Minimal Equivalent Binary Knapsack Inequalities

Authors:
Gary J. Koehler
Affiliations:
Department of Information Systems and Operations Management, Warrington College of Business Administration, University of Florida, Gainesville, Florida 32611
Venue:
INFORMS Journal on Computing
Year:
2011

Citing 6
Cited 0

Integer and combinatorial optimization

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The complexity of lifted inequalities for the knapsack problem

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Linear time algorithms for knapsack problems with bounded weights

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Where are the hard knapsack problems?

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Abstract

It is known that a knapsack inequality can be reduced to one having the same solutions but with “minimal” integer coefficients. Although this procedure is not practical because an exponential amount of work may be required to find such minimal equivalent knapsacks, knowledge of minimal equivalent knapsacks can reduce hard knapsacks to trivial ones, as we show for both Todd and Avis knapsacks. In this paper, we show that even with an oracle able to supply minimal equivalent knapsacks at no computational cost, their practical value may not materialize because there are minimal knapsack inequalities with exponential values.