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On the complexity of approximating the independent set problem

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STACS 89 (STACS 1989)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 349))

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Abstract

We show that for some positive constant c it is not feasible to approximate Independent Set (for graphs of n nodes) within a factor of n c, provided Maximum 2-Satisfiability does not have a randomized polynomial time approximation scheme. We also study reductions preserving the quality of approximations and exhibit complete problems.

Supported by NSF-DCR-8407256, ONR-N0014-80-0517 and AFOSR-87-0400.

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References

  1. AUSIELLO, G., D'ATRI, A., AND PROTASSI,M. (1977). On the Structure of Combinatorial Problems and Structure Preserving Reductions, Proc. 4th Intl. Coll. on Automata, Languages and Programming, 45–57.

    Google Scholar 

  2. AUSIELLO, G., D'ATRI, A., and PROTASSI, M. (1980). Structure Preserving Reductions among Convex Optimization Problems, J. Comp. Sys. Sc. 21, 136–153.

    Google Scholar 

  3. AUSIELLO, G., MARCHETTI-SPACCAMELA, A., and PROTASSI, M. (1980). Towards a Unified Approach for the Classification of NP-Complete Optimization Problems", 12, 83–96.

    Google Scholar 

  4. CHERNOFF, H. (1952). A Measure of Asymptotic Efficiency for Tests of a Hypothesis Based on the Sum of Observations, Ann. of Math. Stat. 23, 493–507.

    Google Scholar 

  5. ERDOES, P., AND SPENCER, J. (1974). Probabilistic Methods in Combinatorics, Academic Press.

    Google Scholar 

  6. FELLER, W., An Introduction to Probability Theory and its Applications, John Wiley & Sons, Vol. 1, 3rd edition.

    Google Scholar 

  7. GONZALEZ, T.F., AND KURKI-GOWDARA, S. (1987). An Approximation Algorithm for the Via Placement and Related Problems. Technical Report, University of California at Santa Barbara.

    Google Scholar 

  8. GAREY, M.R., AND JOHNSON, D.S.(1979). Computers and Intractability: A Guide to the Theory of NP-completeness, W.H. Freeman.

    Google Scholar 

  9. JOHNSON, D.S. (1974). Approximation Algorithms for Combinatorial Problems, J. Comp. Sys. Sci. 9, 256–278.

    Google Scholar 

  10. KRENTEL, M.W. (1986). The Complexity of Optimization problems, Proc. 18th Annual ACM Symp. on Theory of Computing, 69–76.

    Google Scholar 

  11. LEIGHTON, T., AND RAO, S. (1988). An Approximate Max-Flow Min-Cut Theorem for Uniform Multicommodity Flow Problems with Applications to Approximate Algorithms. Proc. 29th Annual Symp. on Foundations of Computer Science, 422–431.

    Google Scholar 

  12. MAIER, D. (1978). The Complexity of Some Problems on Subsequences and Supersequences, J. Assoc. Comput. Mach. 25, 322–336.

    Google Scholar 

  13. MEHLHORN, K. (1984). Data Structures and Algorithms 2: Graph Algorithms and NP-Completeness, Springer Verlag, 183–184.

    Google Scholar 

  14. PAZ, A., and MORAN, S., (1981). Non Deterministic Polynomial Optimization Problems and their Approximation, Theor. Comput. Sci. 15, 251–277.

    Google Scholar 

  15. PAPADIMITRIOU, C.H., AND YANNAKAKIS, M. (1988). Optimization, Approximation and Complexity Classes, Proc. 20th Annual ACM Symp. on Theory of Computing, 229–234.

    Google Scholar 

  16. WIGDERSON, A. (1982). A New Approximate Graph Coloring Algorithm, Proc. 14th Annual ACM Symp. on Theory of Computing, 325–329.

    Google Scholar 

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B. Monien R. Cori

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© 1989 Springer-Verlag Berlin Heidelberg

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Berman, P., Schnitger, G. (1989). On the complexity of approximating the independent set problem. In: Monien, B., Cori, R. (eds) STACS 89. STACS 1989. Lecture Notes in Computer Science, vol 349. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028990

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  • DOI: https://doi.org/10.1007/BFb0028990

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50840-3

  • Online ISBN: 978-3-540-46098-5

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