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.

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Sheung-Hung Poon, Shripad Thite
• Keywords: CORR 2006, Education, Pants Decomposition, Polynomial-time Approximation Scheme, Shortest Pants Decomposition