TY - GEN
T1 - Light spanners
AU - Elkin, Michael
AU - Neiman, Ofer
AU - Solomon, Shay
PY - 2014/1/1
Y1 - 2014/1/1
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
M3 - Conference contribution
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 -