TY - JOUR

T1 - Beating the logarithmic lower bound

T2 - Randomized preemptive disjoint paths and call control algorithms

AU - Adler, Ran

AU - Azar, Yossi

N1 - Funding Information:
Research supported in part by the ISIS consortium and the Israel Science Foundation.

PY - 2003/3

Y1 - 2003/3

N2 - 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.

AB - 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.

KW - Call control

KW - Competitive

KW - Disjoint paths

KW - On-line

KW - Preemptive

KW - Randomized

KW - Throughput

UR - http://www.scopus.com/inward/record.url?scp=0242514378&partnerID=8YFLogxK

U2 - 10.1023/A:1022933824889

DO - 10.1023/A:1022933824889

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AN - SCOPUS:0242514378

VL - 6

SP - 113

EP - 129

JO - Journal of Scheduling

JF - Journal of Scheduling

SN - 1094-6136

IS - 2

ER -