Hierarchical vertex ordering

The k-way graph partitioning problem has been solved well through vertex ordering and dynamic programming which splits a vertex order into k clusters [2, 12]. In order to obtain "good clusters" in terms of the partitioning objective, tightly connected vertices in a given graph should be closely placed on the vertex order. In this paper we present a simple vertex ordering method called hierarchical vertex ordering (HVO). Given a weighted undirected graph, HVO generates a series of graphs through graph matching to construct a tree. A vertex order is then obtained by visiting each nonleaf node in the tree and by ordering its children properly. In the experiments, dynamic programming [2] is applied to the vertex orders generated by HVO as well as various vertex ordering methods [1,6,9-11] in order to solve the k-way graph partitioning problem. The solutions derived from the vertex orders are then comapred. Our experimental results show that HVO outperforms other methods for almost all cases in terms of the partitioning objective. HVO is also very simple and straightforward.