Hans Raj Tiwary

Exponential Lower Bounds for Polytopes in Combinatorial Optimization

We solve a 20-year old problem posed by Yannakakis and prove that no polynomial-size linear program (LP) exists whose associated polytope projects to the traveling salesman polytope, even if the LP is not required to be symmetric. Moreover, we prove that this holds also for the cut polytope and the stable set polytope. These results were discovered through a new connection that we make between one-way quantum communication protocols and semidefinite programming reformulations of LPs.

Extended formulations, nonnegative factorizations, and randomized communication protocols

An extended formulation of a polyhedron

On the computational complexity of Ham-Sandwich cuts, Helly sets, and related problems

P

A generalization of extension complexity that captures P

P is a linear description of a polyhedron

A proof of the Oja depth conjecture in the plane

Q

Compact linear programs for 2SAT

Q together with a linear map