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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Vydané v:	IET networks Ročník 8; číslo 6; s. 381 - 389
Hlavní autori:	Miri, Mohammadhasan, Mohamedpour, Kamal, Darmani, Yousef, Sarkar, Mahasweta
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	The Institution of Engineering and Technology 01.11.2019
Predmet:	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
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Abstract	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.
AbstractList	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. The vertex colouring problem (VCP) and its generalisations have myriad applications in computer networks. To solve the VCP with Δ+1 colours, numerous distributed algorithms based on LOCAL model have been proposed to reduce time complexity (the number of rounds), where 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 Δ+1 colours. Computational results on Geometry (GEOM) graphs show that the number of used colours to colour each instance using DIAMOND is about 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 (Δ+1) ‐colouring and even to (d¯+1) ‐colouring algorithms, where d¯ is the average vertex degree of the graph. They run in two and Δ rounds. The vertex colouring problem (VCP) and its generalisations have myriad applications in computer networks. To solve the VCP with colours, numerous distributed algorithms based on LOCAL model have been proposed to reduce time complexity (the number of rounds), where 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 colours. Computational results on Geometry (GEOM) graphs show that the number of used colours to colour each instance using DIAMOND is about . 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 ‐colouring and even to ‐colouring algorithms, where is the average vertex degree of the graph. They run in two and rounds.
Author	Mohamedpour, Kamal Sarkar, Mahasweta Darmani, Yousef Miri, Mohammadhasan
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Snippet	The vertex colouring problem (VCP) and its generalisations have myriad applications in computer networks. To solve the VCP with $\Delta + 1$Δ+1 colours,... The vertex colouring problem (VCP) and its generalisations have myriad applications in computer networks. To solve the VCP with Δ+1 colours, numerous... The vertex colouring problem (VCP) and its generalisations have myriad applications in computer networks. To solve the VCP with colours, numerous distributed...
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SubjectTerms	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
Title	DIAMOND: a distributed algorithm for vertex coloring problems and resource allocation
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