Amortized efficiency of list update and paging rules
Communications of the ACM
Approximation of Pareto optima in multiple-objective, shortest-path problems
Operations Research
Competitive algorithms for server problems
Journal of Algorithms
An optimal on-line algorithm for K-servers on trees
SIAM Journal on Computing
Many birds with one stone: multi-objective approximation algorithms
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Journal of the ACM (JACM)
Online computation and competitive analysis
Online computation and competitive analysis
Improving spanning trees by upgrading nodes
Theoretical Computer Science
Service-Constrained Network Design Problems
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
The Constrained Minimum Spanning Tree Problem (Extended Abstract)
SWAT '96 Proceedings of the 5th Scandinavian Workshop on Algorithm Theory
Bicriteria Network Design Problems
ICALP '95 Proceedings of the 22nd International Colloquium on Automata, Languages and Programming
On the bicriteria k-server problem
ACM Transactions on Algorithms (TALG)
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In this paper we consider the bicriteria formulation of the well-known online k-server problem where the cost of moving k servers between given locations is evaluated simultaneously with respect to two different metrics. Every strategy for serving a sequence of requests is thus characterized by a pair of costs, and an online algorithm is said to be (c1, c2)-competitive in the strong sense if it is c1-competitive with respect to the first metric and c2-competitive with respect to the second one. We first prove a lower bound on c1 and c2 that holds for any online bicriteria algorithm for the problem. We then propose an algorithm achieving asymptotically optimal tradeoffs between the two competitive ratios. Finally, we show how to further decrease the competitive ratios when the two metrics are induced by the distances in a complete graph and in a path, respectively, obtaining optimal results for particular cases.