Subexponential-Time Algorithms for Finding Large Induced Sparse Subgraphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F21%3A10438400" target="_blank" >RIV/00216208:11320/21:10438400 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=20H12foL0" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=20H12foL0</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00453-020-00745-z" target="_blank" >10.1007/s00453-020-00745-z</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Subexponential-Time Algorithms for Finding Large Induced Sparse Subgraphs

Popis výsledku v původním jazyce

Let C and D be hereditary graph classes. Consider the following problem: given a graph GELEMENT OF 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.

Název v anglickém jazyce

Subexponential-Time Algorithms for Finding Large Induced Sparse Subgraphs

Popis výsledku anglicky

Let C and D be hereditary graph classes. Consider the following problem: given a graph GELEMENT OF 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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Algorithmica

ISSN

0178-4617

e-ISSN

—

Svazek periodika

83

Číslo periodika v rámci svazku

srpen

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

17

Strana od-do

2634-2650

Kód UT WoS článku

000554348200001

EID výsledku v databázi Scopus

2-s2.0-85088961027