Upper Domination: Towards a Dichotomy Through Boundary Properties

Handle URI:
http://hdl.handle.net/10754/625686
Title:
Upper Domination: Towards a Dichotomy Through Boundary Properties
Authors:
AbouEisha, Hassan M. ( 0000-0003-4560-7175 ) ; Hussain, Shahid; Lozin, Vadim; Monnot, Jérôme; Ries, Bernard; Zamaraev, Viktor ( 0000-0001-5755-4141 )
Abstract:
An upper dominating set in a graph is a minimal dominating set of maximum cardinality. The problem of finding an upper dominating set is generally NP-hard. We study the complexity of this problem in finitely defined classes of graphs and conjecture that the problem admits a complexity dichotomy in this family. A helpful tool to study the complexity of an algorithmic problem is the notion of boundary classes. However, none of such classes has been identified so far for the upper dominating set problem. We discover the first boundary class for this problem and prove the dichotomy for monogenic classes.
KAUST Department:
King Abdullah University of Science and Technology, Thuwal, Saudi Arabia
Citation:
AbouEisha H, Hussain S, Lozin V, Monnot J, Ries B, et al. (2017) Upper Domination: Towards a Dichotomy Through Boundary Properties. Algorithmica. Available: http://dx.doi.org/10.1007/s00453-017-0346-9.
Publisher:
Springer Nature
Journal:
Algorithmica
Issue Date:
14-Jul-2017
DOI:
10.1007/s00453-017-0346-9
Type:
Article
ISSN:
0178-4617; 1432-0541
Sponsors:
Vadim Lozin and Viktor Zamaraev gratefully acknowledge support from EPSRC, Grant EP/L020408/1. Part of this research was carried out when Vadim Lozin was visiting the King Abdullah University of Science and Technology (KAUST). This author thanks the University for hospitality and stimulating research environment.
Additional Links:
http://link.springer.com/article/10.1007/s00453-017-0346-9
Appears in Collections:
Articles

Full metadata record

DC FieldValue Language
dc.contributor.authorAbouEisha, Hassan M.en
dc.contributor.authorHussain, Shahiden
dc.contributor.authorLozin, Vadimen
dc.contributor.authorMonnot, Jérômeen
dc.contributor.authorRies, Bernarden
dc.contributor.authorZamaraev, Viktoren
dc.date.accessioned2017-10-03T12:49:34Z-
dc.date.available2017-10-03T12:49:34Z-
dc.date.issued2017-07-14en
dc.identifier.citationAbouEisha H, Hussain S, Lozin V, Monnot J, Ries B, et al. (2017) Upper Domination: Towards a Dichotomy Through Boundary Properties. Algorithmica. Available: http://dx.doi.org/10.1007/s00453-017-0346-9.en
dc.identifier.issn0178-4617en
dc.identifier.issn1432-0541en
dc.identifier.doi10.1007/s00453-017-0346-9en
dc.identifier.urihttp://hdl.handle.net/10754/625686-
dc.description.abstractAn upper dominating set in a graph is a minimal dominating set of maximum cardinality. The problem of finding an upper dominating set is generally NP-hard. We study the complexity of this problem in finitely defined classes of graphs and conjecture that the problem admits a complexity dichotomy in this family. A helpful tool to study the complexity of an algorithmic problem is the notion of boundary classes. However, none of such classes has been identified so far for the upper dominating set problem. We discover the first boundary class for this problem and prove the dichotomy for monogenic classes.en
dc.description.sponsorshipVadim Lozin and Viktor Zamaraev gratefully acknowledge support from EPSRC, Grant EP/L020408/1. Part of this research was carried out when Vadim Lozin was visiting the King Abdullah University of Science and Technology (KAUST). This author thanks the University for hospitality and stimulating research environment.en
dc.publisherSpringer Natureen
dc.relation.urlhttp://link.springer.com/article/10.1007/s00453-017-0346-9en
dc.subjectUpper dominating seten
dc.subjectBoundary classen
dc.subjectComplexity dichotomyen
dc.subjectNP-harden
dc.titleUpper Domination: Towards a Dichotomy Through Boundary Propertiesen
dc.typeArticleen
dc.contributor.departmentKing Abdullah University of Science and Technology, Thuwal, Saudi Arabiaen
dc.identifier.journalAlgorithmicaen
dc.contributor.institutionHabib University, Karachi, Pakistanen
dc.contributor.institutionMathematics Institute, University of Warwick, Coventry, UKen
dc.contributor.institutionUniversité Paris-Dauphine, PSL Research University, CNRS, LAMSADE, Paris, Franceen
dc.contributor.institutionDepartment of Informatics, University of Fribourg, Fribourg, Switzerlanden
kaust.authorAbouEisha, Hassan M.en
All Items in KAUST are protected by copyright, with all rights reserved, unless otherwise indicated.