Some recent results in the analysis of greedy algorithms for assignment problems

We survey some recent developments in the analysis of greedy algorithms for assignment and transportation problems. We focus on the linear programming model for matroids and linear assignment problems with Monge property, on general linear programs, probabilistic analysis for linear assignment and makespan minimization, and on-line algorithms for linear and non-linear assignment problems

On the recognition of permuted bottleneck Monge matrices

An n × m matrix A is called bottleneck Monge matrix if max{aij, ars} max{aij, 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 deal with the special case of 0–1 bottleneck Monge matrices. Next, we derive several fundamental properties on the combinatorial structure of bottleneck Monge matrices with arbitrary entries. As a main result we show that permuted bottleneck Monge matrices with arbitrary entries can be recognized in O(nm(n + m)) time