Efficient computation of implicit representations of sparse graphs - Arikati, Srinivasa R.; Maheshwari, Anil; Zaroliagis, Christos D. (Discrete Applied Mathematics, 1997)
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 in O(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.