A Note on Scheduling Equal-Length Jobs to Maximize Throughput

TL;DR

This paper examines the scheduling of equal-length jobs with release times and deadlines to maximize throughput, revealing flaws in a classic algorithm and proposing a new algorithm with polynomial runtime.

Contribution

The paper corrects a longstanding algorithm and introduces a new O(n^5) algorithm for maximizing throughput in equal-length job scheduling.

Findings

Carlier's 1981 algorithm is incorrect.

Proposed an O(n^5) algorithm for the problem.

Clarified the problem's computational complexity.

Abstract

We study the problem of scheduling equal-length jobs with release times and deadlines, where the objective is to maximize the number of completed jobs. Preemptions are not allowed. In Graham's notation, the problem is described as 1|r_j;p_j=p|\sum U_j. We give the following results: (1) We show that the often cited algorithm by Carlier from 1981 is not correct. (2) We give an algorithm for this problem with running time O(n^5).