Subexponential-Time Algorithms for Finding Large Induced Sparse Subgraphs
Result description
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.
Keywords
string graphsP t-free graphsfeedback vertex setSubexponential algorithm
The result's identifiers
Result code in IS VaVaI
Result on the web
https://drops.dagstuhl.de/opus/volltexte/2019/11484/pdf/LIPIcs-IPEC-2019-23.pdf
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Subexponential-Time Algorithms for Finding Large Induced Sparse Subgraphs
Original language description
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.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
—
Continuities
S - Specificky vyzkum na vysokych skolach
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
14th International Symposium on Parameterized and Exact Computation (IPEC 2019)
ISBN
978-3-95977-129-0
ISSN
1868-8969
e-ISSN
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Number of pages
11
Pages from-to
1-11
Publisher name
Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik
Place of publication
Dagstuhl, Germany
Event location
Dagstuhl, Germany
Event date
Sep 11, 2019
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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Basic information
Result type
D - Article in proceedings
OECD FORD
Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Year of implementation
2019