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An effective branching strategy based on structural relationship among multiple forbidden induced subgraphs

Author

Listed:
  • Yunlong Liu

    (Central South University
    Hunan Normal University)

  • Jianxin Wang

    (Central South University)

  • Chao Xu

    (Central South University)

  • Jiong Guo

    (Universität des Saarlandes)

  • Jianer Chen

    (Central South University
    Texas A&M University)

Abstract

Branching on forbidden induced subgraphs is a genetic strategy to obtain parameterized algorithms for many edge modification problems. For such a problem in which the graph property is defined by multiple forbidden induced subgraphs, branching process is trivially performed on each subgraph. Thus, the size of the resulting search tree is dominated by the size of the largest forbidden subgraph. In this paper, we present a simple strategy for deriving significantly improved branching rules to deal with multiple forbidden subgraphs by edge modifications. The basic idea hereby is that while constructing branching rules for the largest forbidden subgraph, we sufficiently take into account the structural relationship between it and other forbidden subgraphs. By applying this strategy, we obtain improved parameterized algorithms for edge modification problems for several graph properties such as 3-leaf power, proper interval, threshold and co-trivially perfect graphs.

Suggested Citation

  • Yunlong Liu & Jianxin Wang & Chao Xu & Jiong Guo & Jianer Chen, 2015. "An effective branching strategy based on structural relationship among multiple forbidden induced subgraphs," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 257-275, January.
    • Handle: RePEc:spr:jcomop:v:29:y:2015:i:1:d:10.1007_s10878-014-9733-1
    DOI: 10.1007/s10878-014-9733-1
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