### 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 |
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Title of host publication | Graph Transformation - 1st International Conference, ICGT 2002, Proceedings |

Editors | Grzegorz Rozenberg, Hans-Jörg Kreowski, Andrea Corradini, Hartmut Ehrig |

Publisher | Springer Verlag |

Pages | 393-401 |

Number of pages | 9 |

ISBN (Electronic) | 9783540443100 |

Publication status | Published - 2002 Jan 1 |

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) |
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Volume | 2505 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 1st International Conference on Graph Transformation, ICGT 2002 |
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Country | Spain |

City | Barcelona |

Period | 02/10/7 → 02/10/12 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*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.

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*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.

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

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

TY - GEN

T1 - Hierarchical vertex ordering

AU - Woo, Sung Ho

AU - Yang, Sung Bong

PY - 2002/1/1

Y1 - 2002/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84937232482&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84937232482&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84937232482

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 393

EP - 401

BT - Graph Transformation - 1st International Conference, ICGT 2002, Proceedings

A2 - Rozenberg, Grzegorz

A2 - Kreowski, Hans-Jörg

A2 - Corradini, Andrea

A2 - Ehrig, Hartmut

PB - Springer Verlag

ER -