Output-sensitive cell enumeration in hyperplane arrangements

Authors:
Nora H. Sleumer
Affiliations:
Institut für Theoretische Informatik, ETH Zentrum, 8092 Zürich, Switzerland
Venue:
Nordic Journal of Computing
Year:
1999

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Abstract

We present a simple and practical algorithm for enumerating the set of cells C of an arrangement of m hyperplanes. For fixed dimension its time complexity is O(m.|C|). This is an improvement by a factor of m over the reverse search algorithm by Avis and Fukuda. The algorithm needs little space, is output-sensitive, straightforward to parallelize and the implementation is simple for all dimensions.