Combinatorial Optimization

Abstract

Combinatorial averaging is a supple tool for understanding the solutions of discrete optimization problems. Computer scientists have designed many algorithms to solve such problems. Traditionally, these algorithms have been classified by their worst-case performance. Such an analysis can lead to undue pessimism. The average behavior of an algorithm is usually more relevant. Of course, to evaluate the average complexity of an algorithm, we must have some probability model for generating typical problems on which the algorithm operates. The examples in this chapter on sorting, data compression, and graph coloring illustrate some of the underlying models and the powerful techniques probabilists have created for analyzing algorithms.