Efficient computation of implicit representations of sparse graphs

• Published in: Discrete Applied Mathematics Vol. 78; no. 1; pp. 1 - 16
• Main Authors: Arikati, Srinivasa R., Maheshwari, Anil, Zaroliagis, Christos D.
• Format: Journal Article
• Language: English
• Published: Lausanne Elsevier B.V 21.10.1997; Amsterdam Elsevier; New York, NY
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Arboricity; Computer science; control theory; systems; Exact sciences and technology; Graph algorithms; Implicit representation; Information retrieval. Graph; Parallel computation; Sparse graphs; Theoretical computing; Parallel computation; Graph algorithms; Arboricity; Implicit representation; Sparse graphs; Vertex(graph); Parallel algorithm; Tree(graph); Optimal algorithm; Matroid
• ISSN: 0166-218X; 1872-6771; 1872-6771
• DOI: 10.1016/S0166-218X(97)00007-3

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.