Abstract
In this paper the linear relaxation of the weightedr-covering problem (r-LCP) is considered. The dual problem (c-LMP) is the linear relaxation of the well-knownc-matching problem and hence can be solved in polynomial time. However, we describe a simple, but nonpolynomial algorithm in which ther-LCP is decomposed into a sequence of 1-LCP’s and its optimal solution is obtained by adding the optimal solutions of these 1-LCP’s. An 1-LCP can be solved in polynomial time by solving its dual as a max-flow problem on a bipartite graph. An accelerated algorithm based on this decomposition scheme to solve ar-LCP is also developed and its average case behaviour is studied.
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Agarwal, S., Mittal, A.K. & Sharma, P. A decomposition algorithm for linear relaxation of the weightedr-covering problem. Mathematical Programming 31, 67–77 (1985). https://doi.org/10.1007/BF02591862
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DOI: https://doi.org/10.1007/BF02591862