Minimum-weight partitioning of a set with associated subsets

TL;DR

This paper analyzes the complexity and approximation guarantees of algorithms for a set partitioning problem with applications in software testing and manufacturing, involving scheduling, precedence constraints, and duplication.

Contribution

It introduces new complexity results and performance guarantees for approximation algorithms addressing a complex partitioning and scheduling problem.

Findings

Complexity classifications for the problem.

Performance guarantees for proposed algorithms.

Relevance to software testing and manufacturing applications.

Abstract

The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where each element has an associated subset in another set, but can also be viewed as a scheduling problem with infinitely large communication delay, precedence constraints in the form of a bipartite graph, and duplication.