• Corpus ID: 238354202

Faster algorithm for counting of the integer points number in $\Delta$-modular polyhedra

  title={Faster algorithm for counting of the integer points number in \$\Delta\$-modular polyhedra},
  author={Dmitry V. Gribanov and Dmitriy S. Malyshev},
Let a polytope P be defined by one of the following ways: (i) P = {x ∈ R : Ax ≤ b}, where A ∈ Z, b ∈ Q, rank(A) = n and d := dim(P) = n; (ii) P = {x ∈ R+ : Ax = b}, where A ∈ Z , b ∈ Z, rank(A) = m and d := dim(P) = n−m; and let all the rank-order sub-determinants of A be bounded by ∆ in the absolute values. We show that | P ∩Z | can be computed with an algorithm, having the arithmetic complexity bound O ( ν(d,m,∆) · d ·∆ · log(∆) ) , where ν(d,m,∆) is the maximal possible number of vertices in… 


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