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 -