Probability of unique integer solution to a system of linear equations

O.L. Mangasarian and Benjamin Recht

European Journal of Operational Research, 2011, vol. 214, issue 1, 27-30

Abstract: We consider a system of m linear equations in n variables Ax = d and give necessary and sufficient conditions for the existence of a unique solution to the system that is integer: x [set membership, variant] {-1, 1}n. We achieve this by reformulating the problem as a linear program and deriving necessary and sufficient conditions for the integer solution to be the unique primal optimal solution. We show that as long as m is larger than n/2, then the linear programming reformulation succeeds for most instances, but if m is less than n/2, the reformulation fails on most instances. We also demonstrate that these predictions match the empirical performance of the linear programming formulation to very high accuracy.

Keywords: Unique; integer; solution; Linear; equations; Linear; programming (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:214:y:2011:i:1:p:27-30

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