|Type of publication:||Article|
|Title||Efficient computation of implicit representations of sparse graphs*1|
|Bibtex cite ID||RACTI-RU1-1997-6|
|Journal ||Discrete Applied Mathematics|
|Year published ||1997|
|Keywords ||Implicit representation,Sparse graphs,Arboricity,Graph algorithms,Parallel computation|
The problem of finding an implicit representation for a graph such that vertex adjacency can be tested quickly is fundamental to all graph algorithms. In particular, it is possible to represent sparse graphs on n vertices using O(n) space such that vertex adjacency is tested in O(l) time. We show here how to construct such a representation efficiently by providing simple and optimal algorithms, both in a sequential and a parallel setting. Our sequential algorithm runs in O(n) time. The parallel algorithm runs in O(log n) time using O(n/log n) CRCW PRAM processors, or inO(log n log* n) time using O(n/log n log* n) EREW PRAM processors. Previous results for this problem are based on matroid partitioning and thus have a high complexity.
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