We consider a new nonlinear relaxation for the Constrained Maximum-Entropy Sampling Prob- lem - the problem of choosing the s x s principal submatrix with maximal determinant from a given n x n positive definite matrix, subject to linear constraints. We implement a branch-and- bound algorithm...

We present new facets for the linear ordering polytope. These new facets generalize facets induced by sub graphs called fences, introduced by Grotschel, Junger and Reinelt (1985), and augmented fences, introduced by McLennan (1990). One novelty of the facets introduced here is that each sub...

We survey some analytic methods of volume calculation and introduce a distance function for pairs of polytopes based on their volumes. We study the distance function in the context of three familiar settings of combinatorial optimization: (i) ChvatalGomory rounding, (ii) fixed charge problems,...

We study thep olytopes of binary n-strings that encode (positive) integers that are not divisible by a particular positive integer p - the indivisibility polytopes, as well as the more general "clipped cubes". Also, we discuss a potential application to factoring. Finally, we present some...

For matroids representable over both GF[3] and GF[5], we provide a recipe for constructing an orientation