# A 5/2-Approximation Algorithm for Coloring Rooted Subtrees of a Degree 3 Tree

A rooted tree R⃗ is a rooted subtree of a tree T if the tree obtained by replacing the directed edges of R⃗ by undirected edges is a subtree of T. We study the problem of assigning minimum number of colors to a given set of rooted subtrees R of a given tree T such that if any two rooted subtrees share a directed edge, then they are assigned different colors. The problem is NP hard even in the case when the degree of T is restricted to 3. We present a 5/2-approximation algorithm for this problem. The motivation for studying this problem stems from the problem of assigning wavelengths to multicast traffic requests in all-optical WDM tree networks.

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