Abstract
A characterization ofC-semispaces of partial convexity is obtained. An estimate of the number ofC-semispaces in the case of finitely many directions of partial convexity is given. A polynomial algorithm for the enumeration ofC-semispaces is developed. The problem of recognizing approximations of partially convex hulls generated by intersections ofC-semispaces is proved to be NP-complete.
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Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 399–410, September, 2000.
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Metel’skii, N.N., Naidenko, V.G. Algorithmic aspects of partial convexity. Math Notes 68, 345–354 (2000). https://doi.org/10.1007/BF02674558
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DOI: https://doi.org/10.1007/BF02674558