Approximation algorithms for 2-source minimum routing cost k-tree problems
ICCSA'07 Proceedings of the 2007 international conference on Computational science and its applications - Volume Part III
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In this article, we investigate two spanning tree problems of graphs with k given sources. Let G = (V,E,w) be an undirected graph with nonnegative edge lengths and S ⊂ V a set of k specified sources. The first problem is the k-source maximum vertex shortest paths spanning tree (k-MVST) problem, in which we want to find a spanning tree T such that the maximum total distance from any vertex to all sources is minimized, that is, we want to minimize maxv∈V{∑s∈SdT(s,v)}, in which dT(s,v) is the length of the path between s and v on T. The other problem is the k-source maximum source shortest paths spanning tree (k-MSST)problem, in which the objective function is the maximum total distance from any source to all vertices, that is, max s∈S{∑v∈VdT(s,v)}. In this article, we present a polynomial time approximation scheme (PTAS) for the 2-MVST problem. For the 2-MSST problem, we first give (2 +ε)-approximation algorithm for any ε 0, and then present a PTAS for the case that the input graphs are restricted to metric graphs. Finally, we show that there are simple 3-approximation algorithms for both problems with arbitrary k. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 47(3), 147–156 2006