Channel Assignment for Wireless Networks Modelled as d-Dimensional Square Grids

Dubhashi, Aniket; Mvs, Shashanka; Pati, Amrita; Shashank, R.; Shende, Anil M.

doi:10.1007/3-540-36385-8_14

Cited by 15 publications

(7 citation statements)

References 9 publications

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“…Optimal L(2,1)-labellings for d-dimensional square grids, for each d ! 1 are presented in [64]. These results are extended to any h, k for each d !…”

Section: Regular Gridsmentioning

confidence: 91%

The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography

Calamoneri

2006

The Computer Journal

140

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Given any fixed non-negative integer values h and k, the L(h, k)-labelling problem consists in an assignment of non-negative integers to the nodes of a graph such that adjacent nodes receive values which differ by at least h, and nodes connected by a 2 length path receive values which differ by at least k. The span of an L(h, k)-labelling is the difference between the largest and the smallest assigned frequency. The goal of the problem is to find out an L(h, k)-labelling with minimum span. The L(h, k)-labelling problem has been intensively studied following many approaches and restricted to many special cases, concerning both the values of h and k and the considered classes of graphs. This paper reviews the results from previous by published literature, looking at the problem with a graph algorithmic approach.

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“…Optimal L(2,1)-labellings for d-dimensional square grids, for each d ! 1 are presented in [64]. These results are extended to any h, k for each d !…”

Section: Regular Gridsmentioning

confidence: 91%

The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography

Calamoneri

2006

The Computer Journal

140

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“…The overall network can then be modelled in a suitably higher dimension. Optimal L(2, 1)-labellings for ddimensional square grids, for each d ≥ 1 are presented in [53]. These results are extended to any h, k for each d ≥ 1 in [61].…”

Section: Regular Gridsmentioning

confidence: 99%

The L(h, k)-Labelling Problem: An Updated Survey and Annotated Bibliography

Calamoneri

2011

The Computer Journal

160

104

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Given any fixed nonnegative integer values h and k, the L(h, k)labelling problem consists in an assignment of nonnegative integers to the nodes of a graph such that adjacent nodes receive values which differ by at least h, and nodes connected by a 2 length path receive values which differ by at least k. The span of an L(h, k)-labelling is the difference between the largest and the smallest assigned frequency. The goal of the problem is to find out an L(h, k)-labelling with minimum span. The L(h, k)-labelling problem has been intensively studied following many approaches and restricted to many special cases, concerning both the values of h and k and the considered classes of graphs. This paper reviews the results from previous by published literature, looking at the problem with a graph algorithmic approach. It is an update of a previous survey written by the same author.

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“…The channel assignment problem is usually formulated in the engineering literature as a nonlinear optimization problem. A huge collection of contributions in IEEE journals explore various aspects of current research on radio channel assignment problems, among them "IEEE Transactions on Vehicular Technology" [1,2,4,16,18,20,21,25,33,40,42,49,50,51], "IEEE Transactions on Wireless Communication" [15,30], "IEEE/ACM Transactions on Networking" [3,5], "IEEE/ACM Transactions on Parallel and Distributed Systems" [7,32], "Wireless Networks" [39,46,52], and IEEE Conferences [6,9,10,17,27,44].…”

Section: Recent Progress On Channel Assignmentsmentioning

confidence: 99%

“…Concerning graph models of wireless networks, Dubhashi et al [17] present bounds on the minimum span for L(2, 1, 1, · · · , 1)-labelling of the d-dimensional square lattice (grid), in which V (G) = Z p , and two vertices, say (x 1 , x 2 , . .…”

Section: Future Research Directionsmentioning

confidence: 99%

Recent progress in mathematics and engineering on optimal graph labellings with distance conditions

Griggs

Jin

2007

J Comb Optim

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The problem of radio channel assignments with multiple levels of interference can be modelled using graph theory. The theory of integer vertex-labellings of graphs with distance conditions has been investigated for several years now, and the authors recently introduced a new model of real number labellings that is giving deeper insight into the problems. Here we present an overview of the recent outpouring of papers in the engineering literature on such channel assignment problems, with the goal of strengthening connections to applications. Secondly, we present a new contribution to the theory, the formulas for the optimal span of labellings with conditions at distance two for finite complete bipartite graphs.

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Channel Assignment for Wireless Networks Modelled as d-Dimensional Square Grids

Cited by 15 publications

References 9 publications

The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography

The L(h, k)-Labelling Problem: A Survey and Annotated Bibliography

The L(h, k)-Labelling Problem: An Updated Survey and Annotated Bibliography

Recent progress in mathematics and engineering on optimal graph labellings with distance conditions

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