Succinct Greedy Drawings Do Not Always Exist
Di Battista, Giuseppe and Frati, Fabrizio and Angelini, Patrizio (2010) Succinct Greedy Drawings Do Not Always Exist. In: Graph Drawing 17th International Symposium, GD 2009, September 22-25, 2009, Chicago, IL, USA , pp. 171-182 (Official URL: http://dx.doi.org/10.1007/978-3-642-11805-0_17).
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A greedy drawing is a graph drawing containing a distance-decreasing path for every pair of nodes. A path (v0 , v1 , . . . , vm ) is distance-decreasing if d(vi , vm ) < d(vi−1 , vm ), for i = 1, . . . , m. Greedy drawings easily support geographic greedy routing. Hence, a natural and practical problem is the one of constructing greedy drawings in the plane using few bits for representing vertex Cartesian coordinates and using the Euclidean distance as a metric. We show that there exist greedy-drawable graphs that do not admit any greedy drawing in which the Cartesian coordinates have less than a polynomial number of bits.
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