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On the Effective Enumerability of NP Problems

  • Jianer Chen
  • Iyad A. Kanj
  • Jie Meng
  • Ge Xia
  • Fenghui Zhang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4169)

Abstract

In the field of computational optimization, it is often the case that we are given an instance of an NP problem and asked to enumerate the first few ”best” solutions to the instance. Motivated by this, we propose in this paper a new framework to measure the effective enumerability of NP optimization problems. More specifically, given an instance of an NP problem, we consider the parameterized problem of enumerating a given number of best solutions to the instance, and study its average complexity in terms of the number of solutions. Our framework is different from the previously-proposed ones. For example, although it is known that counting the number of k-paths in a graph is #W[1]-complete, we present a fixed-parameter enumeration algorithm for the problem. We show that most algorithmic techniques for fixed-parameter tractable problems, such as search trees, color coding, and bounded treewidth, can be used for parameterized enumerations. In addition, we design elegant and new enumeration techniques and show how to generate small-size structures and enumerate solutions efficiently.

Keywords

Planar Graph Weighted Graph Vertex Cover Recursive Function Structure Algorithm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jianer Chen
    • 1
  • Iyad A. Kanj
    • 2
  • Jie Meng
    • 1
  • Ge Xia
    • 3
  • Fenghui Zhang
    • 1
  1. 1.Department of Computer ScienceTexas A&M UniversityCollege StationUSA
  2. 2.School of CTIDePaul UniversityChicagoUSA
  3. 3.Department of Computer ScienceLafayette CollegeEastonUSA

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