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.

• Type: Conference
• Year: 2005
• Where: IPPS
• Authors: Jerrold R. Griggs, Xiaohua Teresa Jin
• Keywords: Assigns Real Numbers, Distributed And Parallel Computing, IPPS 2005, Radio Channel Assignments, Real Number