On the Embed and Project Algorithm for the Graph Bandwidth Problem

The graph bandwidth problem, where one looks for a labeling of vertices that gives the minimum difference between labels over all edges, is classical NP-hard problem has drawn lot attention in recent decades. In this paper, we focus on so-called Embed and Project Algorithm (EPA) introduced by Blum et al. 2000, which main part to solve semidefinite programming relaxation with exponentially many linear constraints. We present several theoretical properties special (SDP) cutting-plane-like algorithm it, works very efficiently combination interior-point methods or bundle method. Extensive numerical results demonstrate algorithm, only been studied theoretically so far, practice good graphs n≤1000.