It has been recognized recently that to represent a polyhedron as the projection of a higher dimensional, but simpler, polyhedron, is a powerful tool in polyhedral combinatorics. We develop a general… (More)

L. G. Khachiyan recently published a polynomial algorithm to check feasibility of a system of linear inequalities. The method is an adaptation of an algorithm proposed by Shot for non-linear… (More)

We show that if a sequence of dense graphs Gn has the property that for every fixed graph F , the density of copies of F in Gn tends to a limit, then there is a natural “limit object”, namely a… (More)

We give a randomized algorithm using O(n log n) separation calls to approximate the volume of a convex body with a fixed relative error. The bound is O(n log n) for centrally symmetric bodies and for… (More)

We consider sequences of graphs (Gn) and define various notions of convergence related to these sequences: “left convergence” defined in terms of the densities of homomorphisms from small graphs into… (More)

Sinclair and Jerrum derived a bound on the mixing rate of time-reversible Markov chains in terms of their conductance. We generalize this result, not assuming time-reversibility and using a weaker… (More)