On the Number of Faces of Certain Transportation Polytopes

Abstract

Define the transportation polytope Tn,m to be a polytope of non-negative n × m matrices with row sums equal to m and column sums equal to n. We present a new recurrence relation for the numbers fk of the k-dimensional faces for the transportation polytope Tn,n+1. This gives an efficient algorithm for computing the numbers fk, which solves the problem known to be computationally hard in a general case. © 2000 Academic Press.