Heuristic algorithms for the min-max edge 2-coloring problem

Radu Stefan Mincu, Alexandru Popa

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In multi-channel Wireless Mesh Networks (WMN), each node is able to use multiple non-overlapping frequency channels. Raniwala et al. (MC2R 2004, INFOCOM 2005) propose and study several such architectures in which a computer can have multiple network interface cards. These architectures are modeled as a graph problem named maximum edge q-coloring and studied in several papers by Feng et. al (TAMC 2007), Adamaszek and Popa (ISAAC 2010, JDA 2016). Later on Larjomaa and Popa (IWOCA 2014, JGAA 2015) define and study an alternative variant, named the min-max edge q-coloring. The above mentioned graph problems, namely the maximum edge q-coloring and the min-max edge q-coloring are studied mainly from the theoretical perspective. In this paper, we study the min-max edge 2-coloring problem from a practical perspective. More precisely, we introduce, implement and test four heuristic approximation algorithms for the min-max edge 2-coloring problem. These algorithms are based on a Breadth First Search (BFS)-based heuristic and on local search methods like basic hill climbing, simulated annealing and tabu search techniques, respectively. Although several algorithms for particular graph classes were proposed by Larjomaa and Popa (e.g., trees, planar graphs, cliques, bi-cliques, hypergraphs), we design the first algorithms for general graphs. We study and compare the running data for all algorithms on Unit Disk Graphs, as well as some graphs from the DIMACS vertex coloring benchmark dataset.

Original languageEnglish
Title of host publicationComputing and Combinatorics - 24th International Conference, COCOON 2018, Proceedings
EditorsDaming Zhu, Lusheng Wang
PublisherSpringer Verlag
Pages662-674
Number of pages13
ISBN (Print)9783319947754
DOIs
Publication statusPublished - Jan 1 2018
Event24th International Conference on Computing and Combinatorics Conference, COCOON 2018 - Qing Dao, China
Duration: Jul 2 2018Jul 4 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10976 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other24th International Conference on Computing and Combinatorics Conference, COCOON 2018
CountryChina
CityQing Dao
Period7/2/187/4/18

Fingerprint

Coloring
Heuristic algorithms
Min-max
Heuristic algorithm
Colouring
Graph in graph theory
Clique
Unit Disk Graph
Breadth-first Search
Hill Climbing
Wireless Mesh Networks
Vertex Coloring
Graph Classes
Tabu Search
Wireless mesh networks (WMN)
Tabu search
Hypergraph
Search Methods
Simulated Annealing
Planar graph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Mincu, R. S., & Popa, A. (2018). Heuristic algorithms for the min-max edge 2-coloring problem. In D. Zhu, & L. Wang (Eds.), Computing and Combinatorics - 24th International Conference, COCOON 2018, Proceedings (pp. 662-674). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10976 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-94776-1_55

Heuristic algorithms for the min-max edge 2-coloring problem. / Mincu, Radu Stefan; Popa, Alexandru.

Computing and Combinatorics - 24th International Conference, COCOON 2018, Proceedings. ed. / Daming Zhu; Lusheng Wang. Springer Verlag, 2018. p. 662-674 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10976 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Mincu, RS & Popa, A 2018, Heuristic algorithms for the min-max edge 2-coloring problem. in D Zhu & L Wang (eds), Computing and Combinatorics - 24th International Conference, COCOON 2018, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 10976 LNCS, Springer Verlag, pp. 662-674, 24th International Conference on Computing and Combinatorics Conference, COCOON 2018, Qing Dao, China, 7/2/18. https://doi.org/10.1007/978-3-319-94776-1_55
Mincu RS, Popa A. Heuristic algorithms for the min-max edge 2-coloring problem. In Zhu D, Wang L, editors, Computing and Combinatorics - 24th International Conference, COCOON 2018, Proceedings. Springer Verlag. 2018. p. 662-674. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-94776-1_55
Mincu, Radu Stefan ; Popa, Alexandru. / Heuristic algorithms for the min-max edge 2-coloring problem. Computing and Combinatorics - 24th International Conference, COCOON 2018, Proceedings. editor / Daming Zhu ; Lusheng Wang. Springer Verlag, 2018. pp. 662-674 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{b879606753b14026930831b3b45d035f,
title = "Heuristic algorithms for the min-max edge 2-coloring problem",
abstract = "In multi-channel Wireless Mesh Networks (WMN), each node is able to use multiple non-overlapping frequency channels. Raniwala et al. (MC2R 2004, INFOCOM 2005) propose and study several such architectures in which a computer can have multiple network interface cards. These architectures are modeled as a graph problem named maximum edge q-coloring and studied in several papers by Feng et. al (TAMC 2007), Adamaszek and Popa (ISAAC 2010, JDA 2016). Later on Larjomaa and Popa (IWOCA 2014, JGAA 2015) define and study an alternative variant, named the min-max edge q-coloring. The above mentioned graph problems, namely the maximum edge q-coloring and the min-max edge q-coloring are studied mainly from the theoretical perspective. In this paper, we study the min-max edge 2-coloring problem from a practical perspective. More precisely, we introduce, implement and test four heuristic approximation algorithms for the min-max edge 2-coloring problem. These algorithms are based on a Breadth First Search (BFS)-based heuristic and on local search methods like basic hill climbing, simulated annealing and tabu search techniques, respectively. Although several algorithms for particular graph classes were proposed by Larjomaa and Popa (e.g., trees, planar graphs, cliques, bi-cliques, hypergraphs), we design the first algorithms for general graphs. We study and compare the running data for all algorithms on Unit Disk Graphs, as well as some graphs from the DIMACS vertex coloring benchmark dataset.",
author = "Mincu, {Radu Stefan} and Alexandru Popa",
year = "2018",
month = "1",
day = "1",
doi = "10.1007/978-3-319-94776-1_55",
language = "English",
isbn = "9783319947754",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "662--674",
editor = "Daming Zhu and Lusheng Wang",
booktitle = "Computing and Combinatorics - 24th International Conference, COCOON 2018, Proceedings",
address = "Germany",

}

TY - GEN

T1 - Heuristic algorithms for the min-max edge 2-coloring problem

AU - Mincu, Radu Stefan

AU - Popa, Alexandru

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In multi-channel Wireless Mesh Networks (WMN), each node is able to use multiple non-overlapping frequency channels. Raniwala et al. (MC2R 2004, INFOCOM 2005) propose and study several such architectures in which a computer can have multiple network interface cards. These architectures are modeled as a graph problem named maximum edge q-coloring and studied in several papers by Feng et. al (TAMC 2007), Adamaszek and Popa (ISAAC 2010, JDA 2016). Later on Larjomaa and Popa (IWOCA 2014, JGAA 2015) define and study an alternative variant, named the min-max edge q-coloring. The above mentioned graph problems, namely the maximum edge q-coloring and the min-max edge q-coloring are studied mainly from the theoretical perspective. In this paper, we study the min-max edge 2-coloring problem from a practical perspective. More precisely, we introduce, implement and test four heuristic approximation algorithms for the min-max edge 2-coloring problem. These algorithms are based on a Breadth First Search (BFS)-based heuristic and on local search methods like basic hill climbing, simulated annealing and tabu search techniques, respectively. Although several algorithms for particular graph classes were proposed by Larjomaa and Popa (e.g., trees, planar graphs, cliques, bi-cliques, hypergraphs), we design the first algorithms for general graphs. We study and compare the running data for all algorithms on Unit Disk Graphs, as well as some graphs from the DIMACS vertex coloring benchmark dataset.

AB - In multi-channel Wireless Mesh Networks (WMN), each node is able to use multiple non-overlapping frequency channels. Raniwala et al. (MC2R 2004, INFOCOM 2005) propose and study several such architectures in which a computer can have multiple network interface cards. These architectures are modeled as a graph problem named maximum edge q-coloring and studied in several papers by Feng et. al (TAMC 2007), Adamaszek and Popa (ISAAC 2010, JDA 2016). Later on Larjomaa and Popa (IWOCA 2014, JGAA 2015) define and study an alternative variant, named the min-max edge q-coloring. The above mentioned graph problems, namely the maximum edge q-coloring and the min-max edge q-coloring are studied mainly from the theoretical perspective. In this paper, we study the min-max edge 2-coloring problem from a practical perspective. More precisely, we introduce, implement and test four heuristic approximation algorithms for the min-max edge 2-coloring problem. These algorithms are based on a Breadth First Search (BFS)-based heuristic and on local search methods like basic hill climbing, simulated annealing and tabu search techniques, respectively. Although several algorithms for particular graph classes were proposed by Larjomaa and Popa (e.g., trees, planar graphs, cliques, bi-cliques, hypergraphs), we design the first algorithms for general graphs. We study and compare the running data for all algorithms on Unit Disk Graphs, as well as some graphs from the DIMACS vertex coloring benchmark dataset.

UR - http://www.scopus.com/inward/record.url?scp=85049690191&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049690191&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-94776-1_55

DO - 10.1007/978-3-319-94776-1_55

M3 - Conference contribution

SN - 9783319947754

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

SP - 662

EP - 674

BT - Computing and Combinatorics - 24th International Conference, COCOON 2018, Proceedings

A2 - Zhu, Daming

A2 - Wang, Lusheng

PB - Springer Verlag

ER -