# A faster algorithm for computing straight skeletons

S.W. Cheng, L. Mencel, A. Vigneron

16th European symposium on Algorithms, LNCS 8937, 272-283, (2014)

## Keywords

Computing straight skeletons

## Abstract

We present a new algorithm for computing the straight skeleton of a polygon. For a polygon with n vertices, among which r are reflex vertices, we give a deterministic algorithm that reduces the straight skeleton computation to a motorcycle graph computation in O(n (logn)logr) time. It improves on the previously best known algorithm for this reduction, which is randomized, and runs in expected O(nh+1−−−−−√log2n) time for a polygon with h holes. Using known motorcycle graph algorithms, our result yields improved time bounds for computing straight skeletons. In particular, we can compute the straight skeleton of a non-degenerate polygon in O(n (logn) logr + r 4/3 + ε ) time for any ε > 0. On degenerate input, our time bound increases to O(n (logn) logr + r 17/11 + ε ).

## Code

DOI: 10.1007/978-3-662-44777-2_23