TY - GEN

T1 - Light spanners

AU - Elkin, Michael

AU - Neiman, Ofer

AU - Solomon, Shay

PY - 2014

Y1 - 2014

N2 - A t-spanner of a weighted undirected graph G = (V,E), is a subgraph H such that dH(u,v) ≤ t·dG(u,v) for all u,v ∈ V. The sparseness of the spanner can be measured by its size (the number of edges) and weight (the sum of all edge weights), both being important measures of the spanner's quality - in this work we focus on the latter. Specifically, it is shown that for any parameters k ≥ 1 and ε > 0, any weighted graph G on n vertices admits a (2k - 1)·(1 + ε)-stretch spanner of weight at most w(MST(G))·Oε (kn1/k /logk), where w(MST(G)) is the weight of a minimum spanning tree of G. Our result is obtained via a novel analysis of the classic greedy algorithm, and improves previous work by a factor of O(logk).

AB - A t-spanner of a weighted undirected graph G = (V,E), is a subgraph H such that dH(u,v) ≤ t·dG(u,v) for all u,v ∈ V. The sparseness of the spanner can be measured by its size (the number of edges) and weight (the sum of all edge weights), both being important measures of the spanner's quality - in this work we focus on the latter. Specifically, it is shown that for any parameters k ≥ 1 and ε > 0, any weighted graph G on n vertices admits a (2k - 1)·(1 + ε)-stretch spanner of weight at most w(MST(G))·Oε (kn1/k /logk), where w(MST(G)) is the weight of a minimum spanning tree of G. Our result is obtained via a novel analysis of the classic greedy algorithm, and improves previous work by a factor of O(logk).

UR - http://www.scopus.com/inward/record.url?scp=84904163895&partnerID=8YFLogxK

U2 - 10.1007/978-3-662-43948-7_37

DO - 10.1007/978-3-662-43948-7_37

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AN - SCOPUS:84904163895

SN - 9783662439470

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 442

EP - 452

BT - Automata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings

PB - Springer Verlag

T2 - 41st International Colloquium on Automata, Languages, and Programming, ICALP 2014

Y2 - 8 July 2014 through 11 July 2014

ER -