@inproceedings{5d1ab9f6486941e9a91eb31728e3f36c,

title = "A faster algorithm for computing motorcycle graphs",

abstract = "We present a new algorithm for computing motorcycle graphs that runs in O(n4/3+ε) time for any ε > 0, improving on all previously known algorithms. The main application of this result is to computing the straight skeleton of a polygon. It allows us to compute the straight skeleton of a non-degenerate polygon with h holes in O(n√h+1 log 2 n + n4/3+ε) expected time. If all input coordinates are O(logn)-bit rational numbers, we can compute the straight skeleton of a (possibly degenerate) polygon with h holes in expected time O(n√h+1 log3n). In particular, it means that we can compute the straight skeleton of a simple polygon in O(nlog3n) expected time if all input coordinates are O(log n)-bit rationals, while all previously known algorithms have worst-case running time ω(n3/2).",

keywords = "Algorithms design and analysis, Computational geometry, Straight skeleton",

author = "Antoine Vigneron and Lie Yan",

year = "2013",

doi = "10.1145/2462356.2462396",

language = "English (US)",

isbn = "9781450320313",

series = "Proceedings of the Annual Symposium on Computational Geometry",

publisher = "Association for Computing Machinery",

pages = "17--26",

booktitle = "Proceedings of the 29th Annual Symposium on Computational Geometry, SoCG 2013",

note = "29th Annual Symposium on Computational Geometry, SoCG 2013 ; Conference date: 17-06-2013 Through 20-06-2013",

}