On Some Tighter Inapproximability Results (Extended Abstract)

  • Piotr Berman
  • Marek Karpinski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1644)


We give a number of improved inapproximability results, including the best up to date explicit approximation thresholds for bounded occurence satisfiability problems like MAX-2SAT and E2-LIN-2, and the bounded degree graph problems, like MIS, Node Cover, and MAX CUT. We prove also for the first time inapproximability of the problem of Sorting by Reversals and display an explicit approximation threshold.


Approximation Algorithms Approximation Hardness Bounded Dependency Satisfiability Breakpoint Graphs Independent Set Node Cover MAX-CUT Sorting by Reversals 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AFWZ95]
    N. Alon, U. Feige, A. Wigderson and D. Zuckerman, Derandomized Graph Products, Computational Complexity 5 (1995), pp. 60–75.zbMATHCrossRefMathSciNetGoogle Scholar
  2. [A94]
    S. Arora, Probabilistic Checking of Proofs and Hardness of Approximation Problems, Ph. D. Thesis, UC Berkeley, 1994; available as TR94-476 at ftp://ftp.cs.princeton.eduGoogle Scholar
  3. [ALMSS92]
    S. Arora, C. Lund, R. Motwani, M. Sudan and M. Szegedy, Proof Verification and Hardness of Approximation Problems, Proc. 33rd IEEE FOCS (1992), pp. 14–23.Google Scholar
  4. [BP96]
    V. Bafna and P. Pevzner, Genome rearrangements and sorting by reversals, SIAM J. on Computing 25 (1996), pp. 272–289.zbMATHCrossRefMathSciNetGoogle Scholar
  5. [BF95]
    P. Berman and T. Fujito, Approximating Independent Sets in Degree 3 Graphs, Proc. 4thWorkshop on Algorithms and Data Structures, LNCS Vol. 955, Springer-Verlag, 1995, pp. 449–460.Google Scholar
  6. [BF94]
    P. Berman and M. Fürer, Approximating Maximum Independent Set in Bounded Degree Graphs, Proc. 5th ACM-SIAM SODA (1994), pp. 365–371.Google Scholar
  7. [BH96]
    P. Berman and S. Hannenhali, Fast Sorting by Reversals, Proc. 7th Symp. on Combinatorial Pattern Matching, 1996, pp. 168–185.Google Scholar
  8. [BK99]
    P. Berman and M. Karpinski, On Some Tighter Inapproximbility Results, preliminary version appeared in ECCC TR98-065, the full version available under
  9. [BS92]
    P. Berman and G. Schnitger, On the Complexity of Approximating the Independent Set Problem, Information and Computation 96 (1992), pp. 77–94.zbMATHCrossRefMathSciNetGoogle Scholar
  10. [B78]
    B. Bollobás, Extremal Graph Theory, 1978, Academic Press.Google Scholar
  11. [C97]
    A. Caprara, Sorting by reversals is difficult, Proc. 1st ACM RECOMB (Int. Conf. on Computational Molecular Biology), 1997, pp. 75–83.Google Scholar
  12. [C98]
    D.A. Christie, A 3/2-Approximation Algorithm for Sorting by Reversals, Proc. 9th ACM-SIAM SODA (1998), pp. 244–252.Google Scholar
  13. [CB95]
    D. Cohen and M. Blum, Improved Bounds for Sorting Burnt Pancakes, Discrete Applied Mathematics, Vol. 61, pp. 105–125.Google Scholar
  14. [CK97]
    P. Crescenzi and V. Kann, A Compendium of NP Optimization Problems, Manuscript, 1997; available at
  15. [FG95]
    U. Feige and M. Goemans, Approximating the Value of Two Prover Proof Systems with Applications to MAX-2SAT and MAX-DICUT, Proc. 3rd Israel Symp. on Theory of Computing and Systems, 1995, pp. 182–189.Google Scholar
  16. [GP79]
    W.H. Gates, and C.H. Papadimitriou, Bounds for Sorting by Prefix Reversals, Discrete Mathematics 27 (1979), pp. 47–57.CrossRefMathSciNetGoogle Scholar
  17. [GW94]
    M. Goemans and D. Williamson, 878-Approximation Algorithms for MAX CUT and MAX 2SAT, Proc. 26th ACM STOC (1994), pp. 422–431.Google Scholar
  18. [H96]
    J. Håstad, Clique is Hard to Approximate within n 1-ε, Proc. 37th IEEE FOCS (1996), pp. 627–636.Google Scholar
  19. [H97]
    J. Håstad, Some optimal Inapproximability results, Proc. 29th ACMSTOC, 1997, pp. 1–10.Google Scholar
  20. [HP95]
    S. Hannenhali and P. Pevzner, Transforming Cabbage into Turnip (Polynomial time algorithm for sorting by reversals), Proc. 27th ACM STOC (1995), pp. 178–187.Google Scholar
  21. [KST97]
    H. Kaplan, R. Shamir and R.E. Tarjan, Faster and simpler algorithm for sorting signed permutations by reversals, Proc. 8th ACM-SIAM SODA, 1997, pp. 344–351.Google Scholar
  22. [PY91]
    C. Papadimitriou and M. Yannakakis, Optimization, approximation and complexity classes, JCSS 43, 1991, pp. 425–440.zbMATHMathSciNetGoogle Scholar
  23. [TSSW96]
    L. Trevisan, G. Sorkin, M. Sudan and D. Williamson, Gadgets, Approximation and Linear Programming, Proc. 37th IEEE FOCS (1996), pp. 617–626.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • Piotr Berman
    • 1
  • Marek Karpinski
    • 2
  1. 1.Dept. of Computer SciencePennsylvania State University
  2. 2.Dept. of Computer ScienceUniversity of BonnBonn

Personalised recommendations