In computational geometry, the potato peeling or convex skull problem is a problem of finding the convex polygon of the largest possible area that lies within a given non-convex simple polygon. It was posed independently by Goodman and Woo,[1][2] and solved in polynomial time by Chang and Yap.[3] The exponent of the polynomial time bound is high, but the same problem can also be accurately approximated in near-linear time.[4][5]

References

  1. ↑ Goodman, Jacob E. (1981), "On the largest convex polygon contained in a nonconvex n-gon, or how to peel a potato", Geometriae Dedicata, 11 (1): 99–106, doi:10.1007/BF00183192, MR 0608164, S2CID 121212273
  2. ↑ Woo, T. (1983), The convex skull problem, as cited by Chang & Yap (1986)
  3. ↑ Chang, J. S.; Yap, C.-K. (1986), "A polynomial solution for the potato-peeling problem", Discrete & Computational Geometry, 1 (2): 155–182, doi:10.1007/BF02187692, MR 0834056
  4. ↑ Hall-Holt, Olaf; Katz, Matthew J.; Kumar, Piyush; Mitchell, Joseph S. B.; Sityon, Arik (2006), "Finding large sticks and potatoes in polygons", Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms, New York: ACM, pp. 474–483, CiteSeerX 10.1.1.59.6770, doi:10.1145/1109557.1109610, ISBN 978-0898716054, MR 2368844, S2CID 7212084
  5. ↑ Cabello, Sergio; Cibulka, Josef; Kynčl, Jan; Saumell, Maria; Valtr, Pavel (2017), "Peeling potatoes near-optimally in near-linear time", SIAM Journal on Computing, 46 (5): 1574–1602, arXiv:1406.1368, doi:10.1137/16M1079695, MR 3708542
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