Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
Introduction to algorithms
Lower bounds for on-line graph problems with application to on-line circuit and optical routing
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
On-line routing of virtual circuits with applications to load balancing and machine scheduling
Journal of the ACM (JACM)
Online computation and competitive analysis
Online computation and competitive analysis
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Competitive non-preemptive call control
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
On-line randomized call control revisited
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Independent Sets in Hypergraphs with Applications to Routing via Fixed Paths
RANDOM-APPROX '99 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization Problems: Randomization, Approximation, and Combinatorial Algorithms and Techniques
Developments from a June 1996 seminar on Online algorithms: the state of the art
On-line Competive Algorithms for Call Admission in Optical Networks
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
Disjoint paths in densely embedded graphs
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Hardness of the Undirected Edge-Disjoint Paths Problem with Congestion
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Throughput-competitive on-line routing
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
On-line admission control and circuit routing for high performance computing and communication
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
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We consider the online version of the maximum vertex disjoint path problem when the underlying network is a tree. In this problem, a sequence of requests arrives in an online fashion, where every request is a path in the tree. The online algorithm may accept a request only if it does not share a vertex with a previously accepted request. The goal is to maximize the number of accepted requests. It is known that no online algorithm can have a competitive ratio better than 茂戮驴(logn) for this problem, even if the algorithm is randomized and the tree is simply a line. Obviously, it is desirable to beat the logarithmic lower bound. Adler and Azar [SODA 1999] showed that if preemption is allowed (namely, previously accepted requests may be discarded, but once a request is discarded it can no longer be accepted), then there is a randomized online algorithm that achieves constant competitive ratio on the line. In the current work we present a randomized online algorithm with preemption that has constant competitive ratio on any tree. Our results carry over to the related problem of maximizing the number of accepted paths subject to a capacity constraint on vertices (in the disjoint path problem this capacity is 1). Moreover, if the available capacity is at least 4, randomization is not needed and our online algorithm becomes deterministic.