TY - CHAP
T1 - Approximation algorithms for quickest spanning tree problems
AU - Hassin, Refael
AU - Levin, Asaf
PY - 2004
Y1 - 2004
N2 - Let G = (V, E) be an undirected multi-graph with a special vertex root ε V, and where each edge e ε 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 timeof P is defined as t(P) = ∑eεpl(e)+max eεp 1/c(e). For a spanning tree T, let Pu,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 maxvεV t(Proot,VT) 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 maxu,vεV t(Pu,vT) 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 - ε for any ε > 0.
AB - Let G = (V, E) be an undirected multi-graph with a special vertex root ε V, and where each edge e ε 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 timeof P is defined as t(P) = ∑eεpl(e)+max eεp 1/c(e). For a spanning tree T, let Pu,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 maxvεV t(Proot,VT) 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 maxu,vεV t(Pu,vT) 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 - ε for any ε > 0.
UR - http://www.scopus.com/inward/record.url?scp=35048866355&partnerID=8YFLogxK
U2 - 10.1007/978-3-540-30140-0_36
DO - 10.1007/978-3-540-30140-0_36
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AN - SCOPUS:35048866355
SN - 3540230254
SN - 9783540230250
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 395
EP - 402
BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
A2 - Albers, Susanne
A2 - Radzik, Tomasz
PB - Springer Verlag
ER -