Families with Infants: A General Approach to Solve Hard Partition Problems

  • Alexander Golovnev
  • Alexander S. Kulikov
  • Ivan Mihajlin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8572)

Abstract

We introduce a general approach for solving partition problems where the goal is to represent a given set as a union (either disjoint or not) of subsets satisfying certain properties. Many NP-hard problems can be naturally stated as such partition problems. We show that if one can find a large enough system of so-called families with infants for a given problem, then this problem can be solved faster than by a straightforward algorithm. We use this approach to improve known bounds for several NP-hard problems (the traveling salesman problem, the graph coloring problem, the problem of counting perfect matchings) on graphs of bounded average degree, as well as to simplify the proofs of several known results.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Alexander Golovnev
    • 1
  • Alexander S. Kulikov
    • 2
  • Ivan Mihajlin
    • 2
    • 3
  1. 1.New York UniversityUSA
  2. 2.St. Petersburg Department of SteklovInstitute of MathematicsUSA
  3. 3.St. Petersburg Academic UniversityUSA

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