Upper Domination: Towards a Dichotomy Through Boundary Properties
Type
ArticleAuthors
AbouEisha, Hassan M.
Hussain, Shahid

Lozin, Vadim
Monnot, Jérôme
Ries, Bernard
Zamaraev, Viktor

KAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionComputer Science Program
Date
2017-07-14Online Publication Date
2017-07-14Print Publication Date
2018-10Permanent link to this record
http://hdl.handle.net/10754/625686
Metadata
Show full item recordAbstract
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.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.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.Publisher
Springer NatureJournal
AlgorithmicaarXiv
1609.01510Additional Links
http://link.springer.com/article/10.1007/s00453-017-0346-9ae974a485f413a2113503eed53cd6c53
10.1007/s00453-017-0346-9