eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-08-30
85:1
85:15
10.4230/LIPIcs.ESA.2023.85
article
Algorithms for Computing Maximum Cliques in Hyperbolic Random Graphs
Oh, Eunjin
1
Oh, Seunghyeok
1
Department of Computer Science, POSTECH, Pohang, South Korea
In this paper, we study the maximum clique problem on hyperbolic random graphs. A hyperbolic random graph is a mathematical model for analyzing scale-free networks since it effectively explains the power-law degree distribution of scale-free networks. We propose a simple algorithm for finding a maximum clique in hyperbolic random graph. We first analyze the running time of our algorithm theoretically. We can compute a maximum clique on a hyperbolic random graph G in O(m + n^{4.5(1-α)}) expected time if a geometric representation is given or in O(m + n^{6(1-α)}) expected time if a geometric representation is not given, where n and m denote the numbers of vertices and edges of G, respectively, and α denotes a parameter controlling the power-law exponent of the degree distribution of G. Also, we implemented and evaluated our algorithm empirically. Our algorithm outperforms the previous algorithm [BFK18] practically and theoretically. Beyond the hyperbolic random graphs, we have experiment on real-world networks. For most of instances, we get large cliques close to the optimum solutions efficiently.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol274-esa2023/LIPIcs.ESA.2023.85/LIPIcs.ESA.2023.85.pdf
Maximum cliques
hyperbolic random graphs