novel application 1999 chapter node π methodology https://doi.org/10.1007/3-540-48481-7_47 distinct node (respectively, edge) labels ’s census series string x set of properties planar graphs general methodology 2022-01-01T19:17 labels graph set https://scigraph.springernature.com/explorer/license/ chapters separator simple planar graph minimum number graph G true conjunction plane graph node labels class properties example paper 540-549 applications Fast General Methodology information general class en satisfies certain properties Tutte’s census series A Fast General Methodology for Information—Theoretically Optimal Encodings of Graphs series 1999-01-01 cycle separator binary string x property π encoding number function certain properties bits time problem small cycle separators We propose a fast methodology for encoding graphs with informationtheoretically minimum numbers of bits. The methodology is applicable to general classes of graphs; this paper focuses on simple planar graphs. Specifically, a graph with property π is called a π-graph. If π satisfies certain properties, then an n-node π-graph G can be encoded by a binary string X such that (1) G and X can be obtained from each other in O(n log n) time, and (2)X has at most β(n)+ o(β(n)) bits for any function β(n) = Ω (n) so that there are at most 2β(n)+ o(β(n)) distinct n-node π-graphs. Examples of such π include all conjunctions of the following sets of properties: (1) G is a planar graph or a plane graph; (2) G is directed or undirected; (3) G is triangulated, triconnected, biconnected, merely connected, or not required to be connected; and (4) G has at most ℓ1 (respectively, ℓ2) distinct node (respectively, edge) labels. These examples are novel applications of small cycle separators of planar graphs and settle several problems that have been open since Tutte’s census series were published in 1960’s. optimal encoding fast methodology doi 10.1007/3-540-48481-7_47 Springer Nature - SN SciGraph project Pure Mathematics Springer Nature Department of Computer Science and Engineering, State University of New York at Buffalo, 14260, Buffalo, NY, USA Department of Computer Science and Engineering, State University of New York at Buffalo, 14260, Buffalo, NY, USA Ming-Yang Kao dimensions_id pub.1006627258 Mathematical Sciences 978-3-540-48481-3 978-3-540-66251-8 Algorithms - ESA’ 99 Lu Hsueh-I Jaroslav Nešetřil He Xin Department of Computer Science, Yale University06250, New Haven, CT, USA Department of Computer Science, Yale University06250, New Haven, CT, USA Department of Computer Science and Information Engineering, National Chung-Cheng University, 621, Chia-Yi, Taiwan, ROC Department of Computer Science and Information Engineering, National Chung-Cheng University, 621, Chia-Yi, Taiwan, ROC