TY - JOUR

T1 - Online computation with advice

AU - Emek, Yuval

AU - Fraigniaud, Pierre

AU - Korman, Amos

AU - Rosén, Adi

N1 - Funding Information:
The first author’s work was partially done during a visit to LIAFA, CNRS and University Paris Diderot, supported by Action COST 295 DYNAMO. The second and third authors received additional support from the ANR project ALADDIN, the INRIA project GANG, and COST Action 295 DYNAMO. The fourth author’s research was partially supported by ANR projects AlgoQP, QRAC, and ALADDIN.

PY - 2011/5/27

Y1 - 2011/5/27

N2 - 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 is a function, defined by the online algorithm, of the whole request sequence. 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 b=log|A|⌉, where A 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(log n), 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 kO(1b) for any choice of Θ(1)≤b≤logk.

AB - 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 is a function, defined by the online algorithm, of the whole request sequence. 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 b=log|A|⌉, where A 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(log n), 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 kO(1b) for any choice of Θ(1)≤b≤logk.

KW - Advice

KW - Competitive analysis

KW - Metrical task systems

KW - Online algorithms

KW - k-server problem

UR - http://www.scopus.com/inward/record.url?scp=79954919703&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2010.08.007

DO - 10.1016/j.tcs.2010.08.007

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:79954919703

SN - 0304-3975

VL - 412

SP - 2642

EP - 2656

JO - Theoretical Computer Science

JF - Theoretical Computer Science

IS - 24

ER -