Fast Unimodular Counting

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Fast Unimodular Counting
This paper describes methods for counting the number of non-negative integer solutions of the system Ax = b when A is a non-negative totally unimodular matrix and b an integral vector of fixed dimension. The complexity (under a unit cost arithmetic model) is strong in the sense that it depends only on the dimensions of A and not on the size of the entries of b. For the special case of "contingency tables" the run time is 2O( d log d) (d the dimension of the polytope). The method is complementary to Barvinok's in that our algorithm is effective on problems of high dimension with a fixed number of (non-sign) constraints whereas Barvinok's algorithms are effective on problems of low dimension and an arbitrary number of constraints.
John Mount
Added 17 Dec 2010
Updated 17 Dec 2010
Type Journal
Year 2000
Where CPC
Authors John Mount
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