Abstract
Given two n-vertex plane graphs G 1 and G 2 embedded in the n × n grid with straight-line segments as edges, we show that with a sequence of O(n) point moves (all point moves stay within a 5n× 5n grid) and O(n 2) edge moves, we can transform G 1 into G 2. In the case of n-vertex trees, we can perform the transformation with O(n) point and edge moves, and show this is optimal. We also study the equivalent problems in the labelled setting.
This work was initiated when the authors were attending a workshop at the Universidad de Zaragoza. The second and sixth authors were on sabbatical leave at UPC. This work is partially supported by MCYT TIC02-4486-C02-1, SAB 2000-0234 grant of MECD Spain, a grant by Conacyt Mexico, a PIV 2001 grant of Generalitat de Catalunya, NSERC Canada, MCYT-FEDER BFM2002-0557, MCYT-FEDERBFM2003-0368, Gen. Cat 2001SGR00224, and DGA-2002-22861.
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Abellanas, M. et al. (2004). On Local Transformations in Plane Geometric Graphs Embedded on Small Grids. In: Laganá, A., Gavrilova, M.L., Kumar, V., Mun, Y., Tan, C.J.K., Gervasi, O. (eds) Computational Science and Its Applications – ICCSA 2004. ICCSA 2004. Lecture Notes in Computer Science, vol 3045. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24767-8_3
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DOI: https://doi.org/10.1007/978-3-540-24767-8_3
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