These are the joint refereed proceedings of the 4th International Workshop on Approximation Algorithms for Optimization Problems, APPROX 2001 and of the 5th International Workshop on Randomization and Approximation Techniques in Computer Science, RANDOM 2001, held in Berkeley, California, USA in August 2001. The 26 revised full papers presented were carefully reviewed and selected from a total of 54 submissions. Among the issues addressed are design and analysis of approximation algorithms, inapproximability results, on-line problems, randomization, de-randomization, average-case analysis,...