An efficient algorithm for the symmetric principal minor assignment problem

We consider the problem of reconstructing a symmetric matrix from its principal minors, which has several applications in information theory and statistical modeling. We develop a theory of symmetric matrices with equal corresponding principal minors based on a simple equivalent property due to Oeding (2011) [10]. We then use this theory to provide a method for choosing a canonical representative from the class of all symmetric matrices with specified principal minors. Finally, we provide an efficient algorithm for computing this canonical representative given its principal minors as input.