This book constitutes the thoroughly refereed post proceedings of the 4th International Workshop on Approximation and Online Algorithms, WAOA 2006, held in Zurich, Switzerland in September 2006 as part of the ALGO 2006 conference event.

The 26 revised full papers presented were carefully reviewed and selected from 62 submissions. Topics addressed by the workshop are algorithmic game theory, approximation classes, coloring and partitioning, competitive analysis, computational finance, cuts and connectivity, geometric problems, inapproximability results, mechanism design, network design, packing and covering, paradigms, randomization techniques, real-world applications, and scheduling problems.