Pants Decomposition of the Punctured Plane

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Pants Decomposition of the Punctured Plane
A pants decomposition of an orientable surface is a collection of simple cycles that partition into pants, i.e., surfaces of genus zero with three boundary cycles. Given a set P of n points in the plane E2 , we consider the problem of computing a pants decomposition of = E2 \ P of minimum total length. We give a polynomial-time approximation scheme using Mitchell's guillotine rectilinear subdivisions. We give an O(n4 )-time algorithm to compute the shortest pants decomposition of when the cycles are restricted to be axis-aligned boxes, and an O(n2 )-time algorithm when all the points lie on a line; both exact algorithms use dynamic programming with Yao's speedup.
Sheung-Hung Poon, Shripad Thite
Added 11 Dec 2010
Updated 11 Dec 2010
Type Journal
Year 2006
Where CORR
Authors Sheung-Hung Poon, Shripad Thite
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