Fast Algorithm for Finding Maximum Clique in Scale-Free Networks

Andrej Jursa
2016 Conference on Theory and Practice of Information Technologies  
The maximum clique problem in graph theory concerns finding the largest subset of vertices in which all vertices are connected with an edge. Computation of such subset is a well-known NP-hard problem and there exist many algorithms to solve it. For our purposes we created an algorithm specially targeted for solving this problem in scale-free networks, where many significant search improvements may be introduced. We use the general purpose algorithm developed by Östergård in 2002 as subroutine
more » ... r our new algorithm. We improved the search process by initial heuristic. Firstly we compute preliminary clique size and then reduce the graph by k-core decomposition of this size. Subsequently, we employ greedy algorithm for coloring of chosen vertex as well as its neighbors. Our algorithm is able to solve maximum clique problem for arbitrary graphs, but together with these and some other, less significant pruning techniques, the overall algorithm performs exceptionally well on scale-free networks, which was tested on many real graphs as well as randomly generated graphs.
dblp:conf/itat/Jursa16 fatcat:7sxl33qznfawfghyyv7jan2xfu