Approximate Deadline-Scheduling with Precedence Constraints

TL;DR

This paper addresses a classic scheduling problem with precedence constraints, proposing an O(log k)-approximation algorithm for instances with k distinct deadlines, advancing understanding of its computational complexity.

Contribution

The paper introduces the first logarithmic approximation algorithm for scheduling with precedence constraints and multiple deadlines, improving upon previous hardness results.

Findings

Developed an O(log k)-approximation algorithm for the problem.

Proved the problem is strongly NP-hard even with unit processing times and weights.

Extended the understanding of approximability in deadline scheduling with precedence constraints.

Abstract

We consider the classic problem of scheduling a set of n jobs non-preemptively on a single machine. Each job j has non-negative processing time, weight, and deadline, and a feasible schedule needs to be consistent with chain-like precedence constraints. The goal is to compute a feasible schedule that minimizes the sum of penalties of late jobs. Lenstra and Rinnoy Kan [Annals of Disc. Math., 1977] in their seminal work introduced this problem and showed that it is strongly NP-hard, even when all processing times and weights are 1. We study the approximability of the problem and our main result is an O(log k)-approximation algorithm for instances with k distinct job deadlines.