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Santanu S. Dey(santanu.deyisye.gatech.edu ) Abstract: Motivated by the need to better understand the properties of sparse cuttingplanes used in mixed integer programming solvers, the paper [1] studied the idealized problem of how well a polytope is approximated by the use of sparse valid inequalities. As an extension to this work, we study the following “less idealized” questions in this pa per: (1) Are there integer programs, such that sparse inequalities do not approximate the integer hull well even when added to a linear programming relaxation? (2) Are there polytopes, where the quality of approximation by sparse inequalities cannot be significantly improved by adding a budgeted number of arbitrary (possibly dense) valid in equalities? (3) Are there polytopes that are difficult to approximate under every rotation? (4) Are there polytopes that are difficult to approximate in all directions using sparse inequalities? We answer each of the above questions in the positive. Keywords: Sparse inequalities, approximations of polytopes Category 1: Integer Programming Citation: ISyE Georgia Tech, TU Delft, 12/2014 Download: [PDF] Entry Submitted: 12/11/2014 Modify/Update this entry  
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