Improved Parallel Approximation of a Class of Integer Programming Problems

Algorithmica (New York)

Volumn 17, Issue 4, 1997, Pages 449-462

  Alon, N ^a,c   Srinivasan, A ^b  

^a TEL AVIV UNIVERSITY   (Israel)

^b NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^c INSTITUTE FOR ADVANCED STUDY   (United States)

Author keywords

Approximation algorithms; Combinatorial optimization; De randomization; Integer programming; Linear programming; Linear relaxation; Parallel algorithms; Randomized rounding; Rounding theorems

Indexed keywords

EID: 0004529652     PISSN: 01784617     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02523683     Document Type: Article

References (25)

1. R. Aharoni, P. Erdös, and N. Linial. Optima of dual integer linear programs. Combinatorica, 8:13-20, 1988.
2. N. Alon, J. Bruck, J. Naor, M. Naor, and R. Roth. Construction of asymptotically good, low-rate error-correcting codes through pseudo-random graphs. IEEE Transactions on Information Theory, 38:509-516, 1992.
3. N. Alon, O. Goldreich, J. Håstad, and R. Peralta, Simple constructions of almost k-wise independent random variables. Random Structures and Algorithms, 3(3):289-303, 1992.
4. N. Alon and M. Naor. Derandomization, witnesses for Boolean matrix multiplication and construction of perfect hash functions. Algorithmica, 16:434-449, 1996.
5. c n)-wise independence in NC. Journal of the Association for Computing Machinery, 38:1026-1046, 1991.
6. S. Chari, P. Rohatgi, and A. Srinivasan. Improved algorithms via approximations of probability distributions. Proc. ACM Symposium on Theory of Computing, pages 584-592, 1994.
7. H. Chernoff. A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Annals of Mathematical Statistics, 23:493-509, 1952.
8. A. M. Ferrenberg, D. P. Landau, and Y. J. Wong. Monte Carlo simulations: hidden errors from "good" random number generators. Physical Review Letters, 69(23):3382-3384, 1992.
9. W. Hoeffding. Probability inequalities for sums of bounded random variables. American Statistical Association Journal, 58:13-30, 1963.
10. T.-S. Hsu. Graph augmentation and related problems: theory and practice. Ph.D. thesis, Department of Computer Sciences, University of Texas at Austin, October 1993.
11. T.-S. Hsu, V. Ramachandran, and N. Dean. Parallel implementation of algorithms for finding connected components. In DIMACS International Algorithm Implementation Challenge, pages 1-14, 1994.
12. H. J. Karloff and P. Raghavan. Randomized algorithms and pseudorandom numbers. Journal of the Association for Computing Machinery, 40(3):454-476, 1993.
13. L. Lovász. On the ratio of optimal integral and fractional covers. Discrete Mathematics, 13:383-390, 1975.
14. M. Luby. Removing randomness in parallel computation without a processor penalty. Journal of Computer and System Sciences, 47(2):250-286, 1993.
15. M. Luby and N. Nisan. A parallel approximation algorithm for positive linear programming. Proc. ACM Symposium on Theory of Computing, pages 448-457, 1993.
16. R. Motwani, J. Naor, and M. Naor. The probabilistic method yields deterministic parallel algorithms. Journal of Computer and System Sciences, 49:478-516, 1994.
17. J. Naor and M. Naor. Small-bias probability spaces: efficient constructions and applications. SIAM Journal on Computing, 22(4):838-856, 1993.
18. S. A. Plotkin, D. B. Shmoys, and É. Tardos. Fast approximation algorithms for fractional packing and covering problems. Mathematics of Operations Research, 20:257-301, 1995.
19. P. Raghavan. Randomized Rounding and Discrete Ham-Sandwich Theorems: Provably Good Algorithms for Routing and Packing Problems. Ph.D. thesis, University of California at Berkeley, July 1986. Also available as Computer Science Department Report UCB/CSD 87/312.
20. P. Raghavan. Probabilistic construction of deterministic algorithms: approximating packing integer programs. Journal of Computer and System Sciences, 37:130-143, 1988.
21. P. Raghavan and C. D. Thompson. Randomized rounding: a technique for provably good algorithms and algorithmic proofs. Combinatorica, 7:365-374, 1987.
22. J. P. Schmidt, A. Siegel, and A. Srinivasan. Chernoff-Hoeffding bounds for applications with limited independence. SIAM Journal on Discrete Mathematics, 8:223-250, 1995.
23. A. Schrijver, P. Seymour, and P. Winkler. The ring loading problem. In preparation.
24. A. Srinivasan. Improved approximations of packing and covering problems. Proc. ACM Symposium on Theory of Computing, pages 268-276, 1995.
25. A. Srinivasan. An extension of the Lovász local lemma, and its applications to integer programming. Proc. ACM/SIAM Symposium on Discrete Algorithms, pages 6-15, 1996.