Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alpert, C., Kahng, A.: A general framework for vertex orderings, with applications to netlist clustering. IEEE Trans. Very Large Scale Integrations Systems. 4(2) (1996)
Alpert, C., Kahng, A.: Multiway partitioning via geometric embeddings, orderings, and dynamic programming. IEEE Trans. Computer-Aided Design of Integrated Circuits and Systems. 14(11) (1995)
Banerjee, J., Kim, W., Kim, S., Garza, J.: Clustering a DAG for CAD databases. IEEE Trans. Software Engineering. 14(11) (1988) 1684–1699
Garey, M., Johnson, D.: Computers and intractability: A guide to the theory of NP-completeness. Freeman and Company (1979)
Hendrickson B., Leland R.: The Chaco user’s guide Version 2.0. Tech. Rep. Sandia National Laboratories (1995)
Juvan, M., Mohar, B.: Optimal linear labelings and eigenvalues of graphs. Discrete Applied Mathematics. 36 (1992) 153–168
Kaddoura, M., Ou, C., Ranka, S.: Partitioning unstructured computational graphs for nonuniform and adaptive environments. IEEE Parallel and Distributd Technology. 3(3) (1995) 63–69
Karypis, G., Kumar, V.: METIS, a software package for partitioning graphs. Available on WWW at URL: http://www.cs.umn.edu/karypis/metis/.
Karypis, G., Kumar, V.: A fast and high quality scheme for partitioning irregular graphs. SIAM Journal on Scientific Computing. 20(1) (1999) 359–392
Nagamochi, H., Ibaraki, T.: Computing edge-connectivity in multi-graphs and capacitated graphs. SIAM Journal on Discerete Mathematics. 5(1) (1992) 54–66
Petit, J.: Approximation heuristics and benchmarkings for the MINLA problem. Algorithms and Experiments. (1998) 112–128
Riess, B., Doll, K., Johannes, F.: Partitioning very large circuits using analytical placement techniques. Proc. ACM/IEEE Design Automation Conf. (1994) 645–651
Shekhar, S., Liu, D.: CCAM: A connectivity-clustered access method for networks and network computations. IEEE Trans. Knowledge and Data Engineering. 9(1) (1997)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2002 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Woo, SH., Yang, SB. (2002). Hierarchical Vertex Ordering. In: Corradini, A., Ehrig, H., Kreowski, H.J., Rozenberg, G. (eds) Graph Transformation. ICGT 2002. Lecture Notes in Computer Science, vol 2505. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45832-8_29
Download citation
DOI: https://doi.org/10.1007/3-540-45832-8_29
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-44310-0
Online ISBN: 978-3-540-45832-6
eBook Packages: Springer Book Archive