## On the Approximability of Minimizing Nonzero Variables Or Unsatisfied Relations in Linear Systems (1997)

Citations: | 72 - 4 self |

### BibTeX

@MISC{Amaldi97onthe,

author = {Edoardo Amaldi and Viggo Kann},

title = {On the Approximability of Minimizing Nonzero Variables Or Unsatisfied Relations in Linear Systems},

year = {1997}

}

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### OpenURL

### Abstract

We investigate the computational complexity of two closely related classes of combinatorial optimization problems for linear systems which arise in various fields such as machine learning, operations research and pattern recognition. In the first class (Min ULR) one wishes, given a possibly infeasible system of linear relations, to find a solution that violates as few relations as possible while satisfying all the others. In the second class (Min RVLS) the linear system is supposed to be feasible and one looks for a solution with as few nonzero variables as possible. For both Min ULR and Min RVLS the four basic types of relational operators =, , ? and 6= are considered. While Min RVLS with equations was known to be NP-hard in [27], we established in [2, 5] that Min ULR with equalities and inequalities are NP-hard even when restricted to homogeneous systems with bipolar coefficients. The latter problems have been shown hard to approximate in [8]. In this paper we determine strong bou...