Fast Scheduling of Weighted Unit Jobs with Release Times and Deadlines

Abstract

We present a fast algorithm for the following classic scheduling problem: Determine a maximum-weight schedule for a collection of unit jobs, each of which has an associated release time, deadline, and weight. All previous algorithms for this problem have at least quadratic worst-case complexity. This job scheduling problem can also be viewed as a special case of weighted bipartite matching: each job represents a vertex on the left side of the bipartite graph; each time slot represents a vertex on the right side; each job is connected by an edge to all time slots between its release time and deadline; all of the edges adjacent to a given job have weight equal to the weight of the job. Letting U denote the set of jobs and V denote the set of time slots, our algorithm runs in O(|U| + klog2 k) time, where k ≤ min {|U|,|V|} denotes the cardinality of a maximum-cardinality matching. Thus our algorithm runs in nearly linear time, a dramatic improvement over the previous quadratic bounds.KeywordsBipartite GraphGreedy AlgorithmLogarithmic TimeBipartite MatchNode MethodThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.