A Faster Algorithm for Computing Straight Skeletons

Handle URI:
http://hdl.handle.net/10754/316713
Title:
A Faster Algorithm for Computing Straight Skeletons
Authors:
Mencel, Liam A.
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 (log n) log r) time. It improves on the previously best known algorithm for this reduction, which is randomised, and runs in expected O(n √(h+1) log² n) 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 (log n) log r + r^(4/3 + ε)) time for any ε > 0. On degenerate input, our time bound increases to O(n (log n) log r + r^(17/11 + ε))
Advisors:
Vigneron, Antoine E. ( 0000-0003-3586-3431 )
Committee Member:
Hadwiger, Markus ( 0000-0003-1239-4871 ) ; Moshkov, Mikhail ( 0000-0003-0085-9483 )
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Program:
Computer Science
Issue Date:
6-May-2014
Type:
Thesis
Appears in Collections:
Theses; Computer Science Program; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.advisorVigneron, Antoine E.en
dc.contributor.authorMencel, Liam A.en
dc.date.accessioned2014-05-11T07:02:12Z-
dc.date.available2014-05-11T07:02:12Z-
dc.date.issued2014-05-06en
dc.identifier.urihttp://hdl.handle.net/10754/316713en
dc.description.abstractWe 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 (log n) log r) time. It improves on the previously best known algorithm for this reduction, which is randomised, and runs in expected O(n √(h+1) log² n) 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 (log n) log r + r^(4/3 + ε)) time for any ε > 0. On degenerate input, our time bound increases to O(n (log n) log r + r^(17/11 + ε))en
dc.language.isoenen
dc.subjectstraight skeletonen
dc.subjectalgorithmen
dc.subjectcomputional geometryen
dc.subjecttheoryen
dc.titleA Faster Algorithm for Computing Straight Skeletonsen
dc.typeThesisen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
thesis.degree.grantorKing Abdullah University of Science and Technologyen_GB
dc.contributor.committeememberHadwiger, Markusen
dc.contributor.committeememberMoshkov, Mikhailen
thesis.degree.disciplineComputer Scienceen
thesis.degree.nameMaster of Scienceen
dc.person.id124179en
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