We study integrality gaps for SDP relaxations of constraint satisfaction problems, in the hierarchy of SDPs defined by Lasserre. Schoenebeck [25] recently showed the first integra...
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 ...
We present an approximation scheme for optimizing certain Quadratic Integer Programming problems with positive semidefinite objective functions and global linear constraints. Thi...
The Densest k-subgraph problem (i.e. find a size k subgraph with maximum number of edges), is one of the notorious problems in approximation algorithms. There is a significant g...