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

Noname manuscript No. (will be inserted by the editor) 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. Keywords Graph Partitioning · Greedy Algorithm · Demand vertex · Supply vertex 1 Introduction A wide range of practical problems can be efficiently represented by means of graph partitioning. Present address: Qatar Environment and Energy Research Institute (QEERI), PO Box 5825, Doha, Qatar Abdelkader Bousselham Qatar Environment and Energy Research Institute (QEERI), PO Box 5825, Doha, Qatar Email: abousselham@qf.org.qa In this paper the focus is on the problem of maximum partitioning of a graph with supply and demand (MPGSD). This problem is defined on a graph G, in which each node is either a supply or a demand node. Each vertex v has a corresponding positive number, which is called the supply of node v; otherwise, if v is a demand node, this value would be called demand.