Computing almost shortest paths

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

67 Scopus citations


We study the s-sources almost shortest paths (shortly, s-ASP) problem. Given an unweighted graph G = (V, E), and a subset S ⊆ V of s nodes, the goal is to compute almost shortest paths between all the pairs of nodes S × V. We devise an algorithm with running time O(|E|nρ + s · n1+ζ) for this problem that computes the paths Pu,w for all pairs (u, w) ε S × V such that the length of Pu,w is at most (1 + ε)dG(u, w) + β(ζ, ρ, ε) is constant when ζ, ρ and ε are (one can choose arbitrarily small constants ζ, ρ and ε). We also devise a distributed protocol for the s-ASP problem that computes the paths Pu,w as above, and has time and communication complexities of O(s · Diam(G)+n1+ζ/2) (resp., O(s · Diam(G) log3 n + n1+ζ/2 log n)) and O(|E|nρ + s · n1+ζ) (resp., O(|E|nρ + s · n1+ζ + n1+ρ+ζ(ρ-ζ/2)/2)) in the synchronous (resp., asynchronous) setting. Our sequential algorithm, as well as the distributed protocol, is based on a novel algorithm for constructing (1 + ε, β(ζ, ρ, ε))-spanners of size O(n1+δ), developed in this paper. This algorithm has running time of O(|E|nρ), which is significantly faster than the previously known algorithm of [20], whose running time is Õ(n2+ρ). We also develop the first distributed protocol for constructing (1 + ε, β)-spanners. The time and communication complexities of this protocol are near-optimal.

Original languageEnglish GB
Title of host publicationProceedings of the twentieth annual ACM symposium on Principles of distributed computing
Number of pages10
StatePublished - 1 Jan 2001
Externally publishedYes
Event20th Annual ACM Symposium on Principles of Distributed Computing - Newport, Rhode Island, United States
Duration: 26 Aug 200129 Aug 2001


Conference20th Annual ACM Symposium on Principles of Distributed Computing
Country/TerritoryUnited States
CityNewport, Rhode Island


  • Approximation algorithms
  • Distributed computing

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications


Dive into the research topics of 'Computing almost shortest paths'. Together they form a unique fingerprint.

Cite this