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Parameterized Counting and Randomization

  • Rodney G. Downey
  • Michael R. Fellows
Part of the Texts in Computer Science book series (TCS)

Abstract

In this chapter, we will first look at parameterized counting problems as an analog to the classical problem of counting. We establish the classes #W[t] and related issues, and prove completeness results. We present the Flum–Grohe results on the hardness of counting k-cycles. Later we introduce a formal model for parameterized randomization. We prove an analog of the Valiant–Vazirani Theorem.

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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Rodney G. Downey
    • 1
  • Michael R. Fellows
    • 2
  1. 1.School of Mathematics, Statistics and Operations ResearchVictoria UniversityWellingtonNew Zealand
  2. 2.School of Engineering and Information TechnologyCharles Darwin UniversityDarwinAustralia

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