Online computation with advice

Yuval Emek, Pierre Fraigniaud, Amos Korman, Adi Rosén

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

Abstract

We consider a model for online computation in which the online algorithm receives, together with each request, some information regarding the future, referred to as advice. The advice provided to the online algorithm may allow an improvement in its performance, compared to the classical model of complete lack of information regarding the future. We are interested in the impact of such advice on the competitive ratio, and in particular, in the relation between the size b of the advice, measured in terms of bits of information per request, and the (improved) competitive ratio. Since b=0 corresponds to the classical online model, and , where is the algorithm's action space, corresponds to the optimal (offline) one, our model spans a spectrum of settings ranging from classical online algorithms to offline ones. In this paper we propose the above model and illustrate its applicability by considering two of the most extensively studied online problems, namely, metrical task systems (MTS) and the k-server problem. For MTS we establish tight (up to constant factors) upper and lower bounds on the competitive ratio of deterministic and randomized online algorithms with advice for any choice of 1≤b≤Θ(logn) , where n is the number of states in the system: we prove that any randomized online algorithm for MTS has competitive ratio Ω( log(n) / b) and we present a deterministic online algorithm for MTS with competitive ratio O (log(n) / b) . For the k-server problem we construct a deterministic online algorithm for general metric spaces with competitive ratio k O (1 / b) for any choice of Θ(1)≤b≤logk .

Original languageEnglish
Title of host publicationAutomata, Languages and Programming - 36th International Colloquium, ICALP 2009, Proceedings
Pages427-438
Number of pages12
EditionPART 1
DOIs
StatePublished - 2009
Externally publishedYes
Event36th International Colloquium on Automata, Languages and Programming, ICALP 2009 - Rhodes, Greece
Duration: 5 Jul 200912 Jul 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
NumberPART 1
Volume5555 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference36th International Colloquium on Automata, Languages and Programming, ICALP 2009
Country/TerritoryGreece
CityRhodes
Period5/07/0912/07/09

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science

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