We prove that for any dimension d there exists a polynomial time algorithm for counting integral points in polyhedra in the d-dimensional Euclidean space. Previously such algorithms were known forâ€¦ (More)

be the set of all non-negative integer combinations of a1, . . . , ad, or, in other words, the semigroup S âŠ‚ Z+ of non-negative integers generated by a1, . . . , ad. What does S look like? Inâ€¦ (More)

We present real, complex, and quaternionic versions of a simple ran-domized polynomial time algorithm to approximate the permanent of a non-negative matrix and, more generally, the mixed discriminantâ€¦ (More)

We present a deterministic algorithm, which, for any given 0 < < 1 and an n Ã— n real or complex matrix A = (aij) such that |aij âˆ’ 1| â‰¤ 0.19 for all i, j computes the permanent of A within relativeâ€¦ (More)

We present algorithms for the k-Matroid Intersection Problem and for the Matroid k-Pafity Problem when the matroids are represented over the field of rational numbers and k > 2. The computationalâ€¦ (More)

We present a polynomial time algorithm to compute any fixed number of the highest coefficients of the Ehrhart quasi-polynomial of a rational simplex. Previously such algorithms were known for integerâ€¦ (More)