Date of Original Version

2002

Type

Article

Abstract or Description

In this paper, we present a new bicriteria approximation algorithm for the degreebounded minimum spanning tree problem. In this problem, we are given an undirected graph, a nonnegative cost function on the edges, and a positive integer B∗, and the goal is to find a minimumcost spanning tree T with maximum degree at most B∗. In an n-node graph, our algorithm finds a spanning tree with maximum degree O(B∗ + log n) and cost O( opt B∗ ), where opt B∗ is the minimum cost of any spanning tree whose maximum degree is at most B∗. Our algorithm uses ideas from Lagrangean duality. We show how a set of optimum Lagrangean multipliers yields bounds on both the degree and the cost of the computed solution.

DOI

10.1137/S009753970036917X

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Published In

SIAM Journal of Computing, 31, 6, 1783-1793.