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EOR
2011

Probability of unique integer solution to a system of linear equations

13 years 2 months ago
Probability of unique integer solution to a system of linear equations
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 ∈ {−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.
O. L. Mangasarian, Benjamin Recht
Added 27 Aug 2011
Updated 27 Aug 2011
Type Journal
Year 2011
Where EOR
Authors O. L. Mangasarian, Benjamin Recht
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