eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2019-12-04
23:1
23:11
10.4230/LIPIcs.IPEC.2019.23
article
Subexponential-Time Algorithms for Finding Large Induced Sparse Subgraphs
Novotná, Jana
1
Okrasa, Karolina
2
Pilipczuk, Michał
3
Rzążewski, Paweł
2
https://orcid.org/0000-0001-7696-3848
van Leeuwen, Erik Jan
4
Walczak, Bartosz
5
Department of Applied Mathematics, Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
Faculty of Mathematics and Information Science, Warsaw University of Technology, Poland
Institute of Informatics, Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Poland
Department of Information and Computing Sciences, Utrecht University, The Netherlands
Department of Theoretical Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland
Let C and D be hereditary graph classes. Consider the following problem: given a graph G in 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(Delta) or O(sqrt{m}), where Delta and m denote the maximum degree and the number of edges, respectively; and
- the 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 P_t-free graph can be found in 2^{O~(n^{2/3})} time, for every fixed t; and
- a largest induced planar graph in a string graph can be found in 2^{O~(n^{3/4})} time.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol148-ipec2019/LIPIcs.IPEC.2019.23/LIPIcs.IPEC.2019.23.pdf
subexponential algorithm
feedback vertex set
P_t-free graphs
string graphs