DIAMOND: a distributed algorithm for vertex coloring problems and resource allocation

The vertex colouring problem (VCP) and its generalisations have myriad applications in computer networks. To solve the VCP with $\Delta + 1$Δ+1 colours, numerous distributed algorithms based on LOCAL model have been proposed to reduce time complexity (the number of rounds), where $\Delta $Δ is the m...

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Bibliographic Details
Published in:IET networks Vol. 8; no. 6; pp. 381 - 389
Main Authors: Miri, Mohammadhasan, Mohamedpour, Kamal, Darmani, Yousef, Sarkar, Mahasweta
Format: Journal Article
Language:English
Published: The Institution of Engineering and Technology 01.11.2019
Subjects:
computer networks
DIAMOND
distributed algorithm
distributed algorithms
GEOM graphs
graph colouring
greedily generalised VCP
maximum vertex degree
modified LOCAL model
myriad applications
Research Article
resource allocation
resource allocation algorithms
vertex colouring problem
vertex colouring problem
modified LOCAL model
DIAMOND
myriad applications
computer networks
graph colouring
distributed algorithm
resource allocation
maximum vertex degree
greedily generalised VCP
distributed algorithms
resource allocation algorithms
GEOM graphs
ISSN:2047-4954, 2047-4962, 2047-4962
Online Access:Get full text
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Summary:The vertex colouring problem (VCP) and its generalisations have myriad applications in computer networks. To solve the VCP with $\Delta + 1$Δ+1 colours, numerous distributed algorithms based on LOCAL model have been proposed to reduce time complexity (the number of rounds), where $\Delta $Δ is the maximum vertex degree in the graph. In this paper, the authors present a distributed algorithm based on modified LOCAL model (DIAMOND) that reduces the number of rounds to one. It greedily solves the VCP with at most $\Delta + 1$Δ+1 colours. Computational results on Geometry (GEOM) graphs show that the number of used colours to colour each instance using DIAMOND is about $\left({\Delta + 1} \right)/2$Δ+1/2. DIAMOND is easily extended to solve greedily generalised VCPs in only one round. Moreover, they present two efficient resource allocation algorithms using DIAMOND. They allocate more resource to the graph compared with $\lpar \Delta + 1\rpar $(Δ+1)-colouring and even to $\lpar \bar d + 1\rpar $(d¯+1)-colouring algorithms, where $\bar d$d¯ is the average vertex degree of the graph. They run in two and $\Delta $Δ rounds.
ISSN:2047-4954
2047-4962
2047-4962
DOI:10.1049/iet-net.2018.5204