Fulkerson et al. have given two examples of set covering problems that are empirically difficult to solve. They arise from Steiner triple systems and the larger problem, which has a constraint matrix of size 330 × 45 has only recently been solved. In this note, we show that the Steiner triple systems do indeed give rise to a series of problems that are probably hard to solve by implicit enumera...

We extend the classical algorithms of Valiant and Haussler for learning compact conjunctions and disjunctions of Boolean attributes to allow features that are constructed from the data and to allow a trade-off between accuracy and complexity. The result is a generalpurpose learning machine, suitable for practical learning tasks, that we call the set covering machine. We present a version of the...

A satis ability problem can be regarded as a nondisjoint union of set covering problems We show that if the resolution method of theorem proving is applied to the satis ability problem its constraint set de nes an integral polytope if and only if the constraint sets of the set covering problems do In this sense resolution reduces the integrality question for the satis ability problem to that fo...