Greedy Solutions for General Set Covering Problems

  • Gerald Hammer


Set covering problems are well known as hard [4]. Therefore only small problems can be solved effectively by standard methods of integer programming. The solution of larger problems requires the use of methods with polynomial time behaviour. Thus the choice of methods is restricted to heuristics, which can eventually be combined in the framework of branch-and-bound to give ‘hybrid’ algorithms. In [1] Balas and Ho report on an algorithm of this type, based on several heuristics, subgradient optimization, cutting planes, and implicit enumeration.


Mathematical Programming Average Behaviour Large Problem Minimum Element Small Problem 
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  1. [1]
    Balas, E., Ho, A., “Set covering algorithms using cutting planes, heuristics, and subgradient optimization: A computational study”, Mathematical Programming 12 (1980) 37–60Google Scholar
  2. [2]
    Chvatal, V., “A greedy heuristic for the set covering problem”, Mathematics of Operations Research (1979) 233–235Google Scholar
  3. [3]
    Ho, A., “Worst case analysis of a class of set covering heuristics”, Mathematical Programming 23 (1982) 170–180CrossRefGoogle Scholar
  4. [4]
    Karp, R. M., “Reducibility among combinatorial problems”, in: Complexity of Computer Computations, R. E. Miller and J. W. Thatcher, eds. Plenum Press, New York (1972)Google Scholar
  5. [5]
    Lovasz, L., “On the ratio of optimal integral and fractional covers”, Discrete Mathematics 13 (1975) 383–390CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Gerald Hammer
    • 1
  1. 1.Universität KarlsruheKarlsruheGermany

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