Hierarchical vertex ordering

Sung Ho Woo, Sung Bong Yang

Research output: Chapter in Book/Report/Conference proceedingConference 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 languageEnglish
Title of host publicationGraph Transformation - 1st International Conference, ICGT 2002, Proceedings
EditorsGrzegorz Rozenberg, Hans-Jörg Kreowski, Andrea Corradini, Hartmut Ehrig
PublisherSpringer Verlag
Pages393-401
Number of pages9
ISBN (Electronic)9783540443100
Publication statusPublished - 2002 Jan 1
Event1st International Conference on Graph Transformation, ICGT 2002 - Barcelona, Spain
Duration: 2002 Oct 72002 Oct 12

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2505
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other1st International Conference on Graph Transformation, ICGT 2002
CountrySpain
CityBarcelona
Period02/10/702/10/12

Fingerprint

Dynamic programming
Vertex of a graph
Experiments
Graph Partitioning
Dynamic Programming
Partitioning
Graph Matching
Weighted Graph
Graph in graph theory
Undirected Graph

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Woo, S. H., & Yang, S. B. (2002). Hierarchical vertex ordering. In G. Rozenberg, H-J. Kreowski, A. Corradini, & H. Ehrig (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.
Woo, Sung Ho ; Yang, Sung Bong. / Hierarchical vertex ordering. Graph Transformation - 1st International Conference, ICGT 2002, Proceedings. editor / Grzegorz Rozenberg ; Hans-Jörg Kreowski ; Andrea Corradini ; Hartmut Ehrig. Springer Verlag, 2002. pp. 393-401 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{811462b1e7fb4482b7231a4aa606db78,
title = "Hierarchical vertex ordering",
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.",
author = "Woo, {Sung Ho} and Yang, {Sung Bong}",
year = "2002",
month = "1",
day = "1",
language = "English",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "393--401",
editor = "Grzegorz Rozenberg and Hans-J{\"o}rg Kreowski and Andrea Corradini and Hartmut Ehrig",
booktitle = "Graph Transformation - 1st International Conference, ICGT 2002, Proceedings",
address = "Germany",

}

Woo, SH & Yang, SB 2002, Hierarchical vertex ordering. in G Rozenberg, H-J Kreowski, A Corradini & H Ehrig (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.

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

Graph Transformation - 1st International Conference, ICGT 2002, Proceedings. ed. / Grzegorz Rozenberg; Hans-Jörg Kreowski; Andrea Corradini; Hartmut Ehrig. 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 proceedingConference 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 -

Woo SH, Yang SB. Hierarchical vertex ordering. In Rozenberg G, Kreowski H-J, Corradini A, Ehrig H, 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)).