Abstract
In this paper, we introduce a uniform random sampler for linear extensions of Series-Parallel posets. The algorithms we present ensure an essential property of random generation algorithms: entropy. They are in a sense optimal in their consumption of random bits.
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Notes
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The combinatorial embedding allows to distinguish the two successors of a node: the left one and the right one.
References
Bodini, O., Genitrini, A., Peschanski, F.: A quantitative study of pure parallel processes. Electron. J. Comb. 23(1), 39 (2016). P1.11
Felsner, S., Wernisch, L.: Markov chains for linear extensions, the two-dimensional case. In: SODA, pp. 239–247. Citeseer (1997)
Flajolet, P., Sedgewick, R.: Analytic Combinatorics. Cambridge University Press, Cambridge (2009)
Huber, M.: Fast perfect sampling from linear extensions. Discr. Math. 306(4), 420–428 (2006)
Klein, P., Mozes, S.: Optimization Algorithms for Planar Graphs (to appear)
Lumbroso, J.: Optimal discrete uniform generation from coin flips, and applications. CoRR abs/1304.1916 (2013). http://arxiv.org/abs/1304.1916
Möhring, R.H.: Computationally Tractable Classes of Ordered Sets. Report, Institut für Ökonometrie und Operations Research (1987)
Sedgewick, R.: Left-leaning red-black trees. In: Dagstuhl Workshop on Data Structures. p. 17 (2008)
Shannon, C.E.: A mathematical theory of communication. ACM SIGMOBILE Mobile Comput. Commun. Rev. 5(1), 3–55 (2001)
Stanley, R.P.: Enumerative Combinatorics, vol. 1, 2nd edn. Cambridge University Press, New York (2011)
Valdes, J., Tarjan, R.E., Lawler, E.L.: The recognition of series parallel digraphs. In: Proceedings of the Eleventh Annual ACM Symposium on Theory of Computing (STOC 1979), pp. 1–12. ACM, New York (1979). http://doi.acm.org/10.1145/800135.804393
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Bodini, O., Dien, M., Genitrini, A., Peschanski, F. (2017). Entropic Uniform Sampling of Linear Extensions in Series-Parallel Posets. In: Weil, P. (eds) Computer Science – Theory and Applications. CSR 2017. Lecture Notes in Computer Science(), vol 10304. Springer, Cham. https://doi.org/10.1007/978-3-319-58747-9_9
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DOI: https://doi.org/10.1007/978-3-319-58747-9_9
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