An Effective Branching Strategy for Some Parameterized Edge Modification Problems with Multiple Forbidden Induced Subgraphs
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 for dealing 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 proper interval, 3-leaf power, threshold and co-trivially perfect graphs.
KeywordsSearch Tree Polynomial Kernel Graph Property Graph Class Perfect Graph
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- 3.Brandstäda, A., Le, V.B., Spinrad, J.P.: Graph Classes: a Survey. SIAM Monographs on Discrete Mathematics and Applications (1999)Google Scholar
- 13.Sharan, R.: Graph modification problems and their applications to genomic research. PhD Thesis, Tel-Aviv University (2002)Google Scholar
- 15.Wegner, G.: Eigenschaften der Nerven homologisch-einfacher Familien im R n. PhD thesis, Universität Göttingen (1967)Google Scholar