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• W3023053744 abstract "We introduce the integrality number of an integer program (IP). Roughly speaking, the integrality number is the smallest number of integer constraints needed to solve an IP via a mixed integer (MIP) relaxation. One notable property of this number is its invariance under unimodular transformations of the constraint matrix. Considering the largest minor $$varDelta $$ of the constraint matrix, our analysis allows us to make statements of the following form: there exists a number $$tau (varDelta )$$ such that an IP with n many variables and $$n + sqrt{n /tau (varDelta )}$$ many inequality constraints can be solved via a MIP relaxation with fewer than n integer constraints. From our results it follows that IPs defined by only n constraints can be solved via a MIP relaxation with $$O(sqrt{varDelta })$$ many integer constraints." @default.
• W3023053744 created "2020-05-13" @default.
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• W3023053744 date "2021-04-10" @default.
• W3023053744 modified "2023-10-18" @default.
• W3023053744 title "The integrality number of an integer program" @default.
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• W3023053744 doi "https://doi.org/10.1007/s10107-021-01651-0" @default.
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