Abstract
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 enumeration. The main result is that for ann variable problem, branch and bound algorithms using a linear programming relaxation, and/or elimination by dominance require the examination of a super-polynomial number of partial solutions
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This paper was written while the author was a CORE Fellow at the Université de Louvain, Louvain-la-Neuve, Belgium.
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Avis, D. A note on some computationally difficult set covering problems. Mathematical Programming 18, 138–145 (1980). https://doi.org/10.1007/BF01588309
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DOI: https://doi.org/10.1007/BF01588309