To access the full text documents, please follow this link: http://hdl.handle.net/2117/127832

Title:	Compatible Paths on Labelled Point Sets
Author:	Arseneva, Elena; Bahoo, Yeganeh; Biniaz, Ahmad; Cano Vila, María del Pilar; Chanchary, Farah; Iacono, John; Jain, Kshitij; Lubiw, Anna; Mondal, Debajyoti; Sheikhan, Khadijeh; D. Thót, Csaba
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. CGA -Computational Geometry and Applications
Abstract:	Let P and Q be finite point sets of the same cardinality in R 2 , each labelled from 1 to n. Two noncrossing geometric graphs GP and GQ spanning P and Q, respectively, are called compatible if for every face f in GP , there exists a corresponding face in GQ with the same clockwise ordering of the vertices on its boundary as in f. In particular, GP and GQ must be straightline embeddings of the same connected n-vertex graph G. No polynomial-time algorithm is known for deciding whether two labelled point sets admit compatible geometric graphs. The complexity of the problem is open, even when the graphs are constrained to be triangulations, trees, or simple paths. We give polynomial-time algorithms to find compatible paths or report that none exist in three scenarios: O(n) time for points in convex position; O(n 2 ) time for two simple polygons, where the paths are restricted to remain inside the closed polygons; and O(n 2 log n) time for points in general position if the paths are restricted to be monotone
Abstract:	Peer Reviewed
Subject(s):	-Àrees temàtiques de la UPC::Informàtica::Informàtica teòrica -Algorithms -Algorismes
Rights:	Attribution-NonCommercial-NoDerivs 3.0 Spain http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Published version Conference Object
Share:

Show full item record