Related papers: Affine maps between quadratic assignment polytopes…
Given a graph $G$, we study the $2$-edge-connected subgraph polytope $\mathrm{TECSP}(G)$, which is given by the convex hull of the incidence vectors of all $2$-edge-connected subgraphs of $G$. We describe the lattice points of this polytope…
We conjecture that a convex polytope is uniquely determined up to isometry by its edge-graph, edge lengths and the collection of distances of its vertices to some arbitrary interior point, across all dimensions and all combinatorial types.…
The "edge polytope" of a finite graph G is the convex hull of the columns of its vertex-edge incidence matrix. We study extremal problems for this class of polytopes. For k =2, 3, 5 we determine the maximum number of vertices of…
We prove that every finite group is the automorphism group of a finite abstract polytope isomorphic to a face-to-face tessellation of a sphere by topological copies of convex polytopes. We also show that this abstract polytope may be…
Recently various optimization problems, such as Mixed Integer Linear Programming Problems (MILPs), have undergone comprehensive investigation, leveraging the capabilities of machine learning. This work focuses on learning-based solutions…
The degree partition of a simple graph is its degree sequence rearranged in weakly decreasing order. The polytope of degree partitions (respectively, degree sequences) is the convex hull of all degree partitions (respectively, degree…
The extension complexity $\mathsf{xc}(P)$ of a polytope $P$ is the minimum number of facets of a polytope that affinely projects to $P$. Let $G$ be a bipartite graph with $n$ vertices, $m$ edges, and no isolated vertices. Let…
We specify what is meant for a polytope to be reconstructible from its graph or dual graph. And we introduce the problem of class reconstructibility, i.e., the face lattice of the polytope can be determined from the (dual) graph within a…
We consider new polynomially solvable cases of the well-known Quadratic Assignment Problem involving coefficient matrices with a special diagonal structure. By combining the new special cases with polynomially solvable special cases known…
This paper studies the \emph{unimodular isomorphism problem} (UIP) of convex lattice polytopes: given two convex lattice polytopes $P$ and $P'$, decide whether there exists a unimodular affine transformation mapping $P$ to $P'$. We show…
We investigate the combinatorics and geometry of permutation polytopes associated to cyclic permutation groups, i.e., the convex hulls of cyclic groups of permutation matrices. We give formulas for their dimension and vertex degree. In the…
Let S be an nXn real symmetric matrix with spectral decomposition S=Q^T Lambda Q, where Q is an orthogonal matrix and Lambda is diagonal with simple spectrum {lambda_1,..., lambda_n}. Also let O_S e R_S be the orbits by conjugation of S by,…
Let $BQP(n)$ be a boolean quadric polytope, $LOP(m)$ be a linear ordering polytope. It is shown that $BQP(n)$ is linearly isomorphic to a face of $LOP(2n)$.
Multigraph matching is a recent variant of the graph matching problem. In this framework, the optimization procedure considers several graphs and enforces the consistency of the matches along the graphs. This constraint can be formalized as…
We present a new polynomially solvable case of the Quadratic Assignment Problem in Koopmans-Beckman form $QAP(A,B)$, by showing that the identity permutation is optimal when $A$ and $B$ are respectively a Robinson similarity and…
A sweep of a point configuration is any ordered partition induced by a linear functional. Posets of sweeps of planar point configurations were formalized and abstracted by Goodman and Pollack under the theory of allowable sequences of…
This article provides an overview of our joint work on binary polynomial optimization over the past decade. We define the multilinear polytope as the convex hull of the feasible region of a linearized binary polynomial optimization problem.…
We consider several families of combinatorial polytopes associated with the following NP-complete problems: maximum cut, Boolean quadratic programming, quadratic linear ordering, quadratic assignment, set partition, set packing, stable set,…
In this paper we define a construct called a time-graph. A complete time-graph of order n is the cartesian product of a complete graph with n vertices and a linear graph with n vertices. A time-graph of order n is given by a subset of the…
Consider the Quadratic Assignment Problem (QAP): given two matrices A and D, minimize {trace AXDX^T: X is a permutation matrix}. New lower bounds were obtained recently (Mittelmann and peng [8]) for the QAP where D is either the Manhattan…