TY - GEN

T1 - Finding sparser directed spanners

AU - Berman, Piotr

AU - Raskhodnikova, Sofya

AU - Ruan, Ge

PY - 2010/12/1

Y1 - 2010/12/1

N2 - A spanner of a graph is a sparse subgraph that approximately preserves distances in the original graph. More precisely, a subgraph H = (V,E H) is a k-spanner of a graph G = (V,E) if for every pair of vertices u, v ∈ V, the shortest path distance distH(u,v) from u to v in H is at most k · distc(u, v). We focus on spanners of directed graphs and a related notion of transitive-closure spanners. The latter captures the idea that a spanner should have a small diameter but preserve the connectivity of the original graph. We study the computational problem of finding the sparsest k-spanner (resp., k-TC-spanner) of a given directed graph, which we refer to as DIRECTED k-SPANNER (resp., k-TC-SPANNER). We improve all known approximation algorithms for DIRECTED k-SPANNER and k-TC-SPANNER for k ≥ 3. (For k = 2, the current ratios are tight, assuming P≠NP.) Along the way, we prove several structural results about the size of the sparsest spanners of directed graphs.

AB - A spanner of a graph is a sparse subgraph that approximately preserves distances in the original graph. More precisely, a subgraph H = (V,E H) is a k-spanner of a graph G = (V,E) if for every pair of vertices u, v ∈ V, the shortest path distance distH(u,v) from u to v in H is at most k · distc(u, v). We focus on spanners of directed graphs and a related notion of transitive-closure spanners. The latter captures the idea that a spanner should have a small diameter but preserve the connectivity of the original graph. We study the computational problem of finding the sparsest k-spanner (resp., k-TC-spanner) of a given directed graph, which we refer to as DIRECTED k-SPANNER (resp., k-TC-SPANNER). We improve all known approximation algorithms for DIRECTED k-SPANNER and k-TC-SPANNER for k ≥ 3. (For k = 2, the current ratios are tight, assuming P≠NP.) Along the way, we prove several structural results about the size of the sparsest spanners of directed graphs.

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U2 - 10.4230/LIPIcs.FSTTCS.2010.424

DO - 10.4230/LIPIcs.FSTTCS.2010.424

M3 - Conference contribution

AN - SCOPUS:84871542551

SN - 9783939897231

T3 - Leibniz International Proceedings in Informatics, LIPIcs

SP - 424

EP - 435

BT - 30th International Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2010

T2 - 30th Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2010

Y2 - 15 December 2010 through 18 December 2010

ER -