Bounds on the size of branch-and-bound proofs for integer knapsacks

Authors:
Bala Krishnamoorthy
Affiliations:
Department of Mathematics, P.O. Box 643113, Washington State University, Pullman, WA 99164, USA
Venue:
Operations Research Letters
Year:
2008

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Abstract

Using a direct counting argument, we derive lower and upper bounds for the number of nodes enumerated by linear programming-based branch-and-bound(B&B) method to prove the integer infeasibility of a knapsack. We prove by example that the size of the B&Btree could be exponential in the worst case.