A Fast General Methodology for Information - Theoretically Optimal Encodings of Graphs

We propose a fast methodology for encoding graphs with information-theoretically minimum numbers of bits. Specifically, a graph with property π is called a π-graph. If π satisfies certain properties, then an n-node m-edge 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 continuous superadditive function β(n) so that there are at most 2β(n)+o(β(n)) distinct n-node π-graphs. The methodology is applicable to general classes of graphs; this paper focuses on planar graphs. Examples of such π include all conjunctions over the following groups 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; (4) the nodes of G are labeled with labels from {1, . . . , 1} for 1 ≤ n; (5) the edges of G are labeled with labels from {1, . . . ...

• Type: Conference
• Year: 1999
• Where: ESA
• Authors: Xin He, Ming-Yang Kao, Hsueh-I Lu
• Keywords: Algorithms, Continuous Superadditive Function, ESA 1999, Planar Graphs, Satisfies Certain Properties