@inbook{afde742ecbc14e0c9c3b09948d077fd1,

title = "Approximation algorithms for inscribing or circumscribing an axially symmetric polygon to a convex polygon",

abstract = "Given a convex polygon P with n vertices, we present algorithms to determine approximations of the largest axially symmetric convex polygon S contained in P, and the smallest such polygon S′ that contains P. More precisely, for any ε > 0, we can find an axially symmetric convex polygon Q ⊂ P with area |Q| > (1 - ε)|S| in time O(n + 1/ε3/2), and we can find an axially symmetric convex polygon Q′ containing P with area |Q′| < (1 + ε)|S′| in time O(n+(1/ε2)log(1/ε)). If the vertices of P are given in a sorted array, we can obtain the same results in time O((1/√ε) log n+1/ε3/2) and O((1/ε) log n+(1/ε2) log(1/ε)) respectively.",

author = "Ahn, {Hee Kap} and Peter Brass and Otfried Cheong and Na, {Hyeon Suk} and Shin, {Chan Su} and Antoine Vigneron",

note = "Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",

year = "2004",

doi = "10.1007/978-3-540-27798-9_29",

language = "English (US)",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "259--267",

editor = "Kyung-Yong Chwa and {Ian Munro}, J.",

booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

address = "Germany",

}