| Title: | 2-local 3/4-competitive algorithm for multicoloring hexagonal graphs |
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| Authors: | ID Šparl, Petra (Author)
ID Žerovnik, Janez (Author) |
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| Files: |  http://dx.doi.org/10.1016/j.jalgor.2004.09.001
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| Language: | English |
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| Work type: | Unknown |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: | FGPA - Faculty of Civil Engineering, Transportation Engineering and Architecture
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| 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. |
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| Keywords: | mathematics, graph theory, graph colouring, 2-local distributed algorithm, cellular networks, frequency planning |
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| Year of publishing: | 2005 |
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| PID: | 20.500.12556/DKUM-27020  |
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| UDC: | 519.17 |
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| ISSN on article: | 0196-6774 |
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| COBISS.SI-ID: | 9538582 |
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| NUK URN: | URN:SI:UM:DK:BV6K7TAP |
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| Publication date in DKUM: | 01.06.2012 |
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| Views: | 2662 |
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| Downloads: | 100 |
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| Metadata: |    |
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| Categories: | Misc.
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