# Succinct Representation of Labeled Graphs

Abstract : In many applications, the properties of an object being modeled are stored as labels on vertices or edges of a graph. In this paper, we consider succinct representation of labeled graphs. Our main results are the succinct representations of labeled and multi-labeled graphs (we consider vertex labeled planar triangulations, as well as edge labeled planar graphs and the more general $k$-page graphs) to support various label queries efficiently. The additional space cost to store the labels is essentially the information-theoretic minimum. As far as we know, our representations are the first succinct representations of labeled graphs. We also have two preliminary results to achieve the main results. First, we design a succinct representation of unlabeled planar triangulations to support the rank/select of edges in ccw (counter clockwise) order in addition to the other operations supported in previous work. Second, we design a succinct representation for a $k$-page graph when $k$ is large to support various navigational operations more efficiently. In particular, we can test the adjacency of two vertices in $O(\lg k\lg\lg k)$ time, while previous work uses $O(k)$ time.
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Type de document :
Communication dans un congrès
Takeshi Tokuyama. 18th International Symposium on Algorithms and Computation (ISAAC 2007), Dec 2007, Sendai, Japan. Springer, 4835, pp.316-328, 2007, LNCS. 〈10.1007/978-3-540-77120-3_29〉
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https://hal.inria.fr/hal-00713051
Contributeur : Luca Castelli Aleardi <>
Soumis le : jeudi 28 juin 2012 - 23:56:37
Dernière modification le : jeudi 11 janvier 2018 - 06:19:44

### Citation

Jérémy Barbay, Luca Castelli Aleardi, Meng He, Ian Munro. Succinct Representation of Labeled Graphs. Takeshi Tokuyama. 18th International Symposium on Algorithms and Computation (ISAAC 2007), Dec 2007, Sendai, Japan. Springer, 4835, pp.316-328, 2007, LNCS. 〈10.1007/978-3-540-77120-3_29〉. 〈hal-00713051〉

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