NP-Hard Classes of Linear Algebraic Systems with Uncertainties
- Anatoly V. LakeyevAffiliated withIrkutsk Computing Center, Siberian Branch, Russian Academy of Sciences
- , Vladik KreinovichAffiliated withDepartment of Computer Science, University of Texas at
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
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.
- NP-Hard Classes of Linear Algebraic Systems with Uncertainties
Volume 3, Issue 1 , pp 51-81
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links