2020
DOI: 10.1145/3379698
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Covering Small Independent Sets and Separators with Applications to Parameterized Algorithms

Abstract: We present two new combinatorial tools for the design of parameterized algorithms. The first is a simple linear time randomized algorithm that given as input a d -degenerate graph G and an integer k , outputs an independent set Y , such that for every independent set X in G of size at most k , the probability that X is a … Show more

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Cited by 9 publications
(9 citation statements)
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References 67 publications
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“…These algorithms are based on the computation of an independence covering family, a notion which was recently introduced by Lokshtanov et al [25]. We note that even for nowhere dense graphs, such an independence covering family can be computed efficiently [25]. Since our algorithms are based on computation of independence covering families, hence, our results hold even when the conflict graph is a nowhere dense graph.…”
Section: Introductionmentioning
confidence: 79%
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“…These algorithms are based on the computation of an independence covering family, a notion which was recently introduced by Lokshtanov et al [25]. We note that even for nowhere dense graphs, such an independence covering family can be computed efficiently [25]. Since our algorithms are based on computation of independence covering families, hence, our results hold even when the conflict graph is a nowhere dense graph.…”
Section: Introductionmentioning
confidence: 79%
“…In this section, we show that CF-MM and CF-SP both are in FPT, when the conflict graph H is a d-degenerate graphs. These algorithms are based on the notion of independence covering family, which was introduced in [25], defined below.…”
Section: Fpt Algorithm For D-degenerate Conflict Graphsmentioning
confidence: 99%
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“…We will now combine the arguments given so far in this subsection, in order to prove the following lemma. Having small treewidth is particularly useful due to the following proposition, which is a consequence of, e.g., Courcelle's theorem [8] (or, more efficiently, it can be proved using dynamic programming directly as in [30,15]). Proposition 5.29 ([8]).…”
Section: Discussionmentioning
confidence: 99%