Some of the hardest computational problems have been successfully attacked through the use of probabilistic algorithms, which have an element of randomness to them. Concepts from the field of probability are also increasingly useful in analyzing the performance of algorithms, broadening our understanding beyond that provided by the worst-case or average-case analyses.

This book surveys both of these emerging areas on the interface of the mathematical sciences and computer science. It is designed to attract new researchers to this area and provide them with enough background to begin explorations of their own.

• Front Matter
• 1 Introduction
• 2 Simulated Annealing
• 3 Approximate Counting Via Markov Chains
• 4 Probabilistic Algorithms for Speedup
• 5 Probabilistic Algorithms for Defeating Adversaries
• 6 Pseudorandom Numbers
• 7 Probabilistic Analysis of Packing and Related Partitioning Problems
• 8 Probability and Problems in Euclidean Combinatorial Optimization
• 9 Probabilistic Analysis in Linear Programming
• 10 Randomization in Parallel Algorithms
• 11 Randomly Wired Multistage Networks
• 12 Missing Pieces, Derandomization, and Concluding Remarks