Succinct Representations of Separable Graphs

Blelloch, Guy E.; Farzan, Arash

doi:10.1007/978-3-642-13509-5_13

Item

ITEM ACTIONSEXPORT

Add to Basket

Local TagsRelease HistoryDetailsSummary

Released

Conference Paper

Succinct Representations of Separable Graphs

MPS-Authors

/persons/resource/persons44403

Farzan, Arash
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

External Resource

No external resources are shared

Fulltext (restricted access)

There are currently no full texts shared for your IP range.

Fulltext (public)

There are no public fulltexts stored in PuRe

Supplementary Material (public)

There is no public supplementary material available

Citation

Blelloch, G. E., & Farzan, A. (2010). Succinct Representations of Separable Graphs. In A. Amir, & L. Parida (Eds.), Combinatorial Pattern Matching (pp. 138-150). Berlin: Springer. doi:10.1007/978-3-642-13509-5_13.

Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-16F5-4

Abstract

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).