New local search approximation techniques for maximum generalized satisfiability problems

  • Paola Alimonti
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 778)

Abstract

We investigate the relationship beetween the classes MAX-NP and GLO by studying the Maximum Generalized Satisfiability problem, which is in the former class. We present a (2−B)-approximate greedy heuristic for this problem and show that no local search c-approximate algorithm exists, based on an h-bounded neighborhood and on the number of satisfied clauses as objective function. This implies that, with the standard definition of local search, MAX-NP is not contained in GLO.

We then show that, by introducing a different local search technique, that is using a different neighborhood structure for B = 2 and an auxiliary objective function in the general case, a local search (2−B)-approximate algorithms can be found for this problem. The latter result, that holds in the general case, suggests how to modify the definition of local search in order to extend the power of this general approch. In the same way, we can enlarge the class GLO of problems that can be efficiently approximated by local search techniques.

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References

  1. 1.
    G. Ausiello, A. Marchetti-Spaccamela, M. Protasi, Toward a Unified Approach for the Classification of NP-Complete Optimization Problems, Th. Comp. Sci.,12,(1980), 83–96.Google Scholar
  2. 2.
    G.Ausiello, M. Protasi, NP Optimization Problems and Local Optima, Technical Report, Esprit Bra Alcom II, 1992.Google Scholar
  3. 3.
    D. Bruschi, D. Joseph, and P. Young, A Structural Overview of NP Opimization Problems, Rapporto Interno n. 75/90, Dip. di Scienze dell'Informazione, Univ. degli Studi di Milano, 1990.Google Scholar
  4. 4.
    S. A. Cook, The Complexity of Theorem Proving Procedures, Proc. 3th. Annual ACM Symp. on Theory of Computing, (1971), 151–158.Google Scholar
  5. 5.
    M. Garey, and D. Johnson, Computers and Intractability: a Guide to the Theory of NP-Comleteness, Freeman, San Francisco (1979).Google Scholar
  6. 6.
    P. Hansen, and B. Jaumard, Algorithms for the Maximum Satisfiability Problem, Computing, 44, (1990), 279–303Google Scholar
  7. 7.
    D. Johnson, Approssimation Algorithms for Combinatorial Problems, J. Comp. Sys.,Sc.9, (1974),256–278.Google Scholar
  8. 8.
    D.S. Johnson, C.H. Papadimitriou, M. Yannakakis, How Easy Is Local Search? Journal of Computer and System Sciences,37, (1988), 79–100.Google Scholar
  9. 9.
    S. Khanna, R. R. Motwani, M. Sudan, U. Vazirani, On Sintactic versus Computational Views of Approximability, Manuscript, 1993.Google Scholar
  10. 10.
    A. Paz, and S. Moran, Non Deterministic Polynomial Optimization Problems and their Approximation, Th. Comp. Sci.,15 (1981), 251–277.Google Scholar
  11. 11.
    C. Papadimitriou, and K. Steiglitz, Combinatorial Optimization Algorithms and Optimization, Prentice-Hall, Englewood Cliffs, New Jersey (1982).Google Scholar
  12. 12.
    C. Papadimitriou, and M. Yannakakis, Optimization, Approximation, and Complexity Classes, Proc. 20th. Annual ACM Symp. on Theory of Computing, (1988), 229–234. To appear J.Comp.Sys.Sc.Google Scholar
  13. 13.
    M. Yannakakis, On the Approximation of Maximum Satisfiability, Proc. 3rd Annual ACM Symp. on Discrete Algorithm, (1992),1–9.Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Paola Alimonti
    • 1
  1. 1.Dipartimento di Informatica e SistemisticaUniversità di Roma “La Sapienza”RomaItalia

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