Gadgets, approximation, and linear programming

SIAM Journal on Computing

Volumn 29, Issue 6, 2000, Pages 2074-2097

  Trevisan, Luca ^a   Sorkin, Gregory B ^b   Sudan, Madhu ^c   Williamson, David P ^b  

^a Columbia University ^*  (United States)

^b IBM T J WATSON RESEARCH CENTER   (United States)

^c MASSACHUSETTS INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; PROBLEM SOLVING; THEOREM PROVING;

COMBINATORIAL STRUCTURES; PROBABILISTIC PROOF SYSTEMS;

LINEAR PROGRAMMING;

EID: 0034476529     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539797328847     Document Type: Article

References (19)

1. S. ARORA, C. LUND, R. MOTWANI, M. SUDAN, AND M. SZEGEDY, Proof verification and the hardness of approximation problems, J. Assoc. Comput. Mach., 45 (1998), pp. 501-555.
2. M. BELLARE, O. GOLDREICH, AND M. SUDAN, Free bits, PCPs and nonapproximability - towards tight results, SIAM J. Comput., 27 (1998), pp. 804-915.
3. P. CRESCENZI, R. SILVESTRI, AND L. TREVISAN, On weighted vs. unweighted versions of combinatorial optimization problems, Inform, and Comput., to appear.
4. P. CRESCENZI AND L. TREVISAN, MAX NP-completeness made easy, Theoret. Comput. Sci., 225 (1999), pp. 65-79.
5. U. FEIGE AND M. X. GOEMANS, Approximating the value of two prover proof systems, with applications to MAX 2SAT and MAX DICUT, in Proceedings of the Third Israel Symposium on Theory of Computing and Systems, Tel Aviv, Israel, 1995, pp. 182-189.
6. M. GAREY, D. JOHNSON, AND L. STOCKMEYER, Some simplified NP-complete graph problems, Theoret. Comput. Sci., 1 (1976) pp. 237-267.
7. M. X. GOEMANS AND D. P. WILLIAMSON, New 3/4-approximation algorithms for the maximum satisfiability problem, SIAM J. Discrete Math., 7 (1994), pp. 656-666.
8. M. X. GOEMANS AND D. P. WILLIAMSON, Improved approximation algorithms for maximum cut and satisfiability problems using semidefinite programming, J. Assoc. Comput. Mach., 42 (1995), pp. 1115-1145.
9. J. HÅSTAD, Some optimal inapproximability results, in Proceedings of the 29th ACM Symposium on Theory of Computing, El Paso, TX, 1997, pp. 1-10.
10. H. KARLOFF AND U. ZWICK, A 7/8-approximation algorithm for MAX 3SAT?, in Proceedings of the 38th IEEE Symposium on Foundations of Computer Science, Miami, FL, 1997, pp. 406-415.
11. H. KARLOFF AND U. ZWICK, personal communication, 1996.
12. R. KARP, Reducibility among combinatorial problems, in Complexity of Computer Computations, Advances in Computing Research, R. E. Miller and J. W. Thatcher, eds., Plenum Press, New York, 1972, pp. 85-103.
13. S. KHANNA, R. MOTWANI, M. SUDAN, AND U. VAZIRANI, On syntactic versus computational views of approximability. SIAM J. Comput., 28 (1999), pp. 164-191.
14. T. ONO, T. HIRATA, AND T. ASANO, Approximation algorithms for the maximum satisfiability problem, in Proceedings of the Fifth Scandinavian Workshop on Algorithm Theory, Reykjavík, Iceland, Lecture Notes in Comput. Sci. 1097, Springer-Verlag, 1996, pp. 100-111.
15. C. PAPADIMITRIOU AND M .YANNAKAKIS, Optimization, approximation, and complexity classes, J. Comput. System Sci., 43 (1991). pp. 425-440.
16. L. TREVISAN, Parallel approximation algorithms using positive linear programming, Algorithmica, 21 (1998), pp. 72-88.
17. L, TREVISAN, G. B. SORKIN, M. SUDAN, AND D. P. WILLIAMSON, Gadgets, approximation, and linear programming, in Proceedings of the 37th IEEE Symposium on Foundations of Computer Science, Burlington, VT, 1996, pp. 617-626.
18. M. YANNAKAKIS, On the approximation of maximum satisfiability, J. Algorithms, 17 (1994), pp. 475-502.
19. U. ZWICK, Approximation algorithms for constraint satisfaction problems involving at most three variables per constraint, in Proceedings of the Ninth ACM-SIAM Symposium on Discrete Algorithms, San Francisco, CA, 1998, pp. 201-210.