Extending Partial Representations of Proper and Unit Interval Graphs

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F49777513%3A23520%2F14%3A43922461" target="_blank" >RIV/49777513:23520/14:43922461 - isvavai.cz</a>

Výsledek na webu

<a href="http://link.springer.com/chapter/10.1007/978-3-319-08404-6_22" target="_blank" >http://link.springer.com/chapter/10.1007/978-3-319-08404-6_22</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/978-3-319-08404-6_22" target="_blank" >10.1007/978-3-319-08404-6_22</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Extending Partial Representations of Proper and Unit Interval Graphs

Popis výsledku v původním jazyce

The recently introduced problem of extending partial interval representations asks, for an interval graph with some intervals pre-drawn by the input, whether the partial representation can be extended to a representation of the entire graph. In this paper, we give a linear-time algorithm for extending proper interval representations and an almost quadratic-time algorithm for extending unit interval representations. We also introduce the more general problem of bounded representations of unit interval graphs, where the input constrains the positions of some intervals by lower and upper bounds. We show that this problem is NP-complete for disconnected input graphs and give a polynomial-time algorithm for a special class of instances, where the ordering of the connected components of the input graph along the real line is fixed. This includes the case of partial representation extension. The hardness result sharply contrasts the recent polynomial-time algorithm for bounded representations

Název v anglickém jazyce

Extending Partial Representations of Proper and Unit Interval Graphs

Popis výsledku anglicky

The recently introduced problem of extending partial interval representations asks, for an interval graph with some intervals pre-drawn by the input, whether the partial representation can be extended to a representation of the entire graph. In this paper, we give a linear-time algorithm for extending proper interval representations and an almost quadratic-time algorithm for extending unit interval representations. We also introduce the more general problem of bounded representations of unit interval graphs, where the input constrains the positions of some intervals by lower and upper bounds. We show that this problem is NP-complete for disconnected input graphs and give a polynomial-time algorithm for a special class of instances, where the ordering of the connected components of the input graph along the real line is fixed. This includes the case of partial representation extension. The hardness result sharply contrasts the recent polynomial-time algorithm for bounded representations

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

<a href="/cs/project/EE2.3.30.0038" target="_blank" >EE2.3.30.0038: Nová excelence lidských zdrojů</a><br>

Návaznosti

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

Rok uplatnění

2014

Kód důvěrnosti údajů

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

Název statě ve sborníku

Algorithm Theory - SWAT 2014 - LNCS 8503

ISBN

978-3-319-08404-6

ISSN

0302-9743

e-ISSN

—

Počet stran výsledku

12

Strana od-do

253-264

Název nakladatele

Springer

Místo vydání

Heidelberg

Místo konání akce

Kodaň

Datum konání akce

2. 7. 2014

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000349074600022