 
Summary: Mathematical Programming 18 (1980) 138145.
NorthHolland Publishing Company
A NOTE ON SOME COMPUTATIONALLY DIFFICULT
SET COVERING PROBLEMS
David AVIS*
McGill University,MontNal, Quebec, Canada
Received 3 October 1978
Revised manuscript received 25 April 1979
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 an n variable problem, branch and
bound algorithms using a linear programming relaxation, and/or elimination by dominance
require the examination of a superpolynomial number of partial solutions
Key words: Setcovering Problem, Branch and Bound, Lower Bounds, Steiner Triple
Systems.
1. Introduction
Fulkerson et al. [5] have given two empirically difficult to solve set covering
problems arising from Steiner triple systems. In this note, we use a standard
