TY - GEN

T1 - Online computation with advice

AU - Emek, Yuval

AU - Fraigniaud, Pierre

AU - Korman, Amos

AU - Rosén, Adi

PY - 2009

Y1 - 2009

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 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 .

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 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 .

UR - http://www.scopus.com/inward/record.url?scp=70449116200&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-02927-1_36

DO - 10.1007/978-3-642-02927-1_36

M3 - Conference contribution

AN - SCOPUS:70449116200

SN - 3642029264

SN - 9783642029264

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 427

EP - 438

BT - Automata, Languages and Programming - 36th International Colloquium, ICALP 2009, Proceedings

T2 - 36th International Colloquium on Automata, Languages and Programming, ICALP 2009

Y2 - 5 July 2009 through 12 July 2009

ER -