STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
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
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Short length Menger's theorem and reliable optical routing
Theoretical Computer Science
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We deal with a generalization of the Minimum path colouring problem, k-Edge disjoint path systems colouring: given a graph G and a set of pairs of vertices of G, the task is to connect each pair by a system of k-edge disjoint paths (a k-system) and to colour the k-systems by minimal number of colours in such way that any two edge-intersecting k-systems have different colours. Multiple connecting paths between the same pair of vertices are motivated by a need for fault tolerant connections. We propose an O(k2 F) approximation algorithm for this problem where F is the flow number of the graph. As a byproduct of our analysis we also show that any two k-connected vertices in G are connected by k edge disjoint paths of average length O(k F) which improves previously known bounds for many classes of graphs.