Simple lifted cover inequalities and hard knapsack problems

Authors:
Brady Hunsaker;Craig A. Tovey
Affiliations:
Department of Industrial Engineering, University of Pittsburgh, Pittsburgh, PA 15261, USA;School of ISYE and College by Computing, Georgia Institute of Technology, Atlanta 303320205, USA
Venue:
Discrete Optimization
Year:
2005

Citing 3
Cited 1

Lifted Cover Inequalities for 0-1 Integer Programs: Computation

INFORMS Journal on Computing
Lifted Cover Inequalities for 0-1 Integer Programs: Complexity

INFORMS Journal on Computing
The complexity of cover inequality separation11This research was supported by US Army Research Office DAAH04-94-G-0017 and NSF Grant No. DMI-9700285.

Operations Research Letters

Simultaneously lifting sets of binary variables into cover inequalities for knapsack polytopes

Discrete Optimization

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Abstract

We consider a class of random knapsack instances described by Chvatal, who showed that with probability going to 1, such instances require an exponential number of branch-and-bound nodes. We show that even with the use of simple lifted cover inequalities, an exponential number of nodes is required with probability going to 1.