How the structure of precedence constraints may change the complexity class of scheduling problems

TL;DR

This survey explores how the structure of precedence constraints significantly influences the computational complexity of scheduling problems, highlighting cases where constraints alter problems from NP-hard to polynomially solvable.

Contribution

It systematically demonstrates the impact of specific precedence constraint structures on the complexity classification of scheduling problems.

Findings

Many scheduling problems are NP-hard with general constraints.

Certain structured constraints lead to polynomial-time solutions.

Research challenges remain in understanding constraint structures.

Abstract

This survey aims at demonstrating that the structure of precedence constraints plays a tremendous role on the complexity of scheduling problems. Indeed many problems can be NP-hard when considering general precedence constraints, while they become polynomially solvable for particular precedence constraints. We also show that there still are many very exciting challenges in this research area.