Journal of Algorithms
On-line algorithms for weighted bipartite matching and stable marriages
Theoretical Computer Science
A Graph-Theoretic Game and its Application to the $k$-Server Problem
SIAM Journal on Computing
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
On-line Network Optimization Problems
Developments from a June 1996 seminar on Online algorithms: the state of the art
Probabilistic approximation of metric spaces and its algorithmic applications
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
Randomized online algorithms for minimum metric bipartite matching
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Randomized algorithm for the k-server problem on decomposable spaces
Journal of Discrete Algorithms
The online transportation problem: on the exponential boost of one extra server
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
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We study the on-line minimum weighted bipartite matching problem in arbitrary metric spaces. Here, n not necessary disjoint points of a metric space M are given, and are to be matched on-line with n points of M revealed one by one. The cost of a matching is the sum of the distances of the matched points, and the goal is to find or approximate its minimum. The competitive ratio of the deterministic problem is known to be 驴(n), see (Kalyanasundaram, B., Pruhs, K. in J. Algorithms 14(3):478---488, 1993) and (Khuller, S., et al. in Theor. Comput. Sci. 127(2):255---267, 1994). It was conjectured in (Kalyanasundaram, B., Pruhs, K. in Lecture Notes in Computer Science, vol. 1442, pp. 268---280, 1998) that a randomized algorithm may perform better against an oblivious adversary, namely with an expected competitive ratio 驴(log驴n). We prove a slightly weaker result by showing a o(log驴3 n) upper bound on the expected competitive ratio. As an application the same upper bound holds for the notoriously hard fire station problem, where M is the real line, see (Fuchs, B., et al. in Electonic Notes in Discrete Mathematics, vol. 13, 2003) and (Koutsoupias, E., Nanavati, A. in Lecture Notes in Computer Science, vol. 2909, pp. 179---191, 2004).