Randomized path coloring on binary trees
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
On the false-positive rate of Bloom filters
Information Processing Letters
An analysis of reduced error pruning
Journal of Artificial Intelligence Research
Sharp thresholds for Hamiltonicity in random intersection graphs
Theoretical Computer Science
Computing the density of states of Boolean formulas
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
Approximating k-generalized connectivity via collapsing HSTs
Journal of Combinatorial Optimization
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The classical occupancy problem is concerned with studying the number of empty bins resulting from a random allocation of m balls to n bins. We provide a series of tail bounds on the distribution of the number of empty bins. These tail bounds should find application in randomized algorithms and probabilistic analysis. Our motivating application is the following well-known conjecture on threshold phenomenon for the satisfiability problem. Consider random 3-SAT formulas with cn clauses over n variables, where each clause is chosen uniformly and independently from the space of all clauses of size 3. It has been conjectured that there is a sharp threshold for satisfiability at c*/spl ap/4.2. We provide the first non-trivial upper bound on the value of c*, showing that for c4.758 a random 3-SAT formula is unsatisfiable with high probability. This result is based on a structural property, possibly of independent interest, whose proof needs several applications of the occupancy tail bounds.