Deterministic constructions of approximate distance oracles and spanners

Liam Roditty*, Mikkel Thorup, Uri Zwick

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

Abstract

Thorup and Zwick showed that for any integer k ≥ 1, it is possible to preprocess any positively weighted undirected graph G = (V, E), with |E| = m and |V| = n, in Õ(kmn1/k) expected time and construct a data structure (a (2k - 1)-approximate distance oracle) of size O(kn1+1/k) capable of returning in O(k) time an approximation δ̂(u, v) of the distance δ(u, v) from u to v in G that satisfies δ(u, v) ≤ δ̂(u, v) ≤ (2k - 1)·δ(u, v), for any two vertices u, v ∈ V. They also presented a much slower Õ(kmn) time deterministic algorithm for constructing approximate distance oracle with the slightly larger size of O(kn1+1/k log n). We present here a deterministic Õ(kmn1/k) time algorithm for constructing oracles of size O(kn1+1/k). Our deterministic algorithm is slower than the randomized one by only a logarithmic factor. Using our derandomization technique we also obtain the first deterministic linear time algorithm for constructing optimal spanners of weighted graphs. We do that by derandomizing the O(km) expected time algorithm of Baswana and Sen (ICALP'03) for constructing (2k - 1)-spanners of size O(kn1+1/k) of weighted undirected graphs without incurring any asymptotic loss in the running time or in the size of the spanners produced.

Original languageEnglish
Pages (from-to)261-272
Number of pages12
JournalLecture Notes in Computer Science
Volume3580
DOIs
StatePublished - 2005
Event32nd International Colloquium on Automata, Languages and Programming, ICALP 2005 - Lisbon, Portugal
Duration: 11 Jul 200515 Jul 2005

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