We propose two new lower bounds on graph bandwidth and cyclic bandwidth based on semidefinite programming (SDP) relaxations of the quadratic assignment problem. We compare the new bounds with two other SDP bounds in [A. Blum, G. Konjevod, R. Ravi, and S. Vempala, Semi-definite relaxations for minimum bandwidth and other vertex-ordering problems, Theoretical Computer Science, 235(1):25-42, 2000], and [J. Povh and F. Rendl, A copositive programming approach to graph partitioning, SIAM Journal on Optimization, 18(1):223-241, 2007].
Citation
Working paper, Tilburg University, The Netherlands, May 2010.