On the approximability of clique and related maximization problems

Journal of Computer and System Sciences

Volumn 67, Issue 3, 2003, Pages 633-651

  Srinivasan, Aravind ^a  

^a University of Maryland ^*  (United States)

Author keywords

Approximation algorithms; Clique; Inapproximability; Independent set; Packing integer programs; Random sampling

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL METHODS; GRAPH THEORY; INTEGER PROGRAMMING; PROBLEM SOLVING; SAMPLING;

CLIQUE;

SYSTEMS SCIENCE;

EID: 0242581699     PISSN: 00220000     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-0000(03)00110-7     Document Type: Article

References (19)

1. J. Abello, P. Pardalos, M. Resende, On maximum clique problems in very large graphs, in: J. Abello, J. Vitter (Eds.), External Memory Algorithms, American Mathematical Society, Series in Discrete Mathematics and Theoretical Computer Science, Vol. 50, Amer. Math. Soc., Providence, RI, 1999, pp. 119-130.
2. S. Arora, C. Lund, R. Motwani, M. Sudan, M. Szegedy, Proof verification and the hardness of approximation problems, J. ACM 45 (1998) 501-555.
3. S. Arora, S. Safra, Probabilistic checking of proofs: a new characterization of NP, J. ACM 45 (1998) 70-122.
4. A. Blum, Algorithms for approximate graph coloring, Ph.D. Thesis, Dept. of Electrical Engineering and Computer Science, MIT, 1991.
5. R.B. Boppana, M.M. Halldórsson, Approximating maximum independent sets by excluding subgraphs, BIT 32 (1992) 180-196.
6. 1-o(1) in: Proceedings of International Colloquium on Automata, Languages and Programming, Geneva, Switzerland, 2000, pp. 2-12.
7. U. Feige, Randomized graph products, chromatic numbers, and the Lovász 9-function, Combinatorica 17 (1997) 79-90.
8. U. Feige, S. Goldwasser, L. Lovász, S. Safra, M. Szegedy, Interactive proofs and the hardness of approximating cliques, J. ACM 43 (1996) 268-292.
9. L. Fortnow, Time-space trade-offs for satisfiability, J. Comput. System Sci. 60 (2000) 337-353.
10. M.M. Halldórsson, Approximations of independent sets in graphs, in: Proceedings of APPROX '98 Conference, Springer-Verlag Lecture Notes in Computer Science, Vol. 1444, Springer, Berlin, 1998, pp. 1-13.
11. M.M. Halldórsson, Approximations of weighted independent set and hereditary subset problems, J. Graph Algorithms Appl. 4 (2000) 1-16.
12. 1-8, Acta Math. 182 (1999) 105-142.
13. S. Khot, Improved inapproximability results for maxclique, chromatic number and approximate graph coloring, in: Proceedings of IEEE Symposium on Foundations of Computer Science, Las Vegas, NV, 2001, pp. 600-609.
14. M. Krivelevich, V. Vu, Approximating the independence number and the chromatic number in expected polynomial time, in: Proceedings of International Colloquium on Automata, Languages and Programming, Geneva, Switzerland, 2000, pp. 13-24.
15. P. Raghavan. Probabilistic construction of deterministic algorithms: approximating packing integer programs, J. Comput. System Sci. 37 (1988) 130-143.
16. A. Samorodnitsky, L. Trevisan, A PCP characterization of NP with optimal amortized query complexity, in: Proceedings of ACM Symposium on Theory of Computing, Portland, OR, 2000, pp. 191-199.
17. J.P. Schmidt, A. Siegel, A. Srinivasan, Chernoff-Hoeffding bounds for applications with limited independence, SIAM J. Discrete Math. 8 (1995) 223-250.
18. A. Srinivasan, Improved approximation guarantees for packing and covering integer programs, SIAM J. Comput. 29 (1999) 648-670.
19. A.C.-C. Yao, Probabilistic computations: towards a unified measure of complexity, in: Proceedings of IEEE Symposium on Foundations of Computer Science, Providence, RI, 1977, pp. 222-227.