Abstract
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.
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References
N. Alon, U. Feige, A. Wigderson and D. Zuckerman, Derandomized Graph Products, Computational Complexity 5 (1995), pp. 60–75.
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.edu
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.
V. Bafna and P. Pevzner, Genome rearrangements and sorting by reversals, SIAM J. on Computing 25 (1996), pp. 272–289.
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.
P. Berman and M. Fürer, Approximating Maximum Independent Set in Bounded Degree Graphs, Proc. 5th ACM-SIAM SODA (1994), pp. 365–371.
P. Berman and S. Hannenhali, Fast Sorting by Reversals, Proc. 7th Symp. on Combinatorial Pattern Matching, 1996, pp. 168–185.
P. Berman and M. Karpinski, On Some Tighter Inapproximbility Results, preliminary version appeared in ECCC TR98-065, the full version available under http://theory.cs.uni-bonn.de/_marek.
P. Berman and G. Schnitger, On the Complexity of Approximating the Independent Set Problem, Information and Computation 96 (1992), pp. 77–94.
B. Bollobás, Extremal Graph Theory, 1978, Academic Press.
A. Caprara, Sorting by reversals is difficult, Proc. 1st ACM RECOMB (Int. Conf. on Computational Molecular Biology), 1997, pp. 75–83.
D.A. Christie, A 3/2-Approximation Algorithm for Sorting by Reversals, Proc. 9th ACM-SIAM SODA (1998), pp. 244–252.
D. Cohen and M. Blum, Improved Bounds for Sorting Burnt Pancakes, Discrete Applied Mathematics, Vol. 61, pp. 105–125.
P. Crescenzi and V. Kann, A Compendium of NP Optimization Problems, Manuscript, 1997; available at http://www.nada.kth.se/theory/problemlist.html
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.
W.H. Gates, and C.H. Papadimitriou, Bounds for Sorting by Prefix Reversals, Discrete Mathematics 27 (1979), pp. 47–57.
M. Goemans and D. Williamson, 878-Approximation Algorithms for MAX CUT and MAX 2SAT, Proc. 26th ACM STOC (1994), pp. 422–431.
J. Håstad, Clique is Hard to Approximate within n1-ε, Proc. 37th IEEE FOCS (1996), pp. 627–636.
J. Håstad, Some optimal Inapproximability results, Proc. 29th ACMSTOC, 1997, pp. 1–10.
S. Hannenhali and P. Pevzner, Transforming Cabbage into Turnip (Polynomial time algorithm for sorting by reversals), Proc. 27th ACM STOC (1995), pp. 178–187.
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.
C. Papadimitriou and M. Yannakakis, Optimization, approximation and complexity classes, JCSS 43, 1991, pp. 425–440.
L. Trevisan, G. Sorkin, M. Sudan and D. Williamson, Gadgets, Approximation and Linear Programming, Proc. 37th IEEE FOCS (1996), pp. 617–626.
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Berman, P., Karpinski, M. (1999). On Some Tighter Inapproximability Results (Extended Abstract). In: Wiedermann, J., van Emde Boas, P., Nielsen, M. (eds) Automata, Languages and Programming. Lecture Notes in Computer Science, vol 1644. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48523-6_17
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DOI: https://doi.org/10.1007/3-540-48523-6_17
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