Sciweavers

Share
IPPS
2005
IEEE

Optimal Channel Assignments for Lattices with Conditions at Distance Two

10 years 12 months ago
Optimal Channel Assignments for Lattices with Conditions at Distance Two
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 k1, k2, . . . , kp ≥ 0, a L(k1, k2, . . . , kp)-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 ki if u and v are at distance i apart. We denote by λ(G; k1, k2, · · · , kp) 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.
Jerrold R. Griggs, Xiaohua Teresa Jin
Added 25 Jun 2010
Updated 25 Jun 2010
Type Conference
Year 2005
Where IPPS
Authors Jerrold R. Griggs, Xiaohua Teresa Jin
Comments (0)
books