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A new approach to covering

Part of: Discrete geometry

Published online by Cambridge University Press:  26 February 2010

Ulrich Betke ,
Martin Henk  and
Jörg M. Wills
Ulrich Betke
Affiliation:
Mathematisches Institut, Universität Siegen, Hölderlinstrasse 3, D-57068, Siegen, Germany.
Martin Henk
Affiliation:
Technische Universität Berlin, Sekr, MA6-1, Strasse des 17 Juni 136, D-10623 Berlin, Germany.
Jörg M. Wills
Affiliation:
Mathematisches Institut, Universität Siegen, Hölderlinstrasse 3, D-57068, Siegen, Germany.
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Abstract

For finite coverings in euclidean d-space Ed we introduce a parametric density function. Here the parameter controls the influence of the boundary of the covered region to the density. This definition gives a new approach to covering which is similar to the approach for packing in [BHW1], [BHW2]. In this way we obtain a unified theory for finite and infinite covering and generalize similar results, which were developed by various authors since 1950 for d=2, to all dimensions.

MSC classification

Secondary: 52C17: Packing and covering in $n$ dimensions
Type
Research Article
Information
Mathematika , Volume 42 , Issue 2 , December 1995 , pp. 251 - 263
Copyright
Copyright © University College London 1995

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