Succinct representations of separable graphs

Authors:
Guy E. Blelloch;Arash Farzan
Affiliations:
Computer Science Department, Carnegie Mellon University;Max-Planck-Institut für Informatik, Saarbrücken, Germany
Venue:
CPM'10 Proceedings of the 21st annual conference on Combinatorial pattern matching
Year:
2010

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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(nc)-separator theorem where c 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).