Partitioning orthogonal polygons by extension of all edges incident to reflex vertices: lower and upper bounds on the number of pieces

Bajuelos Domínguez, António LeslieTomás, Ana PaulaMarques, Fábio José Reis Luís2017-03-072017-03-072004Bajuelos Domínguez, A.L., Tomás, A.P. y Marques, F.J.R.L. (2004). Partitioning orthogonal polygons by extension of all edges incident to reflex vertices: lower and upper bounds on the number of pieces. En 20th European Workshop on Computational Geometry, Sevilla.http://hdl.handle.net/11441/55464Given an orthogonal polygon P, let |Π(P)| be the number of rectangles that result when we partition P by extending the edges incident to reflex vertices towards INT(P). In Tomás, A. P., Bajuelos, A. L., Marques, F.: Approximation algorithms to minimum vertex cover problems on polygons and terrains. In P.M.A Sloot et al. (Eds): Proc. of ICCS 2003, LNCS 2657, SpringerVerlag (2003) 869-878. we showed that |Π(P)| ≤ 1 + r + r 2, where r is the number of reflex vertices of P. We shall now give sharper bounds both for maxP |Π(P)| and minP |Π(P)|. Moreover, we characterize the structure of orthogonal polygons in general position for which these new bounds are exact.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Orthogonal polygonsDecompositionRectilinear cutSquare gridPartitioning orthogonal polygons by extension of all edges incident to reflex vertices: lower and upper bounds on the number of piecesinfo:eu-repo/semantics/conferenceObjectinfo:eu-repo/semantics/openAccess