Clustering heuristics for set covering

The authors introduce a new class of set covering heuristics, based on clustering techniques. In its simplest form, a heuristic in this class may be described as follows: firstly, partition the column set into clusters formed by columns that are close to each other (e.g. in the Hamming distance sense). Then select a ‘best’ (e.g. a cheapest) column in each cluster; if the selected columns form a cover C, then extract from C a prime cover and stop; else, modify the partition (e.g. by increasing the number of clusters) and repeat. They describe two implementations of this general algorithmic strategy, relying on the Single Linkage and the Leader clustering algorithm, respectively. Numerical experiments performed on 72 randomly generated test problems with 200 or 400 rows and 1000 columns indicate that the above two heuristics often yield cheaper covers than other well-known (greedy-type) heuristics when the cost-range is not too narrow.