NP-Hard Classes of Linear Algebraic Systems with Uncertainties
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For a system of linear equations Ax = b, the following natural questions appear:
• does this system have a solution?
• if it does, what are the possible values of a given objective function f(x1,...,xn) (e.g., of a linear function f(x) = ∑C i X i ) over the system's solution set?
We show that for several classes of linear equations with uncertainty (including interval linear equations) these problems are NP-hard. In particular, we show that these problems are NP-hard even if we consider only systems of n+2 equations with n variables, that have integer positive coefficients and finitely many solutions.
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- NP-Hard Classes of Linear Algebraic Systems with Uncertainties
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