The competitiveness of on-line assignments

Yossi Azar, Joseph Naor, Raphael Rom

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


Consider the on-line problem where a number of servers are ready to provide service to a set of customers. Each customer's job can be handled by any of a subset of the servers. Customers arrive one-by-one and the problem is to assign each customer to an appropriate server in a manner that will balance the load on the servers. This problem can be modeled in a natural way by a bipartite graph where the vertices of one side (customers) appear one at a time and the vertices of the other side (servers) are known in advance. We derive tight bounds on the competitive ratio in both deterministic and randomized cases. Let n denote the number of servers. In the deterministic case we provide an on-line algorithm that achieves a competitive ratio of κ = [log2 n] (up to an additive 1) and prove that this is the best competitive ratio that can be achieved by any deterministic on-line algorithm. In a similar way we prove that the competitive ratio for the randomized case is κ' = ln(n) (up to an additive 1). We conclude that for this problem, randomized algorithms differ from deterministic ones by precisely a constant factor.

Original languageEnglish
Title of host publicationProceedings of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992
PublisherAssociation for Computing Machinery
Number of pages8
ISBN (Electronic)089791466X
StatePublished - 1 Sep 1992
Externally publishedYes
Event3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992 - Orlando, United States
Duration: 27 Jan 199229 Jan 1992

Publication series

NameProceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms
VolumePart F129721


Conference3rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 1992
Country/TerritoryUnited States


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