On a Class of 3SUM-HARD problems in Computational Geometry: Cutting a polygon with a line - Couverture souple

Ruci, Ervin

Couverture souple

ISBN 10 : 3639158377 ISBN 13 : 9783639158373

Editeur : VDM Verlag, 2009

Synopsis

Given a simple polygon P and an integer K > 1, we want to compute the set of straight lines in the Cartesian plane that cut this polygon into exactly K simple polygons. We call this set of lines a K-separator and call this problem the K-separator problem. We present an algorithm that finds the K-separators of an n-vertex simple polygon, for all K > 0, in O(n2) total time. We prove that the decision problem given an integer K > 2 and an edge of the polygon, is there a line through this edge that cuts the polygon in exactly K pieces?, is 3SUM-HARD. For the special case when K = 2, we show that the decision problem can be solved in O(n log(n)) time. Several other complexity results may be obtained. We suspect that the problem of finding the cell of maximum depth is also 3SUM-hard, and as a corollary the problem of identifying the line that cuts the polygon in the maximum possible number of pieces is also 3SUM-hard.

A propos du livre

À propos de l?auteur

Born in Vlore, Albania where he lived until the age of 18, went abroad to study (Applied Math, Mount Allison University; Computational Geometry, Carleton University) and work (MTA, CIRA). Is now back in Vlore, teaching at the University of Vlora.

Détails de l'édition

• Éditeur: VDM Verlag
• Date d'édition: 2009
• Langue: anglais
• ISBN 10: 3639158377
• ISBN 13: 9783639158373
• Reliure: Broché
• Nombre de pages: 76
• Coordonnées du fabricant: non disponible
• Personne responsable: non disponible