Hitting forbidden induced subgraphs on bounded treewidth graphs

Sau, Ignasi; Souza, Uéverton S.

doi:10.1016/j.ic.2021.104812

Cited by 6 publications

(3 citation statements)

References 18 publications

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“…We give a general 2 O(K 2 ) poly(n, |V (H)|) time algorithm. This contrasts the situation for H-free Deletion parameterized by the treewidth t of the graph, where a 2 o(t |V (H)|−2 ) poly(n, |V (H)|) time lower bound is known under the Exponential Time Hypothesis (ETH) [46]. We also construct a graph property Π for which we provide a lower bound of 2 o(K log K) poly(n, |V (H)|) for Π-free Deletion [VC] under ETH.…”

Section: π-Free Deletion [Vc]mentioning

confidence: 92%

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Streaming Deletion Problems Parameterized by Vertex Cover

Oostveen

Leeuwen

2021

Fundamentals of Computation Theory

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Streaming is a model where an input graph is provided one edge at a time, instead of being able to inspect it at will. In this work, we take a parameterized approach by assuming a vertex cover of the graph is given, building on work of Bishnu et al. [COCOON 2020]. We show the further potency of combining this parameter with the Adjacency List streaming model to obtain results for vertex deletion problems. This includes kernels, parameterized algorithms, and lower bounds for the problems of Π-free Deletion, H-free Deletion, and the more specific forms of Cluster Vertex Deletion and Odd Cycle Transversal. We focus on the complexity in terms of the number of passes over the input stream, and the memory used. This leads to a pass/memory tradeoff, where a different algorithm might be favourable depending on the context and instance. We also discuss implications for parameterized complexity in the non-streaming setting.

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Section: π-Free Deletion [Vc]mentioning

confidence: 92%

“…It has also been well studied in the parameterized setting (see e.g. [10,25,46]). When parameterized by the vertex cover number, it has been studied from the perspective of kernelization: while a polynomial kernel cannot exist in general [9,26], polynomial kernels exist for broad classes of families Π [26,30].…”

Section: π-Free Deletion [Vc]mentioning

confidence: 99%

Streaming Deletion Problems Parameterized by Vertex Cover

Oostveen

Leeuwen

2021

Fundamentals of Computation Theory

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“…It is noticeable that there are only a few known cases where the problem can be solved efficiently: cluster-vd is polynomially solvable on block graphs, split graphs and interval graphs [3], and on graphs of bounded treewidth [29]. On the other hand, the complexity status of cluster-vd on many well-studied graph classes is still open, e.g., chordal graphs discussed in [3] and planar bipartite graphs mentioned in [4].…”

Section: Cluster-vdmentioning

confidence: 99%

Complexity of the (Connected) Cluster Vertex Deletion Problem on H-free Graphs

Le,

2024

Theory Comput Syst

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The well-known Cluster Vertex Deletion problem (cluster-vd) asks for a given graph G and an integer k whether it is possible to delete a set S of at most k vertices of G such that the resulting graph $$G-S$$ G - S is a cluster graph (a disjoint union of cliques). We give a complete characterization of graphs H for which cluster-vd on H-free graphs is polynomially solvable and for which it is $$\textsf{NP}$$ NP -complete. Moreover, in the $$\textsf{NP}$$ NP -completeness cases, cluster-vd cannot be solved in sub-exponential time in the vertex number of the H-free input graphs unless the Exponential-Time Hypothesis fails. We also consider the connected variant of cluster-vd, the Connected Cluster Vertex Deletion problem (connected cluster-vd), in which the set S has to induce a connected subgraph of G. It turns out that connected cluster-vd admits the same complexity dichotomy for H-free graphs. Our results enlarge a list of rare dichotomy theorems for well-studied problems on H-free graphs.

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