We exhibit an n-node graph whose independent set polytope requires extended
formulations of size exponential in Ω(n/\logn). Previously, no explicit examples of n …

We use techniques from (tracial noncommutative) polynomial optimization to formulate
hierarchies of semidefinite programming lower bounds on matrix factorization ranks. In …

The hitting number of a polytope P is the smallest size of a subset of vertices of P such that
every facet of P has a vertex in the subset. We show that, if P is the base polytope of any …

Let $ G $ be a connected $ n $-vertex graph in a proper minor-closed class $\mathcal G $.
We prove that the extension complexity of the spanning tree polytope of $ G $ is $ O …

arxiv:1412.0728v2 [math.CO] 29 Feb 2020 Page 1 SUBLINEAR EXTENSIONS OF POLYGONS
YAROSLAV SHITOV Abstract. Every convex polygon with n vertices is a linear projection of a …

For a finite set X⊂ Z d that can be represented as X= Q∩ Z d for some polyhedron Q, we call
Q a relaxation of X and define the relaxation complexity rc (X) of X as the least number of …

Initially developed for the min-knapsack problem, the knapsack cover inequalities are used
in the current best relaxations for numerous combinatorial optimization problems of covering …

We exhibit an n-node graph whose independent set polytope requires extended
formulations of size exponential in Ω (n/log n). Previously, no explicit examples of n …

Furthermore, we study our main geometric tool which we term the glued product of
polytopes. While the glued product of polytopes has been known since the'90s, we are the …

A Euclidean distance matrix D (α) D (α) is defined by D_ ij=(α _i-α _j)^ 2 D ij=(α i-α j) 2,
where α=(α _1, ..., α _n) α=(α 1,…, α n) is a real vector. We prove that D (α) D (α) cannot be …