A very fast method for guaranteed generation of one facet for 0-1 knapsack polyhedron

Document Type : Research Note


1 Department of Industrial Engineering, Sharif University of Technology, Tehran, Iran

2 Department of Industrial and Systems Engineering, Texas A&M University, College Station, TX, 77843-3131


The 0-1 knapsack polyhedron as the most basic relaxation of a 0-1 integer program has attracted attention of many researchers over the years.We present a very fast method that is guaranteed to generate one facet for the 0-1 knapsack polyhedron. Unlike lifting of cover inequlities, our method does not require an initial minimal cover or a predetermined lifting sequencing, and its worst-case complexity is linear in number of variables. Therefore, it is suitable for incorporation into mixed interger programming(MIP) solvers, in order to generate, with negligible computational burden, one strong cut based on any 0-1 knapsack relaxation of a general MIP.


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