Effective Index Construction Algorithm for Optimal $(k,\eta)$-cores Computation

Computing $(k,\eta)$-cores from uncertain graphs is a fundamental problem in uncertain graph analysis. UCF-Index is the state-of-the-art resolution to support $(k,\eta)$-core queries, allowing the $(k,\eta)$-core for any combination of $k$ and $\eta$ to be computed in an optimal time. However, this index constructed by current algorithm is usually incorrect. During decomposition, the key is to obtain the $k$-probabilities of its neighbors when the vertex with minimum $k$-probability is deleted. Current method uses recursive floating-point division to update it, which can lead to serious errors. We propose a correct and efficient index construction algorithm to address this issue. Firstly, we propose tight bounds on the $k$-probabilities of the vertices that need to be updated, and the accurate $k$-probabilities are recalculated in an on-demand manner. Secondly, vertices partitioning and progressive refinement strategy is devised to search the vertex with the minimum $k$-probability, thereby reducing initialization overhead for each $k$ and avoiding unnecessary recalculations. Finally, extensive experiments demonstrate the efficiency and scalability of our approach.