Clustering a DAG for CAD Databases
IEEE Transactions on Software Engineering
Computing edge-connectivity in multigraphs and capacitated graphs
SIAM Journal on Discrete Mathematics
Optimal linear labelings and eigenvalues of graphs
Discrete Applied Mathematics
Partitioning very large circuits using analytical placement techniques
DAC '94 Proceedings of the 31st annual Design Automation Conference
A general framework for vertex orderings with applications to circuit clustering
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs
SIAM Journal on Scientific Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Partitioning Unstructured Computational Graphs for Nonuniform and Adaptive Environments
IEEE Parallel & Distributed Technology: Systems & Technology
CCAM: A Connectivity-Clustered Access Method for Networks and Network Computations
IEEE Transactions on Knowledge and Data Engineering
Multiway partitioning via geometric embeddings, orderings, and dynamic programming
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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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, 10, 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.