What is the best greedy-like heuristic for the weighted set covering problem?

The greedy heuristic for the weighted set covering problem is a “column knowledge” construction heuristic where cost and row coverage information are used to insert columns into the solution. In this paper, we analyze the performance of construction heuristics that expand on the column knowledge functions described by Vasko and Wilson (1984) and row knowledge functions described by Ablanedo-Rosas and Rego (2010). If redundant columns are removed from solutions, then the basic greedy heuristic gives essentially the best results.