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A $$\frac{5}{2}$$52-approximation algorithm for coloring rooted subtrees of a degree 3 tree

Author

Listed:
  • Anuj Rawat

    (Intel Corp.)

  • Mark Shayman

    (University of Maryland)

Abstract

A rooted tree $$\mathbf {R}$$R is a rooted subtree of a tree T if the tree obtained by replacing the directed edges of $$\mathbf {R}$$R 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 $${\mathcal {R}}$$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 at most 3 (Erlebach and Jansen, in: Proceedings of the 30th Hawaii international conference on system sciences, p 221, 1997). We present a $$\frac{5}{2}$$52-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.

Suggested Citation

  • Anuj Rawat & Mark Shayman, 2020. "A $$\frac{5}{2}$$52-approximation algorithm for coloring rooted subtrees of a degree 3 tree," Journal of Combinatorial Optimization, Springer, vol. 40(1), pages 69-97, July.
    • Handle: RePEc:spr:jcomop:v:40:y:2020:i:1:d:10.1007_s10878-020-00564-6
    DOI: 10.1007/s10878-020-00564-6
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