ISSN:
1432-0444
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract. We present a hierarchy of covering properties of rational convex cones with respect to the unimodular subcones spanned by the Hilbert basis. For two of the concepts from the hierarchy we derive characterizations: a description of partitions that leads to a natural integer programming formulation for the HILBERT PARTITION problem, and a characterization of ``binary covers'' that admits a linear algebra test over GF(2) for the existence of BINARY HILBERT COVERS. Implementation of our test leads to interesting new examples, among them: cones that have a HILBERT PARTITION but no REGULAR one; a four-dimensional cone with unimodular facets that has no HILBERT PARTITION; and two five-dimensional cones that do not have any BINARY HILBERT COVER.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/PL00009416
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