Conditional hardness for approximate coloring

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn 2006, Issue , 2006, Pages 344-353

  Dinur, Irit ^a   Mossel, Elchanan ^b   Regev, Oded ^c  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c TEL AVIV UNIVERSITY   (Israel)

Author keywords

Graph Coloring; Hardness of Approximation; Unique Games Conjecture

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; COMPUTATIONAL METHODS; COMPUTER SCIENCE; OPTIMIZATION; PROBLEM SOLVING;

GRAPH COLORING; HARDNESS OF APPROXIMATION; NOISE STABILITY; UNIQUE GAMES CONJECTURE;

GRAPH THEORY;

EID: 33748106639     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1132516.1132567     Document Type: Conference Paper

References (21)

1. N. Alon, I. Dinur, E. Friedgut, and B. Sudakov. Graph products, fourier analysis and spectral techniques. GAFA, 14(5):913-940, 2004.
2. M. Bellare, O. Goldreich, and M. Sudan. Free bits, PCPs, and nonapproximability - towards tight results, SIAM J. Comput., 27(3):804-915, 1998.
3. 3/14)-coloring algorithm for 3-colorable graphs. Inform. Process. Lett., 61(1):49-53, 1997.
4. C. Borell. Geometric bounds on the Ornstein-Uhlenbeck velocity process. Z. Wahrsch. Verw. Gebiete, 70(1):1-13, 1985.
5. M. Charikar, K. Makarychev, and Y. Makarychev. Approximating unique games. In private communication, 2005.
6. I. Dinur and S. Safra. On the hardness of approximating minimum vertex cover. Annals of Mathematics, 162(1), 2005.
7. U. Feige and J. Kilian. Zero knowledge and the chromatic number. J. Comput. System Sci., 57(2):187-199, 1998.
8. M. Fürer. Improved hardness results for approximating the chromatic number. In Proc. 36th IEEE Symp. on Foundations of Computer Science, pages 414-421, 1995.
9. A. Gupta and K. Talwar. Approximating unique games. In SODA, 2006. to appear.
10. V. Guruswami and S. Khanna. On the hardness of 4-coloring a 3-colorable graph. In 15th Annual IEEE Conference on Computational Complexity (Florence, 2000), pages 188-197. IEEE Computer Soc., Los Alamitos, CA, 2000.
11. E. Halperin, R. Nathaniel, and U. Zwick. Coloring k-colorable graphs using relatively small palettes. J. Algorithms, 45(1):72-90, 2002.
12. J. Håstad. Some optimal inapproximability results. J. ACM, 48(4):798-859, 2001.
13. D. Karger, R. Motwani, and M. Sudan. Approximate graph coloring by semidefinite programming. Journal of the ACM, 45(2)-.246-265, 1998.
14. S. Khanna, N. Linial, and S. Safra. On the hardness of approximating the chromatic number. Combinatorica, 20(3):393-415, 2000.
15. S. Khot. Improved inapproximability results for MaxClique, chromatic number and approximate graph coloring. In Proc. 42nd IEEE Symp. on Foundations of Computer Science, pages 600-609, 2001.
16. S. Khot. On the power of unique 2-prover 1-round games. In Proceedings of the thiry-fourth annual ACM symposium on Theory of computing, pages 767-775. ACM Press, 2002.
17. S. Khot, G. Kindler, E. Mossel, and R. ODonnell. Optimal inapproximability results for MAX-CUT and other 2-variable CSPs? In Proc. 45th IEEE Symp. on Foundations of Computer Science, pages 146-154, 2004.
18. S. Khot and O. Regev. Vertex cover might be hard to approximate to within 2 - ε. In Proc. of 18th IEEE Annual Conference on Computational Complexity (CCC), pages 379-386, 2003.
19. E. Mossel, R. O'Donnell, and K. Oleszkiewicz. Noise stability of functions with low influences: invariance and optimality. In Proc. 46th IEEE Symp. on Foundations of Computer Science, 2005.
20. Y. Rinott and V. Rotar′. A remark on quadrant normal probabilities in high dimensions. Statistics and Probability Letters, 51(1):47-51, 2001.
21. L. Trevisan. Approximation algorithms for unique games, In Proc. 46th IEEE Symp. on Foundations of Computer Science, 2005.