van den Heuvel, Jan
(2002)
*Radio channel assignment on 2-dimensional lattices.*
Annals of Combinatorics, 6
(3-4).
pp. 463-477.
ISSN 0218-0006

## Abstract

Given a set V of points in the plane, a sequence d0d1dk of nonnegative numbers and an integer n, we are interested in the problem to assign integers from 0n−1 to the points in V such that if xyV are two points with Euclidean distance less than dj, then the difference between the labels of x and y is not equal to i. This question is inspired by problems occurring in the design of radio networks, where radio channels need to be assigned to transmitters in such a way that interference is minimized. In this paper we consider the case that the set of points are the points of a 2-dimensional lattice. Recent results by McDiarmid and Reed show that if only one constraint d0 is given, good labellings can be obtained by using so-called strict tilings. We extend these results to the case that higher level constraints d0d1dk occur. In particular we study conditions that guarantee that a strict tiling, satisfying only the one constraint d0, can be transformed to a strict tiling satisfying the higher order constraints as well. Special attention is devoted to the case that the points are the points of a triangular lattice.

Item Type: | Article |
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Official URL: | http://www.springerlink.com/content/0218-0006/ |

Additional Information: | © 2002 Springer |

Library of Congress subject classification: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Rights: | http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx |

Date Deposited: | 31 Oct 2008 09:08 |

URL: | http://eprints.lse.ac.uk/15853/ |

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