Orderly spanning trees with applications to graph encoding and graph drawing
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Compact representations of separable graphs
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
An Information-Theoretic Upper Bound of Planar Graphs Using Triangulation
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Compact Encodings of Planar Orthogonal Drawings
GD '02 Revised Papers from the 10th International Symposium on Graph Drawing
Graph compression and the zeros of polynomials
Information Processing Letters
Dictionaries using variable-length keys and data, with applications
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Dissections and trees, with applications to optimal mesh encoding and to random sampling
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Selective decompression of vector maps
Proceedings of the 15th annual ACM international symposium on Advances in geographic information systems
Compact dictionaries for variable-length keys and data with applications
ACM Transactions on Algorithms (TALG)
Dissections, orientations, and trees with applications to optimal mesh encoding and random sampling
ACM Transactions on Algorithms (TALG)
Quick encoding of plane graphs in log 214 bits per edge
Information Processing Letters
Optimal coding and sampling of triangulations
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
A fast and compact web graph representation
SPIRE'07 Proceedings of the 14th international conference on String processing and information retrieval
A compact encoding of plane triangulations with efficient query supports
WALCOM'08 Proceedings of the 2nd international conference on Algorithms and computation
A compact encoding of plane triangulations with efficient query supports
Information Processing Letters
Fast and Compact Web Graph Representations
ACM Transactions on the Web (TWEB)
Succinct representations of separable graphs
CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
Non-linear compression: Gzip Me Not!
HotStorage'12 Proceedings of the 4th USENIX conference on Hot Topics in Storage and File Systems
Tight and simple Web graph compression for forward and reverse neighbor queries
Discrete Applied Mathematics
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We propose a fast methodology for encoding graphs with information-theoretically minimum numbers of bits. Specifically, a graph with property $\pi$ is called a {\em $\pi$-graph}. If $\pi$ satisfies certain properties, then an n-node m-edge $\pi$-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 $\beta(n)+o(\beta(n))$ bits for any continuous superadditive function $\beta(n)$ so that there are at most $2^{\beta(n)+o(\beta(n))}$ distinct $n$-node $\pi$-graphs. The methodology is applicable to general classes of graphs; this paper focuses on planar graphs. Examples of such $\pi$ 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 $\{1,\ldots, \ell_1\}$ for $\ell_1\leq n$; (5) the edges of G are labeled with labels from $\{1,\ldots, \ell_2\}$ for $\ell_2\leq m$; and (6) each node (respectively, edge) of G has at most $\ell_3=O(1)$ self-loops (respectively, $\ell_4=O(1)$ multiple edges). Moreover, $\ell_3$ and $\ell_4$ are not required to be O(1) for the cases of $\pi$ being a plane triangulation. These examples are novel applications of small cycle separators of planar graphs and are the only nontrivial classes of graphs, other than rooted trees, with known polynomial-time information-theoretically optimal coding schemes.