Abstract
Consider a weighted transitive graph, where each vertex is assigned a positive weight. Given a positive integerk, the maximumk-covering problem is to findk disjoint cliques covering a set of vertices with maximum total weight. An 0(kn 2)-time algorithm to solve the problem in a transitive graph is proposed, wheren is the number of vertices. Based on the proposed algorithm the weighted version of a number of problems in VLSI layout (e.g.,k-layer topological via minimization), computational geometry (e.g., maximum multidimensionalk-chain), graph theory (e.g., maximumk-independent set in interval graphs), and sequence manipulation (e.g., maximum increasingk-subsequence) can be solved inO(kn 2), wheren is the input size.
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Communicated by C. K. Wong.
This Work was supported in part by the National Science Foundation under Grant MIP-8709074 and MIP-8921540.
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Sarrafzadeh, M., Lou, R.D. Maximumk-covering of weighted transitive graphs with applications. Algorithmica 9, 84–100 (1993). https://doi.org/10.1007/BF01185340
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DOI: https://doi.org/10.1007/BF01185340