Efficient k-clique Listing with Set Intersection Speedup

Listing all k-cliques is a fundamental problem in graph mining, with applications in finance, biology, and social network analysis. However, owing to the exponential growth of the search space as k increases, listing all k-cliques is algorithmically challenging. DDegree and DDegCol are the state-of-the-art algorithms that exploit ordering heuristics based on degree ordering and color ordering, respectively. Both DDegree and DDegCol induce high time and space overhead for set intersections cause they construct and maintain all induced subgraphs. Meanwhile, it is non-trivial to implement the data level parallelism to further accelerate on DDegree and DDegCol. In this paper, we propose two efficient algorithms SDegree and BitCol for k-clique listing. We mainly focus on accelerating the set intersections for k-clique listing. Both SDegree and BitCol exploit the data level parallelism for further acceleration with single instruction multiple data (SIMD) or vector instruction sets. Furthermore, we propose two preprocessing techniques Pre-Core and Pre-List, which run in linear time. The preprocessing techniques significantly reduce the size of the original graph and prevent exploring a large number of invalid nodes. In the theoretical analysis, our algorithms have a comparable time complexity and a slightly lower space complexity than the state-of-the-art algorithms. The comprehensive experiments reveal that our algorithms outperform the state-of-the-art algorithms by 3.75x for degree ordering and 5.67x for color ordering on average.