Abstract
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 \(t(P)=\sum_{e \in P} l(e) + \max_{e \in P} {1 \over c(e)}\). For a spanning tree T, let P \(_{u,v}^{T}\) 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 \(\max _{v \in V} t(P^T_{root,v})\) 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 – ε for any ε >0. The quickest diameter spanning tree problem is to find a spanning tree T of G such that \(\max_{u,v \in V} t(P^T_{u,v})\) is minimized. We present a \({3 \over 2}\)-approximation to this problem, and prove that unless P=NP there is no approximation algorithm with performance guarantee of \({3 \over 2}-\epsilon\) for any ε >0.
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© 2004 Springer-Verlag Berlin Heidelberg
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Hassin, R., Levin, A. (2004). Approximation Algorithms for Quickest Spanning Tree Problems. In: Albers, S., Radzik, T. (eds) Algorithms – ESA 2004. ESA 2004. Lecture Notes in Computer Science, vol 3221. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30140-0_36
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DOI: https://doi.org/10.1007/978-3-540-30140-0_36
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