Abstract
In this paper we give a new description of the planarity testing and embedding algorithm presented by Boyer and Myrvold [2], providing, in our opinion, new insights on the combinatorial foundations of the algorithm. Especially, we give a detailed illustration of a fundamental phase of the algorithm, called walk-up, which was only succinctly illustrated in [2]. Also, we present an implementation of the algorithm and extensively test its efficiency against the most popular implementations of planarity testing algorithms. Further, as a side effect of the test activity, we propose a general overview of the state of the art (restricted to efficiency issues) of the planarity testing and embedding field.
Work partially supported by European Commission – Fet Open project COSIN – COevolution and Self-organisation In dynamical Networks – IST-2001-33555, by “Progetto ALINWEB: Algoritmica per Internet e per il Web”, MIUR Programmi di Ricerca Scientifica di Rilevante Interesse Nazionale, and by “The Multichannel Adaptive Information Systems (MAIS) Project”, MIUR Fondo per gli Investimenti della Ricerca di Base.
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Boyer, J.M., Cortese, P.F., Patrignani, M., Di Battista, G. (2004). Stop Minding Your P’s and Q’s: Implementing a Fast and Simple DFS-Based Planarity Testing and Embedding Algorithm. In: Liotta, G. (eds) Graph Drawing. GD 2003. Lecture Notes in Computer Science, vol 2912. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24595-7_3
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DOI: https://doi.org/10.1007/978-3-540-24595-7_3
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