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$\begingroup$ I think that for the general case, by standard results any basic feasible solution has polynomial bit complexity, and this extends to any integer solution that is a convex combination of basic feasible solutions. So, in the case that the polytope is bounded, every integer solution is a convex combination of basic feasible solutions, and so has polynomial bit complexity. The unresolved case is when the polytope is unbounded: in an unbounded polytope, if the polytope contains an integer solution, must there be one w/ polynomial bit complexity? $\endgroup$

Neal Young
– Neal Young

2024-10-01 15:13:03 +00:00
Commented Oct 1, 2024 at 15:13

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