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On Hamiltonian alternating cycles and paths
dc.contributor.author | Claverol Aguas, Mercè |
dc.contributor.author | García, Alfredo |
dc.contributor.author | Garijo Royo, Delia |
dc.contributor.author | Seara Ojea, Carlos |
dc.contributor.author | Tejel, Javier |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2017-12-15T10:17:05Z |
dc.date.available | 2017-12-15T10:17:05Z |
dc.date.issued | 2018-03 |
dc.identifier.citation | Claverol, M., García, A., Garijo, D., Seara, C., Tejel, J. On Hamiltonian alternating cycles and paths. "Computational geometry: theory and applications", Març 2018, vol. 68, p. 146-166. |
dc.identifier.issn | 0925-7721 |
dc.identifier.uri | http://hdl.handle.net/2117/112128 |
dc.description.abstract | We undertake a study on computing Hamiltonian alternating cycles and paths on bicolored point sets. This has been an intensively studied problem, not always with a solution, when the paths and cycles are also required to be plane. In this paper, we relax the constraint on the cycles and paths from being plane to being 1-plane, and deal with the same type of questions as those for the plane case, obtaining a remarkable variety of results. For point sets in general position, our main result is that it is always possible to obtain a 1-plane Hamiltonian alternating cycle. When the point set is in convex position, we prove that every Hamiltonian alternating cycle with minimum number of crossings is 1-plane, and provide O(n) and O(n2) time algorithms for computing, respectively, Hamiltonian alternating cycles and paths with minimum number of crossings. |
dc.format.extent | 21 p. |
dc.language.iso | eng |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística |
dc.subject.lcsh | Algorithms |
dc.subject.other | Bicolored point sets |
dc.subject.other | Hamiltonian alternating cycles and paths |
dc.subject.other | 1-plane graphs |
dc.subject.other | Minimum number of crossings |
dc.title | On Hamiltonian alternating cycles and paths |
dc.type | Article |
dc.subject.lemac | Algorismes |
dc.contributor.group | Universitat Politècnica de Catalunya. DCCG - Grup de recerca en geometria computacional, combinatoria i discreta |
dc.identifier.doi | 10.1016/j.comgeo.2017.05.009 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::68 Computer science::68W Algorithms |
dc.relation.publisherversion | http://www.sciencedirect.com/science/article/pii/S0925772117300421?via%3Dihub |
dc.rights.access | Open Access |
local.identifier.drac | 21671341 |
dc.description.version | Postprint (author's final draft) |
local.citation.author | Claverol, M.; García, A.; Garijo, D.; Seara, C.; Tejel, J. |
local.citation.publicationName | Computational geometry: theory and applications |
local.citation.volume | 68 |
local.citation.startingPage | 146 |
local.citation.endingPage | 166 |
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