Block-diagonal semidefinite programming hierarchies for 0/1 programming

TL;DR

This paper introduces new block-diagonal semidefinite programming hierarchies for 0/1 programming that are computationally more efficient and as strong as existing hierarchies, with experimental validation on the stable set problem.

Contribution

The paper proposes two novel block-diagonal hierarchies that improve computational efficiency while maintaining strength comparable to Lovasz-Schrijver hierarchies.

Findings

Hierarchies are computationally less costly.

Hierarchies are at least as strong as Lovasz-Schrijver.

Experimental results on Paley graphs demonstrate effectiveness.

Abstract

Lovasz and Schrijver, and later Lasserre, proposed hierarchies of semidefinite programming relaxations for general 0/1 linear programming problems. In this paper these two constructions are revisited and two new, block-diagonal hierarchies are proposed. They have the advantage of being computationally less costly while being at least as strong as the Lovasz-Schrijver hierarchy. Our construction is applied to the stable set problem and experimental results for Paley graphs are reported.