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International Workshop on Parameterized and Exact Computation

IWPEC 2006: Parameterized and Exact Computation pp 215–226Cite as

On the Effective Enumerability of NP Problems

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,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.

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Author information

Authors and Affiliations

  1. Department of Computer Science, Texas A&M University, College Station, TX, 77843, USA

    Jianer Chen, Jie Meng & Fenghui Zhang

  2. School of CTI, DePaul University, 243 S. Wabash Avenue, Chicago, IL, 60604, USA

    Iyad A. Kanj

  3. Department of Computer Science, Lafayette College, Easton, PA, 18042, USA

    Ge Xia

Authors
  1. Jianer Chen
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  2. Iyad A. Kanj
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  3. Jie Meng
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  4. Ge Xia
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  5. Fenghui Zhang
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Editor information

Editors and Affiliations

  1. Department of Information and Computing Sciences, Utrecht University, The Netherlands

    Hans L. Bodlaender

  2. University of Tennessee, 37996-3450, Knoxville, Tennessee, U.S.A.

    Michael A. Langston

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© 2006 Springer-Verlag Berlin Heidelberg

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Chen, J., Kanj, I.A., Meng, J., Xia, G., Zhang, F. (2006). On the Effective Enumerability of NP Problems. In: Bodlaender, H.L., Langston, M.A. (eds) Parameterized and Exact Computation. IWPEC 2006. Lecture Notes in Computer Science, vol 4169. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11847250_20

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  • DOI: https://doi.org/10.1007/11847250_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-39098-5

  • Online ISBN: 978-3-540-39101-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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