Tridiagonal maximum-entropy sampling and tridiagonal masks

The NP-hard maximum-entropy sampling problem (MESP) seeks a maximum (log-) determinant principal submatrix, of given order, from an input covariance matrix C. We give efficient dynamic-programming algorithm for MESP when C (or its inverse) is tridiagonal and generalize it to the situation where support graph spider with constant number legs (and beyond). class arrowhead matrices which natural greedy solves MESP. A mask M correlation we pre-process C, by taking Hadamard product M∘C. Upper bounds on M∘C upper Most upper-bounding methods are much faster apply, tridiagonal, so consider masks (which yield M∘C). make detailed analysis such masks, develop combinatorial local-search based method that takes advantage fast computations matrices.