The exact weighted independent set problem in perfect graphs and related classes

Milanič, Martin; Monnot, Jérôme

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Title:	The exact weighted independent set problem in perfect graphs and related classes
Authors:	ID Milanič, Martin (Author) ID Monnot, Jérôme (Author)
Files:	http://dx.doi.org/10.1016/j.endm.2009.11.052
Language:	English
Work type:	Not categorized
Typology:	1.08 - Published Scientific Conference Contribution
Organization:	IAM - Andrej Marušič Institute
Abstract:	The exact weighted independent set (EWIS) problem consists in determining whether a given vertex-weighted graph contains an independent set of given weight. This problem is a generalization of two well-known problems, the NP-complete subset sum problem and the strongly NP-hard maximum weight independent set (MWIS) problem. Since the MWIS problem is polynomially solvable for some special graph classes, it is interesting to determine the complexity of this more general EWIS problem for such graph classes. We focus on the class of perfect graphs, which is one of the most general graph classes where the MWIS problem can be solved in polynomial time. It turns out that for certain subclasses of perfect graphs, the EWIS problem is solvable in pseudopolynomial time, while on some others it remains strongly NP-complete.In particular, we show that the EWIS problem is strongly NP-complete for bipartite graphs of maximum degree three, but solvable in pseudo-polynomial time for cographs, interval graphs and chordal graphs, as well as for some other related graph classes.
Keywords:	graf, neodvisna množica, popolni graf, dvodelni graf
Year of publishing:	2009
Number of pages:	Str. 317-322
Numbering:	Vol. 35
PID:	20.500.12556/RUP-2747
ISSN:	1571-0653
UDC:	519.17
COBISS.SI-ID:	1024190548
Publication date in RUP:	15.10.2013
Views:	3870
Downloads:	119
Metadata:
:	MILANIČ, Martin and MONNOT, Jérôme, 2009, The exact weighted independent set problem in perfect graphs and related classes. In : [online]. Published Scientific Conference Contribution. 2009. p. 317–322. [Accessed 21 April 2025]. Retrieved from: http://dx.doi.org/10.1016/j.endm.2009.11.052 Copy citation