We study discrete-time quantum walks on generalized Birkhoff polytope graphs (GBPGs), which arise in the solution-set to certain transportation linear programming problems (TLPs). It is known that quantum walks mix at most ...

The largest volume ratio of a given convex body K ⊂ Rn is defined as lvr(K) := sup L⊂Rn vr(K, L), where the sup runs over all the convex bodies L. We prove the following sharp lower bound: c √n ≤ lvr(K), for every body K ...

This paper presents a new generalization of the graph multicoloring problem. We propose a Branch-and-Cut algorithm based on a new integer programming formulation. The cuts used are valid inequalities that we could identify ...

Let (Y-t : t > 0) be the STIT tessellation process. We show that for all polytopes W with nonempty interior and all a > 1, the renormalized random sequence (a(n)Y(an) : n is an element of Z) induced in W is a finitary ...

Compressed sensing is a technique for recovering an unknown sparse signal from a number of random linear measurements. The number of measurements required for perfect recovery plays a key role and it exhibits a phase ...

This thesis is focused on the limits of performance of large-scale convex optimization algorithms. Classical theory of oracle complexity, first proposed by Nemirovski and Yudin in 1983, successfully established the ...