An investigation of the course-section assignment problem

Abstract

We investigate the problem of enumerating schedules, consisting of course-section assignments, in increasing order of the number of conflicts they contain. We define the problem formally, and then present an algorithm that systematically enumerates solutions for it. The algorithm uses backtracking to perform a depth-first search of the implicit search space defined by the problem, pruning the search space when possible. We derive a mathematical formula for the algorithm's average-case time complexity using a probabilistic approach, and also give a brief overview of its implementation in a WEB application.