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dc.contributor.authorArseneva, Elena
dc.contributor.authorBahoo, Yeganeh
dc.contributor.authorBiniaz, Ahmad
dc.contributor.authorCano Vila, María del Pilar
dc.contributor.authorChanchary, Farah
dc.contributor.authorIacono, John
dc.contributor.authorJain, Kshitij
dc.contributor.authorLubiw, Anna
dc.contributor.authorMondal, Debajyoti
dc.contributor.authorSheikhan, Khadijeh
dc.contributor.authorD. Thót, Csaba
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.identifier.citationArseneva, E. [et al.]. Compatible Paths on Labelled Point Sets. A: Canadian Conference on Computational Geometry. "CCCG 2018: 30th Canadian Conference on Computational Geometry: Manitoba, Canada: August 8-10, 2018: proceedings book". 2019, p. 54-60.
dc.description.abstractLet 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
dc.format.extent7 p.
dc.rightsAttribution-NonCommercial-NoDerivs 3.0 Spain
dc.subjectÀrees temàtiques de la UPC::Informàtica::Informàtica teòrica
dc.titleCompatible Paths on Labelled Point Sets
dc.typeConference report
dc.contributor.groupUniversitat Politècnica de Catalunya. CGA - Computational Geometry and Applications
dc.description.peerreviewedPeer Reviewed
dc.rights.accessOpen Access
dc.description.versionPostprint (published version)
local.citation.authorArseneva, E.; Bahoo, Y.; Biniaz, A.; Cano, M.; Chanchary, F.; Iacono, J.; Jain, K.; Lubiw, A.; Mondal, D.; Sheikhan, K.; D. Thót, C.
local.citation.contributorCanadian Conference on Computational Geometry
local.citation.publicationNameCCCG 2018: 30th Canadian Conference on Computational Geometry: Manitoba, Canada: August 8-10, 2018: proceedings book

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