Maximum Clique Exhaustive Search in Circulant k-Hypergraphs

In this paper, we discuss two algorithms to solve the maximum clique problem in circulant k-hypergraphs, and do an experimental comparison between them. The first is the Necklace algorithm proposed by Tzanakis, Moura, Panario and Stevens [11] which uses an algorithm to generate binary necklaces by Ruskey, Savage and Wang [10]. The second algorithm is a new algorithm which we call Russian Necklace that is based on a Russian doll search for maximum cliques by Ostergard [6] with extra pruning that takes advantages of properties specific to circulant k-hypergraphs. Our experiments indicate that the new algorithm is more effective for hypergraphs with higher edge density.