Fractional and Integral Coloring of Locally-Symmetric Sets of Paths on Binary Trees

Motivated by the problem of allocating optical bandwidth in tree–shaped WDM networks, we study the fractional path coloring problem in trees. We consider the class of locally-symmetric sets of paths on binary trees and prove that any such set of paths has a fractional coloring of cost at most 1.367L, where L denotes the load of the set of paths. Using this result, we obtain a randomized algorithm that colors any locally-symmetric set of paths of load L on a binary tree (with reasonable restrictions on its depth) using at most 1.367L+o(L) colors, with high probability.

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