Abstract
In this paper, we study the minimum degree minimum spanning tree problem: Given a graph G = (V,E) and a non-negative cost function c on the edges, the objective is to find a minimum cost spanning tree T under the cost function c such that the maximum degree of any node in T is minimized.
We obtain an algorithm which returns an MST of maximum degree at most Δ*+k where Δ* is the minimum maximum degree of any MST and k is the distinct number of costs in any MST of G. We use a lower bound given by a linear programming relaxation to the problem and strengthen known graph-theoretic results on minimum degree subgraphs [3,5] to prove our result. Previous results for the problem [1,4] used a combinatorial lower bound which is weaker than the LP bound we use.
Tepper School of Business, Carnegie Mellon University. Supported by NSF ITR grant CCR-0122581 (The ALADDIN project) and NSF grant CCF-0430751.
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Ravi, R., Singh, M. (2006). Delegate and Conquer: An LP-Based Approximation Algorithm for Minimum Degree MSTs. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11786986_16
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DOI: https://doi.org/10.1007/11786986_16
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