Skyline Group Queries in Large Road-Social Networks Revisited

Given a network with social and spatial information, cohesive group queries aim to find a group of strongly connected and closely co-located users. Most existing studies limit to finding groups with either the strongest social ties under certain spatial constraints or the minimum spatial distance under certain social constraints. It is difficult for users to decide which constraints they need to choose and how to prioritize the constraints to meet their real requirements since the social constraint and spatial constraint are different in nature. In this article, we take a new approach to consider the constraints equally and study a skyline query. Specifically, given a road-social network consisting of a road network <inline-formula><tex-math notation="LaTeX">$G_r$</tex-math><alternatives><mml:math><mml:msub><mml:mi>G</mml:mi><mml:mi>r</mml:mi></mml:msub></mml:math><inline-graphic xlink:href="zhu-ieq1-3111868.gif"/></alternatives></inline-formula> and a location-based social network <inline-formula><tex-math notation="LaTeX">$G_s$</tex-math><alternatives><mml:math><mml:msub><mml:mi>G</mml:mi><mml:mi>s</mml:mi></mml:msub></mml:math><inline-graphic xlink:href="zhu-ieq2-3111868.gif"/></alternatives></inline-formula>, we aim to find a set of skyline cohesive groups, in which each group cannot be dominated by any other group in terms of social cohesiveness and spatial cohesiveness. The social cohesiveness is modeled by <inline-formula><tex-math notation="LaTeX">$(k, c)$</tex-math><alternatives><mml:math><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="zhu-ieq3-3111868.gif"/></alternatives></inline-formula>-core/truss (a <inline-formula><tex-math notation="LaTeX">$k$</tex-math><alternatives><mml:math><mml:mi>k</mml:mi></mml:math><inline-graphic xlink:href="zhu-ieq4-3111868.gif"/></alternatives></inline-formula>-core/truss of size <inline-formula><tex-math notation="LaTeX">$c$</tex-math><alternatives><mml:math><mml:mi>c</mml:mi></mml:math><inline-graphic xlink:href="zhu-ieq5-3111868.gif"/></alternatives></inline-formula>), and the spatial cohesiveness is evaluated by the travel cost to a meeting point from group members. Such skyline problem is NP-hard as we need to explore the combinations of <inline-formula><tex-math notation="LaTeX">$c$</tex-math><alternatives><mml:math><mml:mi>c</mml:mi></mml:math><inline-graphic xlink:href="zhu-ieq6-3111868.gif"/></alternatives></inline-formula> vertices to check whether it is a qualified <inline-formula><tex-math notation="LaTeX">$(k,c)$</tex-math><alternatives><mml:math><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="zhu-ieq7-3111868.gif"/></alternatives></inline-formula>-core/truss. In this article, we first provide exact solutions by developing efficient pruning strategies to filter out a large number of combinations that cannot form a <inline-formula><tex-math notation="LaTeX">$(k,c)$</tex-math><alternatives><mml:math><mml:mrow><mml:mo>(</mml:mo><mml:mi>k</mml:mi><mml:mo>,</mml:mo><mml:mi>c</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="zhu-ieq8-3111868.gif"/></alternatives></inline-formula>-core/truss, and then propose highly efficient greedy solutions based on newly designed index <inline-formula><tex-math notation="LaTeX">${\mathsf {cd}}$</tex-math><alternatives><mml:math><mml:mi mathvariant="sans-serif">cd</mml:mi></mml:math><inline-graphic xlink:href="zhu-ieq9-3111868.gif"/></alternatives></inline-formula>-<inline-formula><tex-math notation="LaTeX">${\mathsf {tree}}$</tex-math><alternatives><mml:math><mml:mi mathvariant="sans-serif">tree</mml:mi></mml:math><inline-graphic xlink:href="zhu-ieq10-3111868.gif"/></alternatives></inline-formula>/<inline-formula><tex-math notation="LaTeX">${\mathsf {td}}$</tex-math><alternatives><mml:math><mml:mi mathvariant="sans-serif">td</mml:mi></mml:math><inline-graphic xlink:href="zhu-ieq11-3111868.gif"/></alternatives></inline-formula>-<inline-formula><tex-math notation="LaTeX">${\mathsf {tree}}$</tex-math><alternatives><mml:math><mml:mi mathvariant="sans-serif">tree</mml:mi></mml:math><inline-graphic xlink:href="zhu-ieq12-3111868.gif"/></alternatives></inline-formula> to keep the distance on the road network and social structural information simultaneously. Experimental results show that our exact methods run faster than the baseline methods by 2-4 orders of magnitude in general, and our index-based greedy methods can significantly reduce the computation cost by 1-4 orders of magnitude while the extra travel cost is less than 5% compared to the exact method on multiple real road-social networks.