The Parameterized Complexity of Maximality and Minimality Problems

  • Yijia Chen
  • Jörg Flum
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4169)


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Yijia Chen
    • 1
  • Jörg Flum
    • 2
  1. 1.BASICS,Department of Computer ScienceShanghai Jiaotong UniversityShanghaiChina
  2. 2.Abteilung für Mathematische Logik, Universität FreiburgFreiburgGermany

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