Hierarchical vertex ordering

Sung Ho Woo; Sung Bong Yang

doi:10.1007/3-540-45832-8_29

Hierarchical vertex ordering

Sung Ho Woo, Sung Bong Yang

Department of Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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.

Original language	English
Title of host publication	Graph Transformation - 1st International Conference, ICGT 2002, Proceedings
Editors	Andrea Corradini, Hartmut Ehrig, Hans-Jörg Kreowski, Grzegorz Rozenberg
Publisher	Springer Verlag
Pages	393-401
Number of pages	9
ISBN (Electronic)	9783540443100
DOIs	https://doi.org/10.1007/3-540-45832-8_29
Publication status	Published - 2002
Event	1st International Conference on Graph Transformation, ICGT 2002 - Barcelona, Spain Duration: 2002 Oct 7 → 2002 Oct 12

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	2505
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Other

Other	1st International Conference on Graph Transformation, ICGT 2002
Country	Spain
City	Barcelona
Period	02/10/7 → 02/10/12

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2002.

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Computer Science(all)

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10.1007/3-540-45832-8_29

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Woo, S. H., & Yang, S. B. (2002). Hierarchical vertex ordering. In A. Corradini, H. Ehrig, H-J. Kreowski, & G. Rozenberg (Eds.), Graph Transformation - 1st International Conference, ICGT 2002, Proceedings (pp. 393-401). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2505). Springer Verlag. https://doi.org/10.1007/3-540-45832-8_29

Woo, Sung Ho ; Yang, Sung Bong. / Hierarchical vertex ordering. Graph Transformation - 1st International Conference, ICGT 2002, Proceedings. editor / Andrea Corradini ; Hartmut Ehrig ; Hans-Jörg Kreowski ; Grzegorz Rozenberg. Springer Verlag, 2002. pp. 393-401 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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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.",

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Woo, SH & Yang, SB 2002, Hierarchical vertex ordering. in A Corradini, H Ehrig, H-J Kreowski & G Rozenberg (eds), Graph Transformation - 1st International Conference, ICGT 2002, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2505, Springer Verlag, pp. 393-401, 1st International Conference on Graph Transformation, ICGT 2002, Barcelona, Spain, 02/10/7. https://doi.org/10.1007/3-540-45832-8_29

Hierarchical vertex ordering. / Woo, Sung Ho; Yang, Sung Bong.

Graph Transformation - 1st International Conference, ICGT 2002, Proceedings. ed. / Andrea Corradini; Hartmut Ehrig; Hans-Jörg Kreowski; Grzegorz Rozenberg. Springer Verlag, 2002. p. 393-401 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2505).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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AU - Woo, Sung Ho

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PY - 2002

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Woo SH, Yang SB. Hierarchical vertex ordering. In Corradini A, Ehrig H, Kreowski H-J, Rozenberg G, editors, Graph Transformation - 1st International Conference, ICGT 2002, Proceedings. Springer Verlag. 2002. p. 393-401. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-45832-8_29

Hierarchical vertex ordering

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