Orthogeodesic Point-Set Embedding of Trees
Di Giacomo, Emilio and Frati, Fabrizio and Fulek, Radoslav and Grilli, Luca and Krug, Marcus (2012) Orthogeodesic Point-Set Embedding of Trees. In: Graph Drawing 19th International Symposium, GD 2011, September 21-23, 2011, Eindhoven, The Netherlands , pp. 52-63 (Official URL: http://dx.doi.org/ 10.1007/978-3-642-25878-7_6).
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Let S be a set of N grid points in the plane, and let G a graph with n vertices (n ≤ N ). An orthogeodesic point-set embedding of G on S is a drawing of G such that each vertex is drawn as a point of S and each edge is an orthogonal chain with bends on grid points whose length is equal to the Manhattan distance.We study the following problem. Given a family of trees F what is the minimum value f (n) such that every n-vertex tree in F admits an orthogeodesic point-set embedding on every grid-point set of size f (n)? We provide polynomial upper bounds on f (n) for both planar and non-planar orthogeodesic point-set embeddings as well as for the case when edges are required to be L-shaped chains.
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