Short length menger's theorem and reliable optical routing
Amitabha Bagchi, Amitabh Chaudhary, Petr Kolman · 2003
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.