Semidefinite programs for the design of codes for delay-constrained communication in networks

We consider the problem of designing codes for the problem of delay-constrained communication in packet networks. We show how good codes for this problem can be characterized as the solution of a pair of semidefinite programs plus a rank constraint. Using this characterization, we formulate the design problem as one of finding suitable graph embeddings into Euclidean space, for a certain family of graphs which represent constraints that these codes most satisfy. In the case of codes in dimension 1, our formulation results in a good approximation algorithm for the classical problem of graph bandwidth, which may be of independent interest