Exploring Optimal Parameters for Expected Results on Radius-Bounded k-Core Queries

Radius-bounded$k$-core queries (RB-$k$-core queries) in geo-social networks aim to find all$k$-cores containing a given query vertex$q$while all vertices in each$k$-core fall into a circle under a given query radius$r$, which is widely used in many applications, such as team formulation and event organization. However, the query parameters$k$and$r$are hard to specify by the users without any background knowledge, which means the query results often do not meet the users' requirements, i.e., some expected vertices are missed in the query results. To tackle this issue, we investigate the problem of exploring optimal refined parameters (EOP) for expected results on RB­$k$-core queries, which aims to explore the optimal parameters that make the expected vertex$\omega$and query vertex$q$appear in the same RB-$k$-core. To address the EOP problem, we first propose two baseline algorithms, namely PriorityR and HybridR, which refine the parameters$k$and$r$simultaneously based on the effective bounds of the refined$r^{\prime}$• To enhance the efficiency of exploring optimal parameters, we develop two efficient al-gorithms. The first algorithm, Priority K, simultaneously refines both parameters based on the effective bound of the refined$k$• The second algorithm, HybridK, explores the optimal parameters using the continuous convergence bounds of the refined$k^{\prime}$and$r$• Furthermore, to enhance exploration efficiency, we develop a novel index, called HCR-Tree, based on the hierarchical coreness of vertices and R- Tree. This index accelerates the verification of whether the coreness of a vertex in any sub graph exceeds$k$in the above algorithms. Finally, we conduct extensive experiments using five real geo-social network datasets, which show that the optimal parameters can be explored effectively by the algorithms, and HybridK is the most effective. Meanwhile, the HCR- Tree performs better than the R- Tree for the EOP problem.