Remark on the paper ``A polynomial algorithm for the multi-index choice problem'' (Q1608246)

In this paper the authors construct a counterexample showing that the method of minimum element builds a matrix which is not a plan in the \(p\)-index \((p>2)\) planar choice problem. Thus, the principal statement that the minimum element method almost always builds up an asymptotically optimal plan in the \(p\)-index planar choice problem is incorrect. Note that the authors have elaborated a new algorithm for obtaining an asymptotically optimal solution to the three-planar choice problem of order \(n\) in \(O(n^4)\) steps.