Randomized rounding: a technique for provably good algorithms and algorithmic proofs
Combinatorica - Theory of Computing
Architectures for linear lightwave networks
Architectures for linear lightwave networks
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
Short length versions of Menger's theorem
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
Combinatorial optimization
Finding maximum flows in undirected graphs seems easier than bipartite matching
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Further algorithmic aspects of the local lemma
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Improved bounds for all optical routing
Proceedings of the sixth 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
Approximating Fractional Multicommodity Flow Independent of the Number of Commodities
SIAM Journal on Discrete Mathematics
The complexity of path coloring and call scheduling
Theoretical Computer Science
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
On-Line Routing in All-Optical Networks
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Short length menger's theorem and reliable optical routing
Proceedings of the fifteenth annual ACM symposium on Parallel algorithms and architectures
Efficient access to optical bandwidth
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Disjoint paths in densely embedded graphs
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Faster and Simpler Algorithms for Multicommodity Flow and other Fractional Packing Problems.
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Call Scheduling in Trees, Rings and Meshes
HICSS '97 Proceedings of the 30th Hawaii International Conference on System Sciences: Software Technology and Architecture - Volume 1
Single source multiroute flows and cuts on uniform capacity networks
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Region growing for multi-route cuts
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
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In the minimun path coloring problem, we are given a graph and a set of pairs of vertices of the graph and we are asked to connect the pairs by colored paths in such a way that paths of the same color are edge disjoint. In this paper we deal with a generalization of this problem where we are asked to connect each pail by k edge disjoint paths of the same color. The objective is to minimize the number of colors. The reason for multiple paths between the same pair of vertices is to ensure fault tolerance of the connections. We propose an O(k2F) = O(k2Δα-1 log n) approximation algorithm for this problem where F is the flow number of the graph, Δ is the maximum degree and α is the expansion. This is an improvement even for the special case k = 1 where, to our knowledge, the best previously known bound is weaker by a factor of log n.The underlying problem is that of finding several disjoint paths between a given pair of vertices. Menger's theorem provides a necessary and sufficient condition for the existence of k such paths. However, it does not say anything about the length of the paths although in communication problems the number of links used is an issue. We show that any two k-connected vertices are connected by k edge disjoint paths of average length O(kF) which improves an earlier result of Galil and Yu (Proceedings of the 27th Annual ACM Symposium on Theory of Computing, 1995) for several classes of graphs. In fact, this is only a corollary of a stronger result for multicommodity flow on networks with unit edge capacities: any multicommodity flow with k units for each commodity can be rerouted such that the flow for each commodity is shipped through k-tuples of edge disjoint paths of average length O(kF) without exceeding the edge capacities significantly.