Succinct Representations of Separable Graphs
- Guy E. BlellochAffiliated withComputer Science Department, Carnegie Mellon University
- , Arash FarzanAffiliated withMax-Planck-Institut für Informatik
We consider the problem of highly space-efficient representation of separable graphs while supporting queries in constant time in the RAM with logarithmic word size. In particular, we show constant-time support for adjacency, degree and neighborhood queries. For any monotone class of separable graphs, the storage requirement of the representation is optimal to within lower order terms.
Separable graphs are those that admit a O(n c )-separator theorem where c < 1. Many graphs that arise in practice are indeed separable. For instance, graphs with a bounded genus are separable. In particular, planar graphs (genus 0) are separable and our scheme gives the first succinct representation of planar graphs with a storage requirement that matches the information-theory minimum to within lower order terms with constant time support for the queries.
We, furthers, show that we can also modify the scheme to succinctly represent the combinatorial planar embedding of planar graphs (and hence encode planar maps).
- Succinct Representations of Separable Graphs
- Book Title
- Combinatorial Pattern Matching
- Book Subtitle
- 21st Annual Symposium, CPM 2010, New York, NY, USA, June 21-23, 2010. Proceedings
- pp 138-150
- Print ISBN
- Online ISBN
- Series Title
- Lecture Notes in Computer Science
- Series Volume
- Series ISSN
- Springer Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- Additional Links
- Industry Sectors
- eBook Packages
- Editor Affiliations
- 16. Department of Computer Science, Johns Hopkins University, Baltimore, MD, USA, and Bar-Ilan University
- 17. IBM T.J. Watson Research Center
- Author Affiliations
- 18. Computer Science Department, Carnegie Mellon University,
- 19. Max-Planck-Institut für Informatik, 66123, Saarbrücken, Germany
To view the rest of this content please follow the download PDF link above.