Abstract
Given an undirected graph with two different nonnegative costs associated with every edge e (say, w e for the weight and l e for the length of edge e) and a budget L, consider the problem of finding a spanning tree of total edge length at most L and minimum total weight under this restriction. This constrained minimum spanning tree problem is weakly NP-hard. We present a polynomial-time approximation scheme for this problem. This algorithm always produces a spanning tree of total length at most (1 + ε)L and of total weight at most that of any spanning tree of total length at most L, for any fixed ε >0. The algorithm uses Lagrangean relaxation, and exploits adjacency relations for matroids.
Research supported in part by NSF contract 9302476-CCR, ARPA Contract N00014-95-1-1246, and a Sloan fellowship.
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© 1996 Springer-Verlag Berlin Heidelberg
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Ravi, R., Goemans, M.X. (1996). The constrained minimum spanning tree problem. In: Karlsson, R., Lingas, A. (eds) Algorithm Theory — SWAT'96. SWAT 1996. Lecture Notes in Computer Science, vol 1097. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61422-2_121
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DOI: https://doi.org/10.1007/3-540-61422-2_121
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