Reducing randomness via irrational numbers

SIAM Journal on Computing

Volumn 29, Issue 4, 2000, Pages 1247-1256

  Chen, Zhi Zhong ^a   Kao, Ming Yang ^b  

^a TOKYO DENKI UNIVERSITY   (Japan)

^b Yale University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

GRAPH THEORY; PARALLEL ALGORITHMS; PARALLEL PROCESSING SYSTEMS; POLYNOMIALS; PROBABILITY; PROGRAM DIAGNOSTICS; RANDOM ERRORS; SORTING;

IRRATIONAL NUMBERS; MULTISET EQUALITY TEST; PERFECT MATCHINGS; POLYNOMIAL IDENTIFICATION; PROGRAM CHECKING; RANDOMIZED ALGORITHMS;

APPROXIMATION THEORY;

EID: 0033701650     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539798341600     Document Type: Article

References (22)

1. M. AJTAI, J. KOMLÓS, AND E. SZEMERÉDI, Deterministic simulation in Logspace, in Proceedings of the 19th Annual ACM Symposium on Theory of Computing, 1987, pp. 132-140.
2. C. BERGE, Graphs, second revised ed., North-Holland, Amsterdam, 1985.
3. M. BLUM AND S. KANNAN, Designing programs that check their work, J. ACM, 42 (1995), pp. 269-291.
4. S. CHARI, P. ROHATGI, AND A. SRINIVASAN, Randomness-optimal unique element isolation with applications to perfect matching and related problems, SIAM J. Comput., 24 (1995), pp. 1036-1050.
5. A. COHEN AND A. WIGDERSON, Dispersers, deterministic amplification, and weak random sources (extended abstract), in Proceedings of the 30th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society, Los Alamitos, CA, 1989, pp. 14-19.
6. R. A. DEMILLO AND R. J. LIPTON, A probabilistic remark on algebraic program testing, Inform. Process. Lett., 7 (1978), pp. 193-195.
7. Z. GALIL, S. MICALI, AND H. GABOW, An O(EV log V) algorithm for finding a maximal weighted matching in general graphs, SIAM J. Comput., 15 (1986), pp. 120-130.
8. R. IMPAGLIAZZO AND D. ZUCKERMAN, How to recycle random bits, in Proceedings of the 30th Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society, Los Alamitos, CA, 1989, pp. 248-253.
9. N. JACOBSON, Basic Algebra, W. H. Freeman, San Francisco, CA, 1974.
10. R. M. KARP, E. UPFAL, AND A. WIGDERSON, Constructing a perfect matching is in random NC, Combinatorica, 6 (1986), pp. 35-48.
11. W. J. LEVEQUE, Topics in Number Theory, Vol. 1, Addison-Wesley, Reading, MA, 1956.
12. L. LOVASZ, On determinants, matchings and random algorithms, in Fundamentals of Computing Theory (Proceedings of the Conference on Algebraic, Arith. and Categorical Methods in Comput. Theory, Berlin, Wendisch-Rietz, 1979), Math. Res. 2, L. Budach, ed., Akademia-Verlag, Berlin, 1979, pp. 565-574.
13. S. MICALI AND V. V. VAZIRANI, An O(√|V| · |E|) algorithm for finding maximum matching in general graphs, in Proceedings of the 21st Annual IEEE Symposium on Foundations of Computer Science, IEEE Computer Society, Los Alamitos, CA, 1980, pp. 17-27.
14. P. MORANDI, Field and Galois Theory, Grad. Texts in Math. 167, Springer-Verlag, New York, 1996.
15. R. MOTWANI AND P. RAGHAVAN, Randomized Algorithms, Cambridge University Press, Cambridge, UK, 1995.
16. V. PAN, Complexity of parallel matrix computations, Theoret. Comput. Sci., 54 (1987), pp. 65-85.
17. J. H. ROWLAND AND J. R. COWLES, Small sample algorithms for the identification of polynomials, J. ACM, 33 (1986), pp. 822-829.
18. J. T. SCHWARTZ, Fast probabilistic algorithms for verification of polynomial identities, J. ACM, 27 (1980), pp. 701-717.
19. W. THRASH, A Note on the Least Common Multiples of Dense Sets of Integers, Tech. Report 93-02-04, Department of Computer Science, University of Washington, Seattle, WA, 1993.
20. W. T. TUTTE, The factors of graphs, Canad. J. Math., 4 (1952), pp. 314-328.
21. V. V. VAZIRANI, Maximum Matchings without Blossoms, Ph.D. thesis, University of California, Berkeley, CA, 1984.
22. R. E. ZIPPEL, Probabilistic algorithms for sparse polynomials, in Proceedings of EUROSAM '79, an International Symposium on Symbolic and Algebraic Manipulation, Lecture Notes in Comput. Sci. 72, E. W. Ng, ed., Springer-Verlag, New York, 1979, pp. 216-226.