The parameterized complexity of maximality and minimality problems

Authors:
Yijia Chen;Jörg Flum
Affiliations:
BASICS,Department of Computer Science, Shanghai Jiaotong University, Shanghai, China;Abteilung für Mathematische Logik, Universität Freiburg, Freiburg, Germany
Venue:
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Year:
2006

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Abstract

Many parameterized problems (as the clique problem or the dominating set problem) ask, given an instance and a natural number k as parameter, whether there is a solution of size k. We analyze the relationship between the complexity of such a problem and the corresponding maximality (minimality) problem asking for a solution of size k maximal (minimal) with respect to set inclusion. As our results show maximality problems may increase the parameterized complexity, while “in terms of the W-hierarchy” minimality problems do not increase the complexity.