Huge multiway table problems

Optimization over l x m x n integer threeway tables is NP-hard already for fixed l = 3, but solvable in polynomial time with both l, m fixed. Here we consider huge tables, where the variable dimension n is encoded in binary. Combining recent results on Graver bases and recent results on integer cones, we show how to handle such problems in polynomial time. We also show that a harder variant of the problem lies in both NP and coNP. Our treatment goes through the more general class of n-fold integer programming problems. (C) 2014 Published by Elsevier B.V.