Arboricity and subgraph listing algorithms
SIAM Journal on Computing
On generating all maximal independent sets
Information Processing Letters
Randomized dynamic graph algorithms with polylogarithmic time per operation
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Algorithm 457: finding all cliques of an undirected graph
Communications of the ACM
Finding All Maximal Cliques in Dynamic Graphs
Computational Optimization and Applications
The worst-case time complexity for generating all maximal cliques and computational experiments
Theoretical Computer Science - Computing and combinatorics
Distributed approximate matching
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
Automated social hierarchy detection through email network analysis
Proceedings of the 9th WebKDD and 1st SNA-KDD 2007 workshop on Web mining and social network analysis
Fully dynamic biconnectivity in graphs
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
A scalable, parallel algorithm for maximal clique enumeration
Journal of Parallel and Distributed Computing
| Hi-index | 5.23 |
The problem of enumerating the maximal cliques of a graph is a computationally expensive problem with applications in a number of different domains. Sometimes the benefit of knowing the maximal clique enumeration (MCE) of a single graph is worth investing the initial computation time. However, when graphs are abstractions of noisy or uncertain data, the MCE of several closely related graphs may need to be found, and the computational cost of doing so becomes prohibitively expensive. Here, we present a method by which the cost of enumerating the set of maximal cliques for related graphs can be reduced. By using the MCE for some baseline graph, the MCE for a modified, or perturbed, graph may be obtained by enumerating only the maximal cliques that are created or destroyed by the perturbation. When the baseline and perturbed graphs are relatively similar, the difference set between the two MCEs can be overshadowed by the maximal cliques common to both. Thus, by enumerating only the difference set between the baseline and perturbed graphs' MCEs, the computational cost of enumerating the maximal cliques of the perturbed graph can be reduced. We present necessary and sufficient conditions for enumerating difference sets when the perturbed graph is formed by several different types of perturbations. We also present results of an algorithm based on these conditions that demonstrate a speedup over traditional calculations of the MCE of perturbed, real biological networks.