Core Decomposition on Uncertain Graphs Revisited

Core decomposition on uncertain graphs is a fundamental problem in graph analysis. Given an uncertain graph G, the core decomposition problem is to determine all (k,η)-cores in G, where a (k,η)-core is a maximal subgraph of G such that each node has an η-degree no less than k within the subgraph. The η-degree of a node v is defined as the maximum integer r such that the probability that v has a degree no less than r is larger than or equal to the threshold η ψ [0,1] The state-of-the-art algorithm for solving this problem is based on a peeling technique which iteratively removes the nodes with the smallest η-degrees and also dynamically updates their neighbors' η-degrees. Unfortunately, we find that such a peeling algorithm with the dynamical h-degree updating technique is incorrect due to the inaccuracy of the recursive floating-point number division operations involved in the dynamical updating procedure. To correctly compute the (k,η)-cores, we first propose a bottom-up algorithm based on an on-demand η-degree computational strategy. To further improve the efficiency, we also develop a more efficient top-down algorithm with several nontrivial optimization techniques. Both of our algorithms do not involve any floating-point number division operations, thus the correctness can be guaranteed. In addition, we also develop the parallel variants of all the proposed algorithms. Finally, we conduct extensive experiments to evaluate the proposed algorithms using five large real-life datasets. The results show that our algorithms are at least three orders of magnitude faster than the existing exact algorithms on large uncertain graphs. The results also demonstrate the high scalability and parallel performance of the proposed algorithms.