Faster Algorithms for All-pairs Approximate Shortest Paths in Undirected Graphs

Let G = (V, E) be a weighted undirected graph having non-negative edge weights. An estimate ˆδ(u, v) of the actual distance δ(u, v) between u, v ∈ V is said to be of stretch t iff δ(u, v) ≤ ˆδ(u, v) ≤ t · δ(u, v). Computing all-pairs small stretch distances efficiently (both in terms of time and space) is a well-studied problem in graph algorithms. We present a simple, novel and generic scheme for all-pairs approximate shortest paths. Using this scheme and some new ideas and tools, we design faster algorithms for all-pairs t-stretch distances for a whole range of stretch t, and also answer an open question posed by Thorup and Zwick in their seminal paper [Approximate Distance Oracles, Journal of ACM, 52(1), 2005, pp 1-24]. Key words. shortest path, distance, approximate distance, oracle, randomization. AMS subject classifications. 05C12, 05C85, 68W05, 68W20, 68W25, 68W40

• Type: Journal
• Year: 2010
• Where: SIAMCOMP
• Authors: Surender Baswana, Telikepalli Kavitha
• Keywords: Approximate Distance, Non-negative Edge Weights, Shortest Path, SIAMCOMP 2010