On the benchmark instances for the Bin Packing with Conflicts

TL;DR

This paper investigates the nature of conflict graphs in the Bin Packing Problem with Conflicts, revealing that commonly used random graph generators produce threshold graphs, which are easier to solve than arbitrary conflict graphs.

Contribution

The study proves that the generated conflict graphs are threshold graphs and demonstrates their impact on problem difficulty through computational experiments.

Findings

Generated conflict graphs are threshold graphs.

Instances with threshold conflict graphs are easier to solve.

Threshold graphs influence the complexity of bin packing instances.

Abstract

Many authors, mainly in the context of the Bin Packing Problem with Conflicts, used the random graph generator proposed in "Heuristics and lower bounds for the bin packing problem with conflicts" [M. Gendreau, G. Laporte, and F. Semet, Computers & Operations Research, 31:347-358, 2004]. In this paper we prove that the graphs generated in this way are not arbitrary but threshold ones. Computational results show that instances with threshold conflict graphs are easier to solve w.r.t. instances with arbitrary conflict graphs.