Abstract

Incomplete Monge matrices are a generalization of standard Monge matrices: the values of some entries are not specified and the Monge property only must hold for all specified entries. We derive several combinatorial properties of incomplete Monge matrices and prove that the problem of recognizingpermuted incomplete Monge matrices is NP-complete. For the special case of permutedSupnick matrices, we derive a fast recognition algorithm and thereby identify a special case of then-vertex travelling salesman problem which can be solved inO(n 2logn) time.

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