Scheduling partially ordered jobs faster than 2^n

TL;DR

This paper proves that the SCHED problem, involving scheduling jobs with precedence constraints, can be solved faster than the traditional 2^n exponential time, answering an open question from 2004.

Contribution

It demonstrates the existence of an algorithm for SCHED with a runtime of O(c^n) for some c < 2, improving upon the previous 2^n time complexity.

Findings

Established a faster algorithm for SCHED with exponential base less than 2.

Resolved an open problem posed by Woeginger in 2004.

Advances the understanding of scheduling problems with precedence constraints.

Abstract

In the SCHED problem we are given a set of n jobs, together with their processing times and precedence constraints. The task is to order the jobs so that their total completion time is minimized. SCHED is a special case of the Traveling Repairman Problem with precedences. A natural dynamic programming algorithm solves both these problems in 2^n n^O(1) time, and whether there exists an algorithms solving SCHED in O(c^n) time for some constant c < 2 was an open problem posted in 2004 by Woeginger. In this paper we answer this question positively.