Processing of Top-K Most Influential Location Selection Queries

Facility location selection queries help to evaluate the popularity of different facility locations for a to-be-added facility. Such queries have wide applications in marketing and decision support systems. In this report, we propose and investigate a new type of queries aiming to retrieve the top-k most influential locations from a candidate set in a given context of customers and existing facilities. The influence in the query, which models the potential popularity of the new facility, is defined as the number of reverse nearest customers the new facility can attract if it was added. Specifically, given a candidate set C, an existing facility set F , and a customer set M , the proposed query returns the top-k candidates in C with the greatest influences. The most naive solution for the query employs sequential scan on all data sets and is thus expensive and not scalable to large data sets. To improve the solution, two R-Tree based branch-and-bound algorithms are presented. One of them, named Estimation Expanding Pruning (EEP), uses distance metrics between nodes to tighten the search space, while the other, named Bounding Influence Pruning (BIP), relies on half plane styled geometric properties to achieve the same goal. Both algorithms follow the best-first access strategy guided by “hints” computed during the pruning and meanwhile gradually refine these “hints”. BIP generally outperforms EEP since it avoids repeated estimations on F and M . Yet due to the extensively accesses on R-tree indexes, the complexity in the worst case of both algorithms is unsatisfactory, causing their performance to degrade dramatically when the data set grows. To achieve better scalability, an algorithm named Nearest Facility Circle (NFC) is proposed. Rather than computing all the influence relationships from scratch as EEP and BIP, NFC first pre-computes the influence relationships between customers and existing facilities, then indexes these relationships with an R-Tree, finally processes the query using multiple cheap point enclosure queries. Furthermore, a NFC join (NFCJ) algorithm is propose to construct an R-tree on candidate set and share the common traversal cost of point enclosure query by using R-tree join algorithm. We theoretically and experimentally compare all proposed algorithms. The results show that NFCJ is the the best solution for the proposed query.