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Combinatorial algorithms for the maximum kplex problem
, 2009
"... The maximum clique problem provides a classic framework for detecting cohesive subgraphs. However, this approach can fail to detect much of the cohesive structure in a graph. To address this issue, Seidman and Foster introduced kplexes as a degreebased relaxation of graph completeness. More recen ..."
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The maximum clique problem provides a classic framework for detecting cohesive subgraphs. However, this approach can fail to detect much of the cohesive structure in a graph. To address this issue, Seidman and Foster introduced kplexes as a degreebased relaxation of graph completeness. More recently, Balasundaram et al. formulated the maximum kplex problem as an integer program and designed a branchandcut algorithm. This paper derives a new upper bound on the cardinality of kplexes and adapts combinatorial clique algorithms to find maximum kplexes. 1.
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, 2015
"... This paper introduces four graph orientation problems named Maximize WLight, Minimize WLight, Maximize WHeavy, and Minimize WHeavy, where W can be any fixed nonnegative integer. In each problem, the input is an undirected, unweighted graph G and the objective is to assign a direction to every ..."
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This paper introduces four graph orientation problems named Maximize WLight, Minimize WLight, Maximize WHeavy, and Minimize WHeavy, where W can be any fixed nonnegative integer. In each problem, the input is an undirected, unweighted graph G and the objective is to assign a direction to every edge in G so that the number of vertices with outdegree at most W or at least W in the resulting directed graph is maximized or minimized. A number of results on the computational complexity and polynomialtime approximability of these problems for different values of W and various special classes of graphs are derived. In particular, it is shown that Maximize 0Light and Minimize 1Heavy are identical to Maximum Independent Set and Minimum Vertex Cover, respectively, so by allowing the value of W to vary, we obtain a new generalization of the two latter problems.