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 (10; 14).
This work was supported by NSERC of Canada, the Canada Research Chairs program, the IGM (University of Marne-la-Vallée) and the French “ACI Masses de données” program via the Geocomp project.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Barbay, J., Golynski, A., Munro, J.I., Rao, S.S.: Adaptive searching in succinctly encoded binary relations and tree-structured documents. In: Lewenstein, M., Valiente, G. (eds.) CPM 2006. LNCS, vol. 4009, pp. 24–35. Springer, Heidelberg (2006)
Barbay, J., He, M., Munro, J.I., Rao, S.S.: Succinct indexes for strings, binary relations and multi-labeled trees. In: Proceedings of the 18th Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 680–689. ACM Press, New York (2007)
Benoit, D., Demaine, E.D., Munro, J.I., Raman, R., Raman, V., Rao, S.S.: Representing trees of higher degree. Algorithmica 43(4), 275–292 (2005)
Bernhart, F., Kainen, P.C.: The book thickness of a graph. Journal of Combinatorial Theory, Series B 27(3), 320–331 (1979)
Castelli-Aleardi, L., Devillers, O., Schaeffer, G.: Succinct representation of triangulations with a boundary. In: Dehne, F., López-Ortiz, A., Sack, J.-R. (eds.) WADS 2005. LNCS, vol. 3608, pp. 134–145. Springer, Heidelberg (2005)
Castelli-Aleardi, L., Devillers, O., Schaeffer, G.: Optimal succinct representations of planar maps. In: Proceedings of the 22nd ACM Annual Symposium on Computational Geometry, pp. 309–318 (2006)
Chiang, Y.-T., Lin, C.-C., Lu, H.-I.: Orderly spanning trees with applications to graph encoding and graph drawing. In: Proceedings of the 12th Annual ACM-SIAM symposium on Discrete algorithms, pp. 506–515 (2001)
Chuang, R.C.-N., Garg, A., He, X., Kao, M.-Y., Lu, H.-I.: Compact encodings of planar graphs via canonical orderings and multiple parentheses. In: Proceedings of the 25th International Colloquium on Automata, Languages and Programming, pp. 118–129 (1998)
Chung, F.R.K., Leighton, F.T., Rosenberg, A.L.: Embedding graphs in books: a layout problem with applications to VLSI design. SIAM J. Algebr. Discrete Methods 8(1), 33–58 (1987)
Gavoille, C., Hanusse, N.: On compact encoding of pagenumber k graphs. Discrete Mathematics & Theoretical Computer Science (to appear, 2007)
Isenburg, M., Snoeyink, J.: Face fixer: Compressing polygon meshes with properties. In: Proceedings of SIGGRAPH 2000, pp. 263–270 (2000)
Jacobson, G.: Space-efficient static trees and graphs. In: Proceedings of the 30th Annual Symposium on Foundations of Computer Science, pp. 549–554 (1989)
Lu, H.-I., Yeh, C.-C.: Balanced parentheses strike back. ACM Transactions on Algorithms (accepted, 2007)
Munro, J.I., Raman, V.: Succinct representation of balanced parentheses and static trees. SIAM J. Comput. 31(3), 762–776 (2001)
Rosenberg, A.L.: The diogenes design methodology: toward automatic physical layout. In: Proceedings of the International Workshop on Parallel Algorithms & Architectures, pp. 335–348. North-Holland Publishing Co., Amsterdam (1986)
Schnyder, W.: Embedding planar graphs on the grid. In: Proceedings of the 1st Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 138–148 (1990)
Tarjan, R.E.: Sorting using networks of queues and stacks. J. Assoc. Comput. Mach. 19, 341–346 (1972)
Yannakakis, M.: Four pages are necessary and sufficient for planar graphs. In: Proceedings of the 18th Annual ACM-SIAM Symposium on Theory of Computing, pp. 104–108 (1986)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Barbay, J., Castelli Aleardi, L., He, M., Munro, J.I. (2007). Succinct Representation of Labeled Graphs. In: Tokuyama, T. (eds) Algorithms and Computation. ISAAC 2007. Lecture Notes in Computer Science, vol 4835. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-77120-3_29
Download citation
DOI: https://doi.org/10.1007/978-3-540-77120-3_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-77118-0
Online ISBN: 978-3-540-77120-3
eBook Packages: Computer ScienceComputer Science (R0)