Amortized efficiency of list update and paging rules
Communications of the ACM
Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
Existence and Construction of Edge-Disjoint Pathson Expander Graphs
SIAM Journal on 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
Static and dynamic path selection on expander graphs (preliminary version): a random walk approach
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Online computation and competitive analysis
Online computation and competitive analysis
Approximations for the disjoint paths problem in high-diameter planar networks
Journal of Computer and System Sciences
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Static and dynamic path selection on expander graphs: a random walk approach
Random Structures & Algorithms
Improved bounds for all optical routing
Proceedings of the sixth 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
On-line randomized call control revisited
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms
Journal of the ACM (JACM)
Approximation Algorithms for Disjoint Paths and Related Routing and Packing Problems
Mathematics of Operations Research
Universal Routing Strategies for Interconnection Networks
Universal Routing Strategies for Interconnection Networks
Developments from a June 1996 seminar on Online algorithms: the state of the art
Disjoint paths in densely embedded graphs
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Improved approximations for edge-disjoint paths, unsplittable flow, and related routing problems
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Short paths in expander graphs
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Approximation algorithms for disjoint paths problems
Approximation algorithms for disjoint paths problems
Improved bounds for the unsplittable flow problem
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithms for fault-tolerant routing in circuit switched networks
Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures
Approximation Algorithms for the Unsplittable Flow Problem
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
An Approximation Algorithm for the Disjoint Paths Problem in Even-Degree Planar Graphs
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Improved bounds for the unsplittable flow problem
Journal of Algorithms
Edge Disjoint Paths in Moderately Connected Graphs
SIAM Journal on Computing
Edge disjoint paths in moderately connected graphs
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Approximation algorithms for edge-disjoint paths and unsplittable flow
Efficient Approximation and Online Algorithms
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In this paper we study the problem of finding disjoint paths in graphs. Whereas for specific graphs many (almost) matching upper and lower bounds are known for the competitiveness of on-line path selection algorithms, much less is known about how well on-line algorithms can perform in the general setting. In several papers the expansion has been used to measure the performance of off-line and on-line algorithms in this field. We study a class of simple deterministic on-line algorithms and show that they achieve a competitive ratio that is asymptotically equal to the best possible competitive ratio that can be achieved by any deterministic on-line algorithm. For this we use a parameter caled routing number which allows more precise results than the expansion. Interestingly, our upper bound on the competitive ratio is even better than the best approximation ratio known for off-line algorithms. Furthermore, we show that a refined variant of the routing number allows to construct on-line algorithms with a competitive ratio that is for many graphs significantly below the best possible upper bound for deterministic on-line algorithms if only the routing number or expansion of a graph is known. We also show that our algorithms can be transformed into efficient algorithms for the related unsplittable flow problem.