The Huge Multiway Table Problem
نویسنده
چکیده
Deciding the existence of an l×m×n integer threeway table with given linesums is NP-complete already for fixed l = 3, but is in P with both l,m fixed. Here we consider huge tables, where the variable dimension n is encoded in binary. Combining recent results on integer cones and Graver bases, we show that if the number of layer types is fixed, then the problem is in P, whereas if it is variable, then the problem is in NP intersect coNP. Our treatment goes through the more general class of n-fold integer programming problems.
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Huge Multiway Table Problems
Optimization over l×m× 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 ...
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