Final Report Summary - ACUITY (Algorithms for coping with uncertainty and intractability) The project has led to the development of new several breakthrough techniques in algorithm design, and resolved some of the most outstanding and fundamental questions in the area. Some of these include.1) The first algorithms for problems in discrepancy theory, that made previously non-constructive methods algorithm. 2) Techniques from discrepancy theory were used to develop a very general method for designing approximation algorithms.3) Novel uses of strong convex relaxations to resolve long standing questions in scheduling and graph theory.4) Resolution of long-standing questions in online algorithms on weighted k-server and generalized k-server. This has led to newinsights on a very powerful, but poorly understood method called work-functions. 5) The first polynomial space algorithm for the subset sum problem that runs much faster than in 2^n time.
