Approximating the Spanning k-Tree Forest Problem

Authors:
Chung-Shou Liao;Louxin Zhang
Affiliations:
Department of Computer Science and Information Engineering, National Taiwan University,;Department of Mathematics, National University of Singapore,
Venue:
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
Year:
2009

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Abstract

As a generalization of the spanning star forest problem, the spanning k -tree forest problem is to find a maximum-edge-weight spanning forest in which each tree has a central node and other nodes in the tree are at most k -distance away from the central node. In this paper, we show that it can be approximated with ratio $\frac{k}{k+1}$ in polynomial time for both undirected and directed graphs. In the weighted distance model, a 0.5-approximation algorithm is presented.