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Merve Bodur (merve.bodurgatech.edu) Abstract: In this paper, we study the strength of ChvatalGomory (CG) cuts and more generally aggregation cuts for packing and covering integer programs (IPs). Aggregation cuts are obtained as follows: Given an IP formulation, we first generate a single implied inequality using aggregation of the original constraints, then obtain the integer hull of the set defined by this single inequality with variable bounds, and finally use the inequalities describing the integer hull as cuttingplanes. Our first main result is to show that for packing and covering IPs, the CG and aggregation closures can be 2approximated by simply generating the respective closures for each of the original formulation constraints, without using any aggregations. On the other hand, we use computational experiments to show that aggregation cuts can be arbitrarily stronger than cuts from individual constraints for general IPs. The proof of the above stated results for the case of covering IPs with bounds require the development of some new structural results, which may be of independent interest. Finally, we examine the strength of cuts based on k different aggregation inequalities simultaneously, the socalled multirow cuts, and show that every packing or covering IP with a large integrality gap also has a large kaggregation closure rank. In particular, this rank is always at least of the order of the logarithm of the integrality gap. Keywords: Integer programming, cutting planes, packing, covering, aggregation Category 1: Integer Programming Category 2: Integer Programming (Cutting Plane Approaches ) Citation: Download: [PDF] Entry Submitted: 06/28/2016 Modify/Update this entry  
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