Deleting Vertices to Graphs of Bounded Genus
Algorithmica(2019)
摘要
We show that a problem of deleting a minimum number of vertices from a graph to obtain a graph embeddable on a surface of a given Euler genus is solvable in time 2^C_g · k^2 log k n^𝒪(1) , where k is the size of the deletion set, C_g is a constant depending on the Euler genus g of the target surface, and n is the size of the input graph. On the way to this result, we develop an algorithm solving the problem in question in time 2^𝒪((t+g) log (t+g)) n given a tree decomposition of the input graph of width t . The results generalize previous algorithms for the surface being a sphere by Marx and Schlotter (Algorithmica 62(3–4):807–822, 2012 . https://doi.org/10.1007/s00453-010-9484-z ), Kawarabayashi (in: 50th annual IEEE symposium on foundations of computer science, FOCS 2009, IEEE Computer Society, pp 639–648, 2009 . https://doi.org/10.1109/FOCS.2009.45 ) and Jansen et al. (in: Chekuri (ed) 25th annual ACM-SIAM symposium on discrete algorithms, SODA 2014, SIAM, pp 1802–1811, 2014 . https://doi.org/10.1137/1.9781611973402.130 ).
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关键词
Fixed-parameter tractability,Bounded genus graphs,Bounded treewidth,Graph modification,Vertex deletion,Irrelevant vertex
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