Flexible Aggregate Nearest Neighbor Queries and its Keyword-Aware Variant on Road Networks

Aggregate nearest neighbor (<sc>Ann</sc>) query in both the euclidean space and road networks has been extensively studied, and the flexible aggregate nearest neighbor (<sc>Fann</sc>) problem further generalizes <sc>Ann</sc> by introducing an extra flexibility parameter <inline-formula><tex-math notation="LaTeX">$\phi$</tex-math><alternatives><mml:math><mml:mi>ϕ</mml:mi></mml:math><inline-graphic xlink:href="chen-ieq1-2975998.gif"/></alternatives></inline-formula> that ranges in <inline-formula><tex-math notation="LaTeX">$(0, 1]$</tex-math><alternatives><mml:math><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>]</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="chen-ieq2-2975998.gif"/></alternatives></inline-formula>. In this article, we focus on <sc>Fann</sc> on road networks, denoted as <sc>Fann</sc><inline-formula><tex-math notation="LaTeX">$_\mathcal {R}$</tex-math><alternatives><mml:math><mml:msub><mml:mrow/><mml:mi mathvariant="script">R</mml:mi></mml:msub></mml:math><inline-graphic xlink:href="chen-ieq3-2975998.gif"/></alternatives></inline-formula>, and its keyword-aware variant, denoted as <sc>KFann</sc><inline-formula><tex-math notation="LaTeX">$_\mathcal {R}$</tex-math><alternatives><mml:math><mml:msub><mml:mrow/><mml:mi mathvariant="script">R</mml:mi></mml:msub></mml:math><inline-graphic xlink:href="chen-ieq4-2975998.gif"/></alternatives></inline-formula>. To solve these problems, we propose a series of universal (i.e., suitable for both <italic>max</italic> and <italic>sum</italic>) algorithms, including a Dijkstra-based algorithm that enumerates <inline-formula><tex-math notation="LaTeX">$P$</tex-math><alternatives><mml:math><mml:mi>P</mml:mi></mml:math><inline-graphic xlink:href="chen-ieq5-2975998.gif"/></alternatives></inline-formula> instead of <inline-formula><tex-math notation="LaTeX">$\phi |Q|$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>ϕ</mml:mi><mml:mo>|</mml:mo><mml:mi>Q</mml:mi><mml:mo>|</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="chen-ieq6-2975998.gif"/></alternatives></inline-formula>-combinations of <inline-formula><tex-math notation="LaTeX">$Q$</tex-math><alternatives><mml:math><mml:mi>Q</mml:mi></mml:math><inline-graphic xlink:href="chen-ieq7-2975998.gif"/></alternatives></inline-formula>, a queue-based approach that processes data points from-near-to-far, and a framework that combines <italic>incremental euclidean restriction</italic> (IER) and <inline-formula><tex-math notation="LaTeX">$k$</tex-math><alternatives><mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href="chen-ieq8-2975998.gif"/></alternatives></inline-formula>NN. We also propose a specific exact solution to <italic>max</italic>-<sc>Fann</sc><inline-formula><tex-math notation="LaTeX">$_\mathcal {R}$</tex-math><alternatives><mml:math><mml:msub><mml:mrow/><mml:mi mathvariant="script">R</mml:mi></mml:msub></mml:math><inline-graphic xlink:href="chen-ieq9-2975998.gif"/></alternatives></inline-formula> and a constant-factor ratio approximate solution to <italic>sum</italic>-<sc>Fann</sc><inline-formula><tex-math notation="LaTeX">$_\mathcal {R}$</tex-math><alternatives><mml:math><mml:msub><mml:mrow/><mml:mi mathvariant="script">R</mml:mi></mml:msub></mml:math><inline-graphic xlink:href="chen-ieq10-2975998.gif"/></alternatives></inline-formula>. These specific algorithms are easy to implement and can achieve excellent performance in some scenarios. Besides, we further extend this problem to top-<inline-formula><tex-math notation="LaTeX">$k$</tex-math><alternatives><mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href="chen-ieq11-2975998.gif"/></alternatives></inline-formula> and multiple <sc>Fann</sc><inline-formula><tex-math notation="LaTeX">$_\mathcal {R}$</tex-math><alternatives><mml:math><mml:msub><mml:mrow/><mml:mi mathvariant="script">R</mml:mi></mml:msub></mml:math><inline-graphic xlink:href="chen-ieq12-2975998.gif"/></alternatives></inline-formula> (resp., <sc>KFann</sc><inline-formula><tex-math notation="LaTeX">$_\mathcal {R}$</tex-math><alternatives><mml:math><mml:msub><mml:mrow/><mml:mi mathvariant="script">R</mml:mi></mml:msub></mml:math><inline-graphic xlink:href="chen-ieq13-2975998.gif"/></alternatives></inline-formula>) queries. We conduct a comprehensive experimental evaluation for the proposed algorithms on real datasets to demonstrate their superior efficiency and high quality.