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Characterization and recognition of point-halfspace and related orders

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (1995) 894 234-245
DOI: 10.1007/3-540-58950-3_375
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Abstract

We characterize four classes of geometric membership and containment orders—structurally and in terms of forbidden subposets—and present linear- or near linear-time recognition algorithms for each class. We also show that recognizing point-halfspace orders in ℝd is NP-hard for d ≥ 2.

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Tanenbaum, P. J., Goodrich, M. T., & Scheinerman, E. R. (1995). Characterization and recognition of point-halfspace and related orders. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 894, pp. 234–245). Springer Verlag. https://doi.org/10.1007/3-540-58950-3_375

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