in a graph. The improvement is made on the recent result of Kelsen which requires O(log(4) n) time for computing a maximal matching. Our parallel algorithm is designed on the EREW PRAM model.
An equivalence graph is a disjoint union of cliques. For a graph G let eq(G) be the minimum number of equivalence subgraphs of G needed to cover all edges of G. We call eq(G) the equivalence covering number of G. It w...
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An equivalence graph is a disjoint union of cliques. For a graph G let eq(G) be the minimum number of equivalence subgraphs of G needed to cover all edges of G. We call eq(G) the equivalence covering number of G. It was shown in [8] that computing the equivalence covering number is NP-hard, even when restricted to graphs in which no two triangles have a vertex in common. We show that the equivalence covering number for splitgraphs can be approximated within an additive constant 1. We also show that obtaining the exact value of the equivalence number of a splitgraph is an NP-hard problem. Using a similar method we also show that it is NP-complete to decide whether the equivalence covering number of a graph is 3, even for graphs with maximum degree 6 and with maximum clique number 4.
A general and direct method for computing the Betti numbers of a finite simplicial complex in Bd is given. This method is complete for d less than or equal to 3, where versions of this method run in time O(n alpha(n))...
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A general and direct method for computing the Betti numbers of a finite simplicial complex in Bd is given. This method is complete for d less than or equal to 3, where versions of this method run in time O(n alpha(n)) and O(n), n the number of simplices. An implementation of the algorithm is applied to alpha shapes, which is a novel geometric modeling tool.
The paper considers two decision problems on hypergraphs, hypergraph saturation and recognition of the transversal hypergraph, and discusses their significance for several search problems in applied computer science. ...
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The paper considers two decision problems on hypergraphs, hypergraph saturation and recognition of the transversal hypergraph, and discusses their significance for several search problems in applied computer science. Hypergraph saturation (i.e., given a hypergraph H, decide if every subset of vertices is contained in or contains some edge of H) is shown to be co-NP-complete. A certain subproblem of hypergraph saturation, the saturation of simple hypergraphs (i.e., Sperner families), is shown to be under polynomial transformation equivalent to transversal hypergraph recognition;i.e., given two hypergraphs H-1, H-2, decide if the sets in H-2 are all the minimal transversals of H-1. The complexity of the search problem related to the recognition of the transversal hypergraph, the computation of the transversal hypergraph, is an open problem. This task needs time exponential in the input size;it is unknown whether an output-polynomial algorithm exists. For several important subcases (for instance, if an upper or lower bound is imposed on the edge size or for acyclic hypergraphs) output-polynomial algorithms are presented. Computing or recognizing the minimal transversals of a hypergraph is a frequent problem in practice, which is painted out by identifying important applications in database theory, Boolean switching theory, logic, and artificial intelligence (AI), particularly in model-based diagnosis.
In this paper we introduce and investigate the notion of p-connectedness. As it turns out, this concepts leads naturally to a unique tree representation for arbitrary graphs: the leaves of this tree are the p-connecte...
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In this paper we introduce and investigate the notion of p-connectedness. As it turns out, this concepts leads naturally to a unique tree representation for arbitrary graphs: the leaves of this tree are the p-connected components along with weak vertices, that is, vertices of the graph that belong to no p-connected component. We then show how to refine this decomposition to obtain a new decomposition that extends the well-known modular decomposition.
In this paper, we show that the treewidth and pathwidth of a permutation graph can be computed in polynomial time. In fact we show that, for permutation graphs, the treewidth and pathwidth are equal. These results mak...
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In this paper, we show that the treewidth and pathwidth of a permutation graph can be computed in polynomial time. In fact we show that, for permutation graphs, the treewidth and pathwidth are equal. These results make permutation graphs one of the few nontrivial graph classes for which, at the moment, treewidth is known to be computable in polynomial time. Our algorithm, which decides whether the treewidth (pathwidth) is at most some given integer Ic, can be implemented to run in O(nk) time when the matching diagram is given. We show that this algorithm can easily be adapted to compute the pathwidth of a permutation graph in O(nk) time, where k is the pathwidth.
Die weite Verbreitung der fensterorientierten Benutzerschnittstelle führt zu einem zunehmend intensiven Gebrauch der Fenstertechnik durch komplexe Softwaresysteme etwa in den Bereichen Hypertext oder CAx. Der Ben...
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Among the different processes that entail unification-based grammar parsing, the unification of feature structures is by far the most expensive one in terms of execution time. Unification of the feature structures of ...
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Among the different processes that entail unification-based grammar parsing, the unification of feature structures is by far the most expensive one in terms of execution time. Unification of the feature structures of a given sentence typically takes between 85 and 98 per cent of the total elapsed time during parsing, thus the need to develop faster unification methods. The approach presented in this paper is based on the fact that, in general, between 60 and 85 per cent of unifications attempted in a typical parse result in failure. Our claim is that the efficient treatment of such unification failures reduces unification time significantly. In this paper we present what we call a unification filter or U-filter, that preprocesses the feature structures to be unified. If the U-filter succeeds, unification is then skipped because the attempt to unify the involved structures would result in failure. On the other hand, when the U-filter does not succeed it is not possible to determine at that moment whether or not the structures unify, so unification is performed. The U-filter stops around 87 per cent of unification failures, and speeds up unification time by an average of around 29 per cent over quasi-destructive graph unification, the fastest unification method known so far.
The strong link between matroids and matching is used to extend the ideas that resulted in the design of random NC (RNC) algorithms for matching to obtain RNC algorithms for the matroid union, intersection, and matchi...
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The strong link between matroids and matching is used to extend the ideas that resulted in the design of random NC (RNC) algorithms for matching to obtain RNC algorithms for the matroid union, intersection, and matching problems, and for linearly representable matroids. As a consequence, RNC algorithms for the well-known problems of finding an arborescence and a maximum cardinality set of edge-disjoint spanning trees in a graph are obtained. The key tools used are linear algebra and randomization.
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