TY - GEN

T1 - Improved approximation for the directed spanner problem

AU - Berman, Piotr

AU - Bhattacharyya, Arnab

AU - Makarychev, Konstantin

AU - Raskhodnikova, Sofya

AU - Yaroslavtsev, Grigory

PY - 2011

Y1 - 2011

N2 - We give an -approximation algorithm for the problem of finding the sparsest spanner of a given directed graph G on n vertices. A spanner of a graph is a sparse subgraph that approximately preserves distances in the original graph. More precisely, given a graph G∈=∈(V,E) with nonnegative edge lengths d: E → ℝ≥0 and a stretch k ≥ 1, a subgraph H = (V,E H ) is a k-spanner of G if for every edge (u,v)ε E, the graph H contains a path from u to v of length at most k •d(u,v). The previous best approximation ratio was , due to Dinitz and Krauthgamer (STOC '11). We also present an improved algorithm for the important special case of directed 3-spanners with unit edge lengths. The approximation ratio of our algorithm is which almost matches the lower bound shown by Dinitz and Krauthgamer for the integrality gap of a natural linear programming relaxation. The best previously known algorithms for this problem, due to Berman, Raskhodnikova and Ruan (FSTTCS '10) and Dinitz and Krauthgamer, had approximation ratio .

AB - We give an -approximation algorithm for the problem of finding the sparsest spanner of a given directed graph G on n vertices. A spanner of a graph is a sparse subgraph that approximately preserves distances in the original graph. More precisely, given a graph G∈=∈(V,E) with nonnegative edge lengths d: E → ℝ≥0 and a stretch k ≥ 1, a subgraph H = (V,E H ) is a k-spanner of G if for every edge (u,v)ε E, the graph H contains a path from u to v of length at most k •d(u,v). The previous best approximation ratio was , due to Dinitz and Krauthgamer (STOC '11). We also present an improved algorithm for the important special case of directed 3-spanners with unit edge lengths. The approximation ratio of our algorithm is which almost matches the lower bound shown by Dinitz and Krauthgamer for the integrality gap of a natural linear programming relaxation. The best previously known algorithms for this problem, due to Berman, Raskhodnikova and Ruan (FSTTCS '10) and Dinitz and Krauthgamer, had approximation ratio .

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U2 - 10.1007/978-3-642-22006-7_1

DO - 10.1007/978-3-642-22006-7_1

M3 - Conference contribution

AN - SCOPUS:79960008212

SN - 9783642220050

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

SP - 1

EP - 12

BT - Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings

T2 - 38th International Colloquium on Automata, Languages and Programming, ICALP 2011

Y2 - 4 July 2011 through 8 July 2011

ER -