On the Classes of Interval Graphs of Limited Nesting and Count of Lengths

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F16%3A10332310" target="_blank" >RIV/00216208:11320/16:10332310 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.4230/LIPIcs.ISAAC.2016.45" target="_blank" >http://dx.doi.org/10.4230/LIPIcs.ISAAC.2016.45</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4230/LIPIcs.ISAAC.2016.45" target="_blank" >10.4230/LIPIcs.ISAAC.2016.45</a>

Jazyk výsledku

angličtina

Název v původním jazyce

On the Classes of Interval Graphs of Limited Nesting and Count of Lengths

Popis výsledku v původním jazyce

In 1969, Roberts introduced proper and unit interval graphs and proved that these classes are equal. Natural generalizations of unit interval graphs called k-length interval graphs were considered in which the number of different lengths of intervals is limited by k. Even after decades of research, no insight into their structure is known and the complexity of recognition is open even for k = 2. We propose generalizations of proper interval graphs called k-nested interval graphs in which there are no chains of k + 1 intervals nested in each other. It is easy to see that k-nested interval graphs are a superclass of k-length interval graphs. We give a linear-time recognition algorithm for k-nested interval graphs. This algorithm adds a missing piece to Gajarský et al. [FOCS 2015] to show that testing FO properties on interval graphs is FPT with respect to the nesting k and the length of the formula, while the problem is W[2]-hard when parameterized just by the length of the formula. Further, we show that a generalization of recognition called partial representation extension is polynomial-time solvable for k-nested interval graphs, while it is NP-hard for k-length interval graphs, even when k = 2.

Název v anglickém jazyce

On the Classes of Interval Graphs of Limited Nesting and Count of Lengths

Popis výsledku anglicky

In 1969, Roberts introduced proper and unit interval graphs and proved that these classes are equal. Natural generalizations of unit interval graphs called k-length interval graphs were considered in which the number of different lengths of intervals is limited by k. Even after decades of research, no insight into their structure is known and the complexity of recognition is open even for k = 2. We propose generalizations of proper interval graphs called k-nested interval graphs in which there are no chains of k + 1 intervals nested in each other. It is easy to see that k-nested interval graphs are a superclass of k-length interval graphs. We give a linear-time recognition algorithm for k-nested interval graphs. This algorithm adds a missing piece to Gajarský et al. [FOCS 2015] to show that testing FO properties on interval graphs is FPT with respect to the nesting k and the length of the formula, while the problem is W[2]-hard when parameterized just by the length of the formula. Further, we show that a generalization of recognition called partial representation extension is polynomial-time solvable for k-nested interval graphs, while it is NP-hard for k-length interval graphs, even when k = 2.

Druh

D - Stať ve sborníku

CEP obor

IN - Informatika

OECD FORD obor

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Projekt

<a href="/cs/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2016

Kód důvěrnosti údajů

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

Název statě ve sborníku

27th International Symposium on Algorithms and Computation (ISAAC 2016)

ISBN

978-3-95977-026-2

ISSN

1868-8969

e-ISSN

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Počet stran výsledku

13

Strana od-do

1-13

Název nakladatele

Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik

Místo vydání

Dagstuhl, Germany

Místo konání akce

Sydney

Datum konání akce

12. 12. 2016

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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