Potato peeling

{{about|a problem in computational geometry|the devices used to peel potatoes|peeler}}

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,{{r|g|w}} and solved in polynomial time by Chang and Yap.{{r|cy}} The exponent of the polynomial time bound is high, but the same problem can also be accurately approximated in near-linear time.{{r|hkkms|ccksv}}

References

{{reflist|refs=

{{citation

| last1 = Cabello | first1 = Sergio

| last2 = Cibulka | first2 = Josef

| last3 = Kynčl | first3 = Jan

| last4 = Saumell | first4 = Maria

| last5 = Valtr | first5 = Pavel

| doi = 10.1137/16M1079695

| issue = 5

| journal = SIAM Journal on Computing

| mr = 3708542

| pages = 1574–1602

| title = Peeling potatoes near-optimally in near-linear time

| volume = 46

| year = 2017| arxiv = 1406.1368

}}

{{citation

| last1 = Chang | first1 = J. S.

| last2 = Yap | first2 = C.-K.

| doi = 10.1007/BF02187692

| issue = 2

| journal = Discrete & Computational Geometry

| mr = 834056

| pages = 155–182

| title = A polynomial solution for the potato-peeling problem

| volume = 1

| year = 1986| doi-access = free}}

{{citation

| last = Goodman | first = Jacob E. | authorlink = Jacob E. Goodman

| doi = 10.1007/BF00183192

| issue = 1

| journal = Geometriae Dedicata

| mr = 608164

| pages = 99–106

| title = On the largest convex polygon contained in a nonconvex {{mvar|n}}-gon, or how to peel a potato

| volume = 11

| year = 1981| s2cid = 121212273 }}

{{citation

| last1 = Hall-Holt | first1 = Olaf

| last2 = Katz | first2 = Matthew J.

| last3 = Kumar | first3 = Piyush

| last4 = Mitchell | first4 = Joseph S. B. | author4-link = Joseph S. B. Mitchell

| last5 = Sityon | first5 = Arik

| contribution = Finding large sticks and potatoes in polygons

| doi = 10.1145/1109557.1109610

| mr = 2368844

| pages = 474–483

| publisher = ACM | location = New York

| title = Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms

| year = 2006| isbn = 978-0898716054

| citeseerx = 10.1.1.59.6770| s2cid = 7212084

}}

{{citation|title=The convex skull problem|last=Woo|first=T.|year=1983}}, as cited by {{harvtxt|Chang|Yap|1986}}

}}

Category:Convex hulls

Category:Computational geometry