Related papers: Partitions of the polytope of Doubly Substochastic…
We study the structure of the set of all possible affine hyperplane sections of a convex polytope. We present two different cell decompositions of this set, induced by hyperplane arrangements. Using our decomposition, we bound the number of…
We investigate convex polytopes of doubly stochastic matrices having special structures: symmetric, Hankel symmetric, centrosymmetric, and both symmetric and Hankel symmetric. We determine dimensions of these polytopes and classify their…
We determine the extreme points and facets of the convex hull of all dual degree partitions of simple graphs on $n$ vertices.
We study the calculation of the volume of the polytope B_n of n by n doubly stochastic matrices; that is, the set of real non-negative matrices with all row and column sums equal to one. We describe two methods. The first involves a…
A split of a polytope is a (necessarily regular) subdivision with exactly two maximal cells. A polytope is totally splittable if each triangulation (without additional vertices) is a common refinement of splits. This paper establishes a…
We provide a framework for which one can approach showing the integer decomposition property for symmetric polytopes. We utilize this framework to prove a special case which we refer to as $2$-partition maximal polytopes in the case where…
An $n \times m$ non-negative matrix with row sum $m$ and column sum $n$ is called doubly stochastic. We answer the problem of finding doubly stochastic matrices of smallest posible support for every $1 <n \leq m$. Any matrix of minimum…
In this note, we present an algorithm that yields many new methods for constructing doubly stochastic and symmetric doubly stochastic matrices for the inverse eigenvalue problem. In addition, we introduce new open problems in this area that…
The simulation of the physical movement of multi-body systems at an atomistic level, with forces calculated from a quantum mechanical description of the electrons, motivates a graph partitioning problem studied in this article. Several…
The Sequential Multiple Knapsack Problem is a special case of Multiple knapsack problem in which the items sizes are divisible. A characterization of the optimal solutions of the problem and a description of the convex hull of all the…
A splitting scheme for backward doubly stochastic differential equations is proposed. The main idea is to decompose a backward doubly stochastic differential equation into a backward stochastic differential equation and a stochastic…
We study the convex polytope of n x n stochastic matrices that define locally differentially private mechanisms. We first present invariance properties of the polytope and results reducing the number of constraints needed to define it. Our…
We study a graph partitioning problem motivated by the simulation of the physical movement of multi-body systems on an atomistic level, where the forces are calculated from a quantum mechanical description of the electrons. Several advanced…
In this paper we present a systematic way to describe exceptional Jacobi polynomials via two partitions. We give the construction of these polynomials and restate the known aspects of these polynomials in terms of their partitions. The aim…
A split of a polytope $P$ is a (regular) subdivision with exactly two maximal cells. It turns out that each weight function on the vertices of $P$ admits a unique decomposition as a linear combination of weight functions corresponding to…
In this paper, we develop a polynomial time algorithm to compute a Dulmage-Mendelsohn-type decomposition of a matrix partitioned into submatrices of rank at most $1$.
This paper is about how to partition decision variables while decomposing a large-scale optimization problem for the best performance of distributed solution methods. Solving a large-scale optimization problem sequen- tially can be…
A biconvex polytope is a classical and tropical convex hull of finitely many points. Given a biconvex polytope, for each vertex of it we construct a directed bigraph and a gammoid so that the collection of base polytopes of those gammoids…
Motivated by a connection with the factorization of multivariate polynomials, we study integral convex polytopes and their integral decompositions in the sense of the Minkowski sum. We first show that deciding decomposability of integral…
In this thesis, a new approach for constructing subdivision algorithms for generalized quadratic and cubic B-spline subdivision for subdivision surfaces and volumes is presented. First, a catalog of quality criteria for these subdivision…