This book constitutes the thoroughly refereed post-proceedings of the 4th International Workshop on Algorithm Engineering, WAE 2000, held in Saarbrucken, Germany in September 2000. The 19 revised full papers presented together with one invited paper were carefully reviewed and selected from a total of 30 submissions. Among the topics addressed are software repositories allowing for the use and experimentation with efficient discrete algorithms; novel uses of discrete algorithms; methodological issues on algorithms and data structures; and methodological issues on converting user requirements into efficient algorithmic and implementation solutions.