On the Complexity of Counting the Hilbert Basis of a Linear Diophantine System
Identifieur interne : 00B011 ( Main/Merge ); précédent : 00B010; suivant : 00B012On the Complexity of Counting the Hilbert Basis of a Linear Diophantine System
Auteurs : Miki Hermann [France] ; Laurent Juban [France] ; Phokion G. Kolaitis [États-Unis]Source :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: We investigate the computational complexity of counting the Hilbert basis of a homogeneous system of linear Diophantine equations. We establish lower and upper bounds on the complexity of this problem by showing that counting the Hilbert basis is #P-hard and belongs to the class #NP. Moreover, we investigate the complexity of variants obtained by restricting the number of occurrences of the variables in the system.
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DOI: 10.1007/3-540-48242-3_2
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