Group Processing of Multiple k-Farthest Neighbor Queries in Road Networks

Advances in mobile technologies and map-based applications enables users to utilize sophisticated spatial queries, including <inline-formula> <tex-math notation="LaTeX">${k}$ </tex-math></inline-formula>-nearest neighbor and shortest path queries. Often, location-based servers are used to handle multiple simultaneous queries because of the popularity of map-based applications. This study focuses on the efficient processing of multiple concurrent <inline-formula> <tex-math notation="LaTeX">${k}$ </tex-math></inline-formula>-farthest neighbor (<inline-formula> <tex-math notation="LaTeX">${k}$ </tex-math></inline-formula>FN) queries in road networks. For a positive integer <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula>, query point <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>, and set of data points <inline-formula> <tex-math notation="LaTeX">$P$ </tex-math></inline-formula>, a <inline-formula> <tex-math notation="LaTeX">${k}$ </tex-math></inline-formula>FN query returns <inline-formula> <tex-math notation="LaTeX">$k$ </tex-math></inline-formula> data points farthest from the query point <inline-formula> <tex-math notation="LaTeX">$q$ </tex-math></inline-formula>. For addressing multiple concurrent spatial queries, traditional location-based servers based on one-query-at-a-time processing are unsuitable owing to high redundant computation costs. Therefore, we propose a group processing of multiple <inline-formula> <tex-math notation="LaTeX">${k}$ </tex-math></inline-formula>FN (GMP) algorithm to process multiple <inline-formula> <tex-math notation="LaTeX">${k}$ </tex-math></inline-formula>FN queries in road networks. The proposed GMP algorithm uses group computation to avoid the redundant computation of network distances between the query and data points. The experiments using real-world roadmaps demonstrate the proposed solution’s effectiveness and efficiency.