A heuristic algorithm for the Bin Packing Problem with Conflicts on Interval Graphs

TL;DR

This paper introduces a heuristic for the Bin Packing Problem with Conflicts on interval graphs, along with a new generator for creating such graphs, and evaluates its performance against existing methods.

Contribution

It presents a novel heuristic algorithm and a random interval graph generator for the problem, with extensive testing and comparison to prior algorithms.

Findings

The heuristic performs well on large test sets.

The new generator produces graphs with controllable edge density.

Comparative results show improvements over existing algorithms.

Abstract

In this paper we deal with the Bin Packing Problem with Conflicts on interval graphs: given an interval graph, a nonnegative integer weight for each vertex, and a nonnegative integer B, find a partition of the vertex set of the graph into k subsets such that the sum of the weights of the vertices assigned to same subset is less than or equal to B, two vertices connected by an edge do not belong to the same subset, and k is minimum. We design a heuristic algorithm, and propose a new random interval graph generator which builds interval conflict graphs with desired edge density. We test the algorithm on a huge test bed, and compare the results with existing algorithms.