We show that for k ≥ 3 even the Ω(n) level of the Lasserre hierarchy cannot disprove a random k-CSP instance over any predicate type implied by k-XOR constraints, for example ...
A pseudo-Boolean function is a real-valued function defined on {0, 1}n . A k-bounded function is a pseudo-Boolean function that can be expressed as a sum of subfunctions each of w...
Abstract. The subject of this paper is nding small sample spaces for joint distributions of n discrete random variables. Such distributions are often only required to obey a certa...
The (undirected) Node Connectivity Augmentation (NCA) problem is: given a graph J = (V, EJ ) and connectivity requirements {r(u, v) : u, v ∈ V }, find a minimum size set I of n...
We establish the existence of free energy limits for several sparse random hypergraph models corresponding to certain combinatorial models on Erd¨os-R´enyi graph G(N, c/N) and r...