Optimal Channel Assignments for Lattices with Conditions at Distance Two

Authors:
Jerrold R. Griggs;Xiaohua Teresa Jin
Affiliations:
University of South Carolina, Columbia, SC;University of South Carolina, Columbia, SC
Venue:
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Workshop 12 - Volume 13
Year:
2005

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Abstract

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驴, k驴, ..., k_p 驴 0, a L(k驴, k驴, ..., k_p )-labeling of G assigns real numbers f(x) 驴 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 驴(G; k驴, k驴, ..., 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 驴(G; k, 1) for reals k 驴 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驴k驴4/5.