Subexponential-Time Algorithms for Finding Large Induced Sparse Subgraphs

Jana Novotná , Karolina Okrasa , Michał Pilipczuk , Paweł Rzążewski , Erik Jan van Leeuwen , Bartosz Walczak

Abstract

Let C and D be hereditary graph classes. Consider the following problem: given a graph G∈ D, find a largest, in terms of the number of vertices, induced subgraph of G that belongs to C. We prove that it can be solved in 2 o(n) time, where n is the number of vertices of G, if the following conditions are satisfied:the graphs in C are sparse, i.e., they have linearly many edges in terms of the number of vertices;the graphs in D admit balanced separators of size governed by their density, e.g., O(Δ) or O(m), where Δ and m denote the maximum degree and the number of edges, respectively; andthe considered problem admits a single-exponential fixed-parameter algorithm when parameterized by the treewidth of the input graph. This leads, for example, to the following corollaries for specific classes C and D:a largest induced forest in a Pt-free graph can be found in 2O~(n2/3) time, for every fixed t; anda largest induced planar graph in a string graph can be found in 2O~(n2/3) time.
Author Jana Novotná
Jana Novotná,,
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, Karolina Okrasa (FMIS)
Karolina Okrasa,,
- Faculty of Mathematics and Information Science
, Michał Pilipczuk
Michał Pilipczuk,,
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, Paweł Rzążewski (FMIS / DIPS)
Paweł Rzążewski,,
- Department of Information Processing Systems
, Erik Jan van Leeuwen
Erik Jan van Leeuwen,,
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, Bartosz Walczak
Bartosz Walczak,,
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Journal seriesAlgorithmica, ISSN 0178-4617, e-ISSN 1432-0541
Issue year2020
Pages1-17
Publication size in sheets0.8
ASJC Classification1700 General Computer Science; 1706 Computer Science Applications; 2604 Applied Mathematics
DOIDOI:10.1007/s00453-020-00745-z
URL https://link.springer.com/article/10.1007%2Fs00453-020-00745-z
Languageen angielski
Score (nominal)70
Score sourcejournalList
ScoreMinisterial score = 70.0, 23-09-2020, ArticleFromJournal
Publication indicators Scopus SNIP (Source Normalised Impact per Paper): 2018 = 1.354; WoS Impact Factor: 2018 = 0.882 (2) - 2018=0.931 (5)
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