Coupon collectors, q-binomial coefficients and the unsatisfiability threshold

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 2202, Issue , 2001, Pages 328-338

  Kaporis, Alexis C ^a   Kirousis, Lefteris M ^a   Stamatiou, Yannis C ^a,b   Vamvakari, Malvina ^a,b   Zito, Michele ^c  

^a UNIVERSITY OF PATRAS   (Greece)

^b University of Patras and Computer Technology Institute   (Greece)

^c UNIVERSITY OF LIVERPOOL   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SCIENCE; COMPUTERS;

BINOMIAL COEFFICIENTS; COUPON COLLECTORS; LOCAL MAXIMUM; LOWER AND UPPER BOUNDS; Q-BINOMIAL COEFFICIENTS; THRESHOLD-VALUE; TRUTH ASSIGNMENT; VARIABLE RATIO;

ARTIFICIAL INTELLIGENCE;

EID: 84962798211     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45446-2_21     Document Type: Conference Paper

References (22)

1. D. Achlioptas, G. B. Sorkin, “Optimal Myopic Algorithms for Random 3-SAT” in: Proc. 41st Annual Symposium on Foundations of Computer Science (FOCS), 2000. pp 590–600.
2. N. Alon, J. H. Spencer, P. Erdos, The Probabilistic Method, John Wiley and Sons, 1992.
3. B. Bollobás, Random Graphs, Academic Press, London, 1985.
4. V. Chvátal, “Almost all graphs with 1.44n edges are 3-colourable,” Random Structures and Algorithms 2, pp 11–28, 1991.
5. L. Comtet, Advanced Combinatorics; The Art of Finite and Infinite Expansions. D. Reidel, 1974.
6. R. M. Corless, G. H. Gonnet, D. E. G. Hare, D. J. Jeffrey, D. E. Knuth, “On the Lambert W function,” manuscript, Computer Science Department, University of Waterloo.
7. O. Dubois, Y. Boufkhad, J. Mandler, “Typical random 3-SAT formulae and the satisfiability threshold,” in: Proc. 11th Symposium on Discrete Algorithms (SODA), pp 126–127, 2000.
8. C. M. Fortuin, R. W. Kasteleyn, J. Ginibre, Correlation inequalities on some partially ordered sets, Commun. Math. Physics 22, pp. 89–103, 1971.
9. N. J. Fine, Basic Hypergeometric Series and Applications, Mathematical Surveys and Monographs, Number 27, 1980.
10. E. Friedgut, appendix by J. Bourgain, “Sharp thresholds of graph properties, and the k-sat problem,” J. Amer. Math. Soc. 12, pp 1017–1054, 1999.
11. G. Gasper, M. Rahman, Basic Hypergeometric Series, Encyclopedia of Mathematics and its Applications, vol 35, Cambridge University Press, Cambridge, 1990.
12. S. Janson, Y. C. Stamatiou, M. Vamvakari, “Bounding the unsatisfiability threshold of random 3-SAT,” Random Structures and Algorithms, 17, pp 108–116, 2000.
13. L.M. Kirousis, Y. C. Stamatiou, An inequality for reducible, increasing properties of randomly generated words, Tech. Rep. TR-96.10.34, C. T. I., University of Patras, Greece, 1996.
14. L. M. Kirousis, E. Kranakis, D. Krizanc, Y. C. Stamatiou, “Approximating the unsatisfiability threshold of random formulas,” Random Structures and Algorithms 12, pp 253–269, 1998.
15. D. E. Knuth, Fundamental Algorithms, The Art of Computer Programming, 2nd ed., 1973.
16. M. B. Monagan, K. O. Geddes, K. M. Heal, G. Labahn, S. M. Vorkoetter, Programming Guide, Maple V Release 5, Springer–Verlag, 1998.
17. R. Motwani, P. Raghavan. Randomized Algorithms. Cambridge University Press, 1995.
18. A. M. Odlyzko, “Asymptotic Enumeration Methods,” in: R. L. Graham, M. Grötschel, and L. Lovász, eds. Handbook of Combinatorics, Chapter 22, 1063–1229, Elsevier, 1995.
19. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd ed., Cambridge University Press, 1993.
20. A. E. Taylor, W.R Mann, Advanced Calculus, 3rd ed., John Wiley & Sons, 1983.
21. F. J. Wright: http://centaur.maths.qmw.ac.uk/Computer Algebra/. A Maple (V-5) implementation of Downhill Simplex based on code given in [19].
22. M. Zito, Randomised Techniques in Combinatorial Algorithmics, PhD Thesis, Department of Computer Science, University of Warwick, November 1999.