An overview of some single machine scheduling problems: polynomial algorithms, complexity and approximability

TL;DR

This paper reviews recent advances in polynomial algorithms, complexity, and approximability of single machine scheduling problems, highlighting key results and encouraging further research in the field.

Contribution

It provides a comprehensive overview of recent results on algorithms and complexity for single machine scheduling problems, focusing on works involving the authors.

Findings

Summary of polynomial algorithms for scheduling

Complexity classifications of various problems

Approximation results and bounds

Abstract

Since the publication of the first scheduling paper in 1954, a huge number of works dealing with different types of single machine problems appeared. They addressed many heuristics and enumerative procedures, complexity results or structural properties of certain problems. Regarding surveys, often particular subjects like special objective functions are discussed, or more general scheduling problems were surveyed, where a substantial part is devoted to single machine problems. In this paper we present some results on polynomial algorithms, complexity and approximation issues, where the main focus is on results, which have been published during the last decades in papers, where at least one of the first two authors of this paper was involved. We hope that the reviewed results will stimulate further investigation in related research fields.