Approximation Algorithms for Quickest Spanning Tree Problems

Let G = (V, E) be an undirected multi-graph with a special vertex root ∈ V , and where each edge e ∈ E is endowed with a length l(e) ≥ 0 and a capacity c(e) > 0. For a path P that connects u and v, the transmission time of P is defined as t(P) = e∈P l(e) + maxe∈P 1 c(e) . For a spanning tree T, let PT u,v be the unique u − v path in T. The quickest radius spanning tree problem is to find a spanning tree T of G such that maxv∈V t(PT root,v) is minimized. In this paper we present a 2-approximation algorithm for this problem, and show that unless P = NP, there is no approximation algorithm with performance guarantee of 2 − for any > 0. The quickest diameter spanning tree problem is to find a spanning tree T of G such that maxu,v∈V t(PT u,v) is minimized. We present a 3 2 -approximation to this problem, and prove that unless P = NP there is no approximation algorithm with performance guarantee of 3 2 − for any > 0.

• Type: Conference
• Year: 2004
• Where: ESA
• Authors: Refael Hassin, Asaf Levin
• Keywords: ESA 2004, Spanning Tree, Spanning Tree T, Tree Problem