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# Dissections and trees, with applications to optimal mesh encoding and to random sampling

@inproceedings{Fusy2005DissectionsAT, title={Dissections and trees, with applications to optimal mesh encoding and to random sampling}, author={{\'E}ric Fusy and Dominique Poulalhon and Gilles Schaeffer}, booktitle={SODA}, year={2005} }

- Published 2005 in SODA

We present a bijection between some quadrangular dissections of an hexagon and unrooted binary trees. This correspondence has interesting consequences for enumeration, mesh compression and random graph sampling.It yields a succinct representation for the set <i>P(n)</i> of <i>n</i>-edge 3-connected planar graphs matching the entropy bound 1/<i>n</i> log |<i>P</i>(<i>n</i>)| = 2+<i>o</i>(1) bits per edge. This solves a theoretical problem in mesh compression, as these graphs abstract the… CONTINUE READING

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