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Kramling, A.; Scheibenbogen, M.; Walke, Bernhard

doi:10.1023/a:1019170405215

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Cited by 11 publications

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“…Wireless networks include cellular mobile networks, wireless computer networks [3], wireless ATM networks [17], and private mobile radio networks [23]. Bertossi, Maurizio and Bonuccelli [3](1995) introduced an integer "control code" assignment in Packet Radio Networks to avoid hidden terminal interference.…”

Section: Introductionmentioning

confidence: 99%

Optimal Channel Assignments for Lattices with Conditions at Distance Two

Griggs

Jin

19th IEEE International Parallel and Distributed Processing Symposium

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The problem of radio channel assignments with multiple levels of interference can be modeled using graph theory. Given a graph G, possibly infinite, and real numbers. . , k p )-labeling of G assigns real numbers f (x) ≥ 0 to the vertices x, such that the labels of vertices u and v differ by at least k i if u and v are at distance i apart. We denote by λ(G; k 1 , k 2 , · · · , k p ) the infimum span over such labelings f . We survey this new theory of real number labelings. When p = 2 it is enough to determine λ(G; k, 1) for reals k ≥ 0, which will be a piecewise linear function. We present the function for the square lattice (grid) and for the hexagonal lattice. For the triangular lattice, we have also solved it except for the range 1/2 ≤ k ≤ 4/5.

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Section: Introductionmentioning

confidence: 99%