A Heuristic Method for Solving the Problem of Partitioning Graphs with Supply and Demand

TL;DR

This paper introduces a two-stage greedy heuristic with correction procedures to efficiently solve large instances of the graph partitioning problem with supply and demand, achieving near-optimal solutions quickly.

Contribution

The paper proposes a novel two-stage greedy algorithm combined with hill climbing correction for large-scale MPGSD, demonstrating effective performance across various instances.

Findings

Solutions are within a few percent of optimal.

Performance depends on specific heuristic functions used.

Small solution sets can yield high-quality results.

Abstract

In this paper we present a greedy algorithm for solving the problem of the maximum partitioning of graphs with supply and demand (MPGSD). The goal of the method is to solve the MPGSD for large graphs in a reasonable time limit. This is done by using a two stage greedy algorithm, with two corresponding types of heuristics. The solutions acquired in this way are improved by applying a computationally inexpensive, hill climbing like, greedy correction procedure. In our numeric experiments we analyze different heuristic functions for each stage of the greedy algorithm, and show that their performance is highly dependent on the properties of the specific instance. Our tests show that by exploring a relatively small number of solutions generated by combining different heuristic functions, and applying the proposed correction procedure we can find solutions within only a few percent of the optimal ones.