Abstract
We consider the Sherali-Adams (SA) operator as a proof system for integer linear programming and prove linear lower bounds on the SA rank required to prove both the pigeon hole and least number principles. We also define the size of a SA proof and show that that while the pigeon hole principle requires linear rank, it only requires at most polynomial size.
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Rhodes, M. (2007). Rank Lower Bounds for the Sherali-Adams Operator. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_67
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DOI: https://doi.org/10.1007/978-3-540-73001-9_67
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-73000-2
Online ISBN: 978-3-540-73001-9
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