Efficient routing in all-optical networks
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Approximations for the disjoint paths problem in high-diameter planar networks
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Bounding the power of preemption in randomized scheduling
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Bandwidth allocation with preemption
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
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
Efficient on-line call control algorithms
Journal of Algorithms
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
Improved bounds for all optical routing
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
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
Efficient routing and scheduling algorithms for optical networks
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
On-line randomized call control revisited
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
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
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Maximizing job completions online
Journal of Algorithms
Admission control to minimize rejections and online set cover with repetitions
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Admission control to minimize rejections and online set cover with repetitions
ACM Transactions on Algorithms (TALG)
Online time-constrained scheduling in linear and ring networks
Journal of Discrete Algorithms
Space-constrained interval selection
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Online selection of intervals and t-intervals
Information and Computation
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We consider the maximum disjoint paths problem and its generalization, the call control problem, in the on-line setting. In the maximum disjoint paths problem, we are given a sequence of connection requests for some communication network. Each request consists of a pair of nodes, that wish to communicate over a path in the network. The request has to be immediately connected or rejected, and the goal is to maximize the number of connected pairs, such that no two paths share an edge. In the call control problem, each request has an additional bandwidth specification, and the goal is to maximize the total bandwidth of the connected pairs (throughput), while satisfying the bandwidth constraints (assuming each edge has unit capacity). These classical problems are central in routing and admission control in high speed networks and in optical networks.We present the first known constant-competitive algorithms for both problems on the line. This settles an open problem of Garay et al. and of Leonardi. Moreover, to the best of our knowledge, all previous algorithms for any of these problems, are Ω(log n)-competitive, where n is the number of vertices in the network (and obviously noncompetitive for the continuous line). Our algorithms are randomized and preemptive. Our results should be contrasted with the Ω(log n) lower bounds for deterministic preemptive algorithms of Garay et al. and the Ω(log n) lower bounds for randomized non-preemptive algorithms of Lipton and Tomkins and Awerbuch et al. Interestingly, nonconstant lower bounds were proved by Canetti and Irani for randomized preemptive algorithms for related problems but not for these exact problems.