Extending Partial Representations of Proper and Unit Interval Graphs
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Extending Partial Representations of Proper and Unit Interval Graphs
Original language description
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
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
BA - General mathematics
OECD FORD branch
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Result continuities
Project
<a href="/en/project/EE2.3.30.0038" target="_blank" >EE2.3.30.0038: New excellence in human resources</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Algorithm Theory - SWAT 2014 - LNCS 8503
ISBN
978-3-319-08404-6
ISSN
0302-9743
e-ISSN
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Number of pages
12
Pages from-to
253-264
Publisher name
Springer
Place of publication
Heidelberg
Event location
Kodaň
Event date
Jul 2, 2014
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000349074600022