On the succinct representation of graphs

Turán, György

doi:10.1016/0166-218x(84)90126-4

Cited by 150 publications

(94 citation statements)

References 4 publications

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“…This distribution follows a power law similar to the node degree distribution displayed in Figure 1 (bottom). The problem of graph compression has been approached by several authors over the years, perhaps beginning with the paper [9]. Among the most recent works, Feder and Motwani [10] looked at graph compression from the algorithmic standpoint, with the goal of carrying out algorithms on compressed versions of a graph.…”

Section: Preliminariesmentioning

confidence: 99%

Graph Compression by BFS

2009

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Abstract:The Web Graph is a large-scale graph that does not fit in main memory, so that lossless compression methods have been proposed for it. This paper introduces a compression scheme that combines efficient storage with fast retrieval for the information in a node. The scheme exploits the properties of the Web Graph without assuming an ordering of the URLs, so that it may be applied to more general graphs. Tests on some datasets of use achieve space savings of about 10% over existing methods.

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Section: Preliminariesmentioning

confidence: 99%

Graph Compression by BFS

2009

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“…One of our main motivations for generalizing Schnyder woods to higher genus is the great number of existing works in the domain of graph encoding and mesh compression that take advantage of spanning tree decompositions [23,30,33], and in particular of the ones underlying Schnyder woods (and related extensions) for planar graphs [1,11,12,20,21,29]. The combinatorial properties of Schnyder woods and the related characterizations (canonical orderings [22]) for planar graphs yield efficient procedures for encoding tree structures based on multiple parenthesis words.…”

Section: Schnyder Trees and Graph Encodingmentioning

confidence: 99%

Schnyder Woods for Higher Genus Triangulated Surfaces, with Applications to Encoding

Aleardi

Fusy

Lewiner

2009

Discrete Comput Geom

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Schnyder woods are a well known combinatorial structure for planar graphs, which yields a decomposition into 3 vertexspanning trees. Our goal is to extend definitions and algorithms for Schnyder woods designed for planar graphs (corresponding to combinatorial surfaces with the topology of the sphere, i.e., of genus 0) to the more general case of graphs embedded on surfaces of arbitrary genus. First, we define a new traversal order of the vertices of a triangulated surface of genus g together with an orientation and coloration of the edges that extends the one proposed by Schnyder for the planar case. As a by-product we show how some recent schemes for compression and compact encoding of graphs can be extended to higher genus. All the algorithms presented here have linear time complexity.

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“…Turán [17] pioneered a 4m bit encoding, that has been improved later by Keeler and Westbrook [18] to 3.58m. Munro and Raman [19] then proposed a 2m + 8n bit encoding based on the 4-page embedding of planar graphs (see [20]).…”

Section: Related Workmentioning

confidence: 99%

Planar Graphs, via Well-Orderly Maps and Trees

Gavoille

Hanusse

Poulalhon

et al. 2004

Graph-Theoretic Concepts in Computer Science

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Abstract. The family of well-orderly maps is a family of planar maps with the property that every connected planar graph has at least one plane embedding which is a well-orderly map. We show that the number of well-orderly maps with n nodes is at most 2 αn+O(log n) , where α ≈ 4.91. A direct consequence of this is a new upper bound on the number p(n) of unlabeled planar graphs with n nodes, log 2 p(n) 4.91n. The result is then used to show that asymptotically almost all (labeled or unlabeled), (connected or not) planar graphs with n nodes have between 1.85n and 2.44n edges. Finally we obtain as an outcome of our combinatorial analysis an explicit linear time encoding algorithm for unlabeled planar graphs using, in the worst-case, a rate of 4.91 bits per node and of 2.82 bits per edge.

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On the succinct representation of graphs

Cited by 150 publications

References 4 publications

Graph Compression by BFS

Graph Compression by BFS

Schnyder Woods for Higher Genus Triangulated Surfaces, with Applications to Encoding

Planar Graphs, via Well-Orderly Maps and Trees

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