Abstract
We present a dynamic data structure that allows for incrementally constructing a planar embedding of a planar graph with n vertices and m edges. The data structure supports the following operations: (1) testing if a new edge can be added to the embedding without introducing crossings; (2) adding and removing vertices and edges. In each case the time complexity is O (log m). The space used and the preprocessing time are O(m). If the graph is simple (i.e. it has no self-loops and no parallel edges), the above bounds become O(log n) and O(n), respectively. This work finds applications in circuit layout, graphics, motion planning, and computer-aided design.
(Extended abstract)
Research partially supported by the National Science Foundation under grant ECS-84-10902.
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Tamassia, R. (1988). A dynamic data structure for planar graph embedding. In: Lepistö, T., Salomaa, A. (eds) Automata, Languages and Programming. ICALP 1988. Lecture Notes in Computer Science, vol 317. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-19488-6_143
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DOI: https://doi.org/10.1007/3-540-19488-6_143
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