Properly Weighted Independence Systems and Applications to Scheduling Problems

The theory of independence systems is powerful in combinatorial optimization. Itis well-known that the greedy algorithm solves the maximum weight independent setproblem for a matroid with any weight function. However, this may not be true fora general independence system. In this paper we propose a condition on the weightfunctions (called the proper weight functions) that guarantees the greedy solvability foran independence system. Applying this general result to scheduling problems, some newinsights, as well as new algorithms, are obtained.