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

We develop and experiment with new upper bounds for the constrained maximum-entropy sampling problem. Our partition bounds are based on Fischer's inequality. Further new upper bounds combine the use of Fischer's inequality with previously developed bounds. We demonstrate this in detail by using...

Motivated by the NP-Hard problem of finding a minimum-weight balanced bipartition of an edge-weighted complete graph, we study the class of graphs having the same degrees as bipartite 'fur.an graphs. In particular, we establish a maximal set of linear equations satisfied by the counts of the...