On the recognition of permuted bottleneck monge matrices

Abstract

An n × m matrix A is called bottleneck Monge matrix if max {aij, ars} ≤ max {ais, arj} for all 1 ≤ i < r ≤ n, 1 ≤j < s≤m. The matrix A is termed permuted bottleneck Monge matrix, if there exist row and column permutations such that the permuted matrix becomes a bottleneck Monge matrix. We first show that the class of permuted 0-1 bottleneck Monge matrices can be recognized in O(nm) time. Then we present an O(nm(n+m)) time algorithm for the recognition of permuted bottleneck Monge matrices with arbitrary entries.