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IPPS

2005

IEEE

2005

IEEE

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.

Related Content

Added |
25 Jun 2010 |

Updated |
25 Jun 2010 |

Type |
Conference |

Year |
2005 |

Where |
IPPS |

Authors |
Jerrold R. Griggs, Xiaohua Teresa Jin |

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