An improved parameterized algorithm for the p-cluster vertex deletion problem

Bang Ye Wu () and Li-Hsuan Chen ()
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Bang Ye Wu: National Chung Cheng University
Li-Hsuan Chen: National Chung Cheng University

Journal of Combinatorial Optimization, 2017, vol. 33, issue 2, No 2, 373-388

Abstract: Abstract In the p-Cluster Vertex Deletion problem, we are given a graph $$G=(V,E)$$ G = ( V , E ) and two parameters k and p, and the goal is to determine if there exists a subset X of at most k vertices such that the removal of X results in a graph consisting of exactly p disjoint maximal cliques. Let $$r=p/k$$ r = p / k . In this paper, we design a branching algorithm with time complexity $$O(\alpha ^k+|V||E|)$$ O ( α k + | V | | E | ) , where $$\alpha $$ α depends on r and has a rough upper bound $$\min \{1.618^{1+r},2\}$$ min { 1 . 618 1 + r , 2 } . With a more precise analysis, we show that $$\alpha =1.28\cdot 3.57^{r}$$ α = 1.28 · 3 . 57 r for $$r\le 0.219$$ r ≤ 0.219 ; $$\alpha =(1-r)^{r-1}r^{-r}$$ α = ( 1 - r ) r - 1 r - r for $$0.219

Keywords: Parameterized algorithm; Exact algorithm; Cluster graph; Graph modification (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10878-015-9969-4

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