Constructing light spanning trees with small routing cost

Authors:
Bang Ye Wu;Kun-Mao Chao;Chuan Yi Tang
Affiliations:
Dept. of Computer Science, National Tsing Hua University, Hsinchu, Taiwan, R.O.C.;Dept. of Computer Science and Information Management, Providence University, Shalu, Taiwan, R.O.C.;Dept. of Computer Science, National Tsing Hua University, Hsinchu, Taiwan, R.O.C.
Venue:
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Year:
1999

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Abstract

Let G = (V, E, w) be an undirected graph with nonnegative edge weight. For any spanning tree T of G, the weight of T is the total weight of its tree edges and the routing cost of T is Σu, v∈V dT(u, v), where dT(u, v) is the distance between u and v on T. In this paper, we present an algorithm providing a trade off among tree weight, routing cost and time complexity. For any real number α 1 and an integer 1 ≤ k ≤ 6α-3, in O(nk+1+n3) time, the algorithm finds a spanning tree whose routing cost is at most (1 + 2/k + 1))α times the one of the minimum routing cost tree, and the tree weight is at most (f(k) + 2/(α-1)) times the one of the minimum spanning tree, where f(k) = 1 if k = 1 and f(k) = 2 if k 1.