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Inapproximability and approximability of maximal tree routing and coloring

Author

Listed:
  • Xujin Chen

    (Chinese Academy of Sciences)

  • Xiaodong Hu

    (Chinese Academy of Sciences)

  • Tianping Shuai

    (Chinese Academy of Sciences)

Abstract

Let G be a undirected connected graph. Given g groups each being a subset of V(G) and a number of colors, we consider how to find a subgroup of subsets such that there exists a tree interconnecting all vertices in each subset and all trees can be colored properly with given colors (no two trees sharing a common edge receive the same color); the objective is to maximize the number of subsets in the subgroup. This problem arises from the application of multicast communication in all optical networks. In this paper, we first obtain an explicit lower bound on the approximability of this problem and prove Ω(g 1−ε)-inapproximability even when G is a mesh. We then propose a simple greedy algorithm that achieves performance ratio O√|E(G)|, which matches the theoretical bounds.

Suggested Citation

  • Xujin Chen & Xiaodong Hu & Tianping Shuai, 2006. "Inapproximability and approximability of maximal tree routing and coloring," Journal of Combinatorial Optimization, Springer, vol. 11(2), pages 219-229, March.
    • Handle: RePEc:spr:jcomop:v:11:y:2006:i:2:d:10.1007_s10878-006-7135-8
    DOI: 10.1007/s10878-006-7135-8
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