55 citations · 115 across the 15 of their papers we have counts for
6 papers · 1 filter
How to Find the Convex Hull of All Integer Points in a Polyhedron?
S. O. Semenov, N. Yu. Zolotykh
We propose a cut-based algorithm for finding all vertices and all facets of the convex hull of all integer points of a polyhedron defined by a system of linear inequalities. Our al…
Linear read-once and related Boolean functions
Vadim Lozin, Igor Razgon, Viktor Zamaraev +2
It is known that a positive Boolean function f depending on n variables has at least n + 1 extremal points, i.e. minimal ones and maximal zeros. We show that f has exactly n + 1 ex…
Specifying a positive threshold function via extremal points
Vadim Lozin, Igor Razgon, Viktor Zamaraev +2
An extremal point of a positive threshold Boolean function is either a maximal zero or a minimal one. It is known that if depends on all its variables, then the set of its…
On the minimal teaching sets of two-dimensional threshold functions
Max A. Alekseyev, Marina G. Basova, Nikolai Yu. Zolotykh
It is known that a minimal teaching set of any threshold function on the twodimensional rectangular grid consists of 3 or 4 points. We derive exact formulae for the numbers of func…
On the number of irreducible points in polyhedra
A. Yu. Chirkov, N. Yu. Zolotykh
An integer point in a polyhedron is called irreducible iff it is not the midpoint of two other integer points in the polyhedron. We prove that the number of irreducible integer poi…
On the number of vertices in integer linear programming problems
Nikolai Yu. Zolotykh
We give a survey of work on the number of vertices of the convex hull of integer points defined by the system of linear inequalities. Also, we present our improvement of some of th…