Abstract
We consider the combinatorial problem MAXFLS which consists, given a system of linear relations, of finding a maximum feasible subsystem, that is a solution satisfying as many relations as possible. The approximability of this general problem is investigated for the three types of relations =, ≥ and >. Various constrained versions of MAXFLS where a subset of relations must be satisfied or where the variables take bounded discrete values, are also considered. We show that MAXFLS with =, ≥ or > relations is NP-hard even when restricted to homogeneous systems with bipolar coefficients. The various NP-hard versions of MAXFLS belong to different approximability classes depending on the type of relations and the additional constraints. While MAXFLS with equations and integer coefficients cannot be approximated within ε for some ε > 0 where p is the number of relations, MAXFLS with strict or nonstrict inequalities can be approximated within 2 but not within every constant factor.
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© 1994 Springer-Verlag Berlin Heidelberg
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Amaldi, E., Kann, V. (1994). On the approximability of finding maximum feasible subsystems of linear systems. In: Enjalbert, P., Mayr, E.W., Wagner, K.W. (eds) STACS 94. STACS 1994. Lecture Notes in Computer Science, vol 775. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-57785-8_168
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DOI: https://doi.org/10.1007/3-540-57785-8_168
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