The properties and algorithm of the interval scheduling problems based on the conflict set

In interval scheduling, the processing times of jobs and their starting times are given. These interval scheduling problems are popular in practice, such as classes timetabling, crew scheduling, airport gate assignment and bandwidth trading problem. Based on the idea of conflict sets and the limited array product, we formulate the interval scheduling problems, give the expression of solution space, structure, all solutions and the related properties. Finally, a dynamic programming method and a heuristic algorithm for the interval scheduling problem is given, by which we get good results.