2-local 3/4-competitive algorithm for multicoloring hexagonal graphs

Šparl, Petra; Žerovnik, Janez

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Title:	2-local 3/4-competitive algorithm for multicoloring hexagonal graphs
Authors:	ID Šparl, Petra (Author) ID Žerovnik, Janez (Author)
Files:	http://dx.doi.org/10.1016/j.jalgor.2004.09.001
Language:	English
Work type:	Unknown
Typology:	1.01 - Original Scientific Article
Organization:	FGPA - Faculty of Civil Engineering, Transportation Engineering and Architecture
Abstract:	An important optimization problem in the design of cellular networks is to assign sets of frequencies to transmitters to avoid unacceptable interference.A cellular network is generally modeled as a subgraph of the infinite triangular lattice. Frequency assignment problem can be abstracted asa multicoloring problem on a weighted hexagonal graph, where the weights represent the number of calls to be assigned at vertices. In this paper we present a distributed algorithm for multicoloring hexagonal graphs using only the local clique numbers $omega_1(v)$ and $omega_2(v)$ at each vertex v of the given hexagonal graph, which can be computed from local information available at thevertex. We prove the algorithm uses no more than $4omega(G)/3$ colors for any hexagonal graph G, without explicitly computing the global clique number $omega(G)$ . We also prove that our algorithm is 2-local, i.e., the computation at a vertex v $in$ G uses only information about the demands of vertices whose graph distance from v is less than or equal to 2.
Keywords:	mathematics, graph theory, graph colouring, 2-local distributed algorithm, cellular networks, frequency planning
Year of publishing:	2005
PID:	20.500.12556/DKUM-27020
UDC:	519.17
ISSN on article:	0196-6774
COBISS.SI-ID:	9538582
NUK URN:	URN:SI:UM:DK:BV6K7TAP
Publication date in DKUM:	01.06.2012
Views:	2403
Downloads:	97
Metadata:
Categories:	Misc.
:	ŠPARL, Petra and ŽEROVNIK, Janez, 2005, 2-local 3/4-competitive algorithm for multicoloring hexagonal graphs. Journal of algorithms [online]. 2005. [Accessed 22 March 2025]. Retrieved from: http://dx.doi.org/10.1016/j.jalgor.2004.09.001 Copy citation

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Record is a part of a journal

Title:	Journal of algorithms
Shortened title:	J. algorithms
Publisher:	Academic Press.
ISSN:	0196-6774
COBISS.SI-ID:	25704704

Secondary language

Language:	English
Keywords:	matematika, teorija grafov, barvanje grafov, algoritem

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