### Abstract

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 dist_{H}(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.

Original language | English (US) |
---|---|

Title of host publication | 30th International Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2010 |

Pages | 424-435 |

Number of pages | 12 |

Volume | 8 |

DOIs | |

State | Published - Dec 1 2010 |

Event | 30th Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2010 - Chennai, India Duration: Dec 15 2010 → Dec 18 2010 |

### Other

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

Country | India |

City | Chennai |

Period | 12/15/10 → 12/18/10 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Software

### Cite this

*30th International Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2010*(Vol. 8, pp. 424-435) https://doi.org/10.4230/LIPIcs.FSTTCS.2010.424

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*30th International Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2010.*vol. 8, pp. 424-435, 30th Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2010, Chennai, India, 12/15/10. https://doi.org/10.4230/LIPIcs.FSTTCS.2010.424

**Finding sparser directed spanners.** / Berman, Piotr; Raskhodnikova, Sofya; Ruan, Ge.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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.

UR - http://www.scopus.com/inward/record.url?scp=84871542551&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84871542551&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.FSTTCS.2010.424

DO - 10.4230/LIPIcs.FSTTCS.2010.424

M3 - Conference contribution

AN - SCOPUS:84871542551

SN - 9783939897231

VL - 8

SP - 424

EP - 435

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

ER -