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On a posterior evaluation of a simple greedy method for set packing

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Abstract

We consider an approach for ex post evaluation of approximate solutions obtained by a well known simple greedy method for set packing. A performance bound is derived that is a function of the highest average reward per item over subsets as well as the number of allocated subsets and ground items. This a posterior bound can enable much revelation of optimality when the solution is near optimal. One of the advantages of the ex post analysis is that it does not require computing the optimal solution to the LP relaxation. The ex post bound will not be guaranteed to reveal substantial levels of optimality for all problem instances but can be a useful tool that is complementary to other traditional methods for ex post evaluation for the set packing problem.

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Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, University of Toronto, 5 King’s College Road, Toronto, ON, M5S 3G8, Canada

    Roy H. Kwon & Cheng Wang

  2. Department of Industrial and Systems Engineering, University of Florida, 303 Weil Hall, P. O. Box 116595, Gainesville, FL, 32611-6595, USA

    Georgios V. Dalakouras

Authors
  1. Roy H. Kwon
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  2. Georgios V. Dalakouras
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  3. Cheng Wang
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Correspondence to Roy H. Kwon.

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Kwon, R.H., Dalakouras, G.V. & Wang, C. On a posterior evaluation of a simple greedy method for set packing. Optim Lett 2, 587–597 (2008). https://doi.org/10.1007/s11590-008-0085-6

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  • DOI: https://doi.org/10.1007/s11590-008-0085-6

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