ROAM: A Fundamental Routing Query on Road Networks with Efficiency

Novel road-network applications often recommend a moving object (e.g., a vehicle) about interesting services or tasks on its way to a destination. A taxi-sharing system, for instance, suggests a new passenger to a taxi while it is serving another one. The traveling cost is then shared among these passengers. A fundamental query is: given two nodes <inline-formula><tex-math notation="LaTeX">$s$</tex-math><alternatives><mml:math><mml:mi>s</mml:mi></mml:math><inline-graphic xlink:href="luo-ieq1-2906188.gif"/></alternatives></inline-formula> and <inline-formula><tex-math notation="LaTeX">$t$</tex-math><alternatives><mml:math><mml:mi>t</mml:mi></mml:math><inline-graphic xlink:href="luo-ieq2-2906188.gif"/></alternatives></inline-formula>, and an area <inline-formula><tex-math notation="LaTeX">$\mathcal {A}$</tex-math><alternatives><mml:math><mml:mi mathvariant="script">A</mml:mi></mml:math><inline-graphic xlink:href="luo-ieq3-2906188.gif"/></alternatives></inline-formula> on road network graph <inline-formula><tex-math notation="LaTeX">$\mathcal {G}$</tex-math><alternatives><mml:math><mml:mi mathvariant="script">G</mml:mi></mml:math><inline-graphic xlink:href="luo-ieq4-2906188.gif"/></alternatives></inline-formula>, is there a “good” route (e.g., short enough path) <inline-formula><tex-math notation="LaTeX">$P$</tex-math><alternatives><mml:math><mml:mi>P</mml:mi></mml:math><inline-graphic xlink:href="luo-ieq5-2906188.gif"/></alternatives></inline-formula> from <inline-formula><tex-math notation="LaTeX">$s$</tex-math><alternatives><mml:math><mml:mi>s</mml:mi></mml:math><inline-graphic xlink:href="luo-ieq6-2906188.gif"/></alternatives></inline-formula> to <inline-formula><tex-math notation="LaTeX">$t$</tex-math><alternatives><mml:math><mml:mi>t</mml:mi></mml:math><inline-graphic xlink:href="luo-ieq7-2906188.gif"/></alternatives></inline-formula> that crosses <inline-formula><tex-math notation="LaTeX">$\mathcal {A}$</tex-math><alternatives><mml:math><mml:mi mathvariant="script">A</mml:mi></mml:math><inline-graphic xlink:href="luo-ieq8-2906188.gif"/></alternatives></inline-formula> in <inline-formula><tex-math notation="LaTeX">$\mathcal {G}$</tex-math><alternatives><mml:math><mml:mi mathvariant="script">G</mml:mi></mml:math><inline-graphic xlink:href="luo-ieq9-2906188.gif"/></alternatives></inline-formula>? In a taxi-sharing system, <inline-formula><tex-math notation="LaTeX">$s$</tex-math><alternatives><mml:math><mml:mi>s</mml:mi></mml:math><inline-graphic xlink:href="luo-ieq10-2906188.gif"/></alternatives></inline-formula> and <inline-formula><tex-math notation="LaTeX">$t$</tex-math><alternatives><mml:math><mml:mi>t</mml:mi></mml:math><inline-graphic xlink:href="luo-ieq11-2906188.gif"/></alternatives></inline-formula> can be a taxi's current and destined locations, and <inline-formula><tex-math notation="LaTeX">$\mathcal {A}$</tex-math><alternatives><mml:math><mml:mi mathvariant="script">A</mml:mi></mml:math><inline-graphic xlink:href="luo-ieq12-2906188.gif"/></alternatives></inline-formula> contains all the places to which a person waiting for a taxi is willing to walk. Answering this <italic>Route and Area Matching</italic> (ROAM) Query allows the application involved to recommend appropriate services to users efficiently. In this paper, we examine efficient ROAM query algorithms. Particularly, we develop solutions for finding a <italic><inline-formula><tex-math notation="LaTeX">$\rho$</tex-math><alternatives><mml:math><mml:mi>ρ</mml:mi></mml:math><inline-graphic xlink:href="luo-ieq13-2906188.gif"/></alternatives></inline-formula>-route</italic>, which is an <inline-formula><tex-math notation="LaTeX">$s$</tex-math><alternatives><mml:math><mml:mi>s</mml:mi></mml:math><inline-graphic xlink:href="luo-ieq14-2906188.gif"/></alternatives></inline-formula>-<inline-formula><tex-math notation="LaTeX">$t$</tex-math><alternatives><mml:math><mml:mi>t</mml:mi></mml:math><inline-graphic xlink:href="luo-ieq15-2906188.gif"/></alternatives></inline-formula> path that passes <inline-formula><tex-math notation="LaTeX">$\mathcal {A}$</tex-math><alternatives><mml:math><mml:mi mathvariant="script">A</mml:mi></mml:math><inline-graphic xlink:href="luo-ieq16-2906188.gif"/></alternatives></inline-formula>, with a length of at most <inline-formula><tex-math notation="LaTeX">$(1+\rho)$</tex-math><alternatives><mml:math><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>+</mml:mo><mml:mi>ρ</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="luo-ieq17-2906188.gif"/></alternatives></inline-formula> times the shortest distance between <inline-formula><tex-math notation="LaTeX">$s$</tex-math><alternatives><mml:math><mml:mi>s</mml:mi></mml:math><inline-graphic xlink:href="luo-ieq18-2906188.gif"/></alternatives></inline-formula> and <inline-formula><tex-math notation="LaTeX">$t$</tex-math><alternatives><mml:math><mml:mi>t</mml:mi></mml:math><inline-graphic xlink:href="luo-ieq19-2906188.gif"/></alternatives></inline-formula>. The existence of a <inline-formula><tex-math notation="LaTeX">$\rho$</tex-math><alternatives><mml:math><mml:mi>ρ</mml:mi></mml:math><inline-graphic xlink:href="luo-ieq20-2906188.gif"/></alternatives></inline-formula>-route implies that a service or task located at <inline-formula><tex-math notation="LaTeX">$\mathcal {A}$</tex-math><alternatives><mml:math><mml:mi mathvariant="script">A</mml:mi></mml:math><inline-graphic xlink:href="luo-ieq21-2906188.gif"/></alternatives></inline-formula> can be found for a given moving object <inline-formula><tex-math notation="LaTeX">$m$</tex-math><alternatives><mml:math><mml:mi>m</mml:mi></mml:math><inline-graphic xlink:href="luo-ieq22-2906188.gif"/></alternatives></inline-formula>, and that <inline-formula><tex-math notation="LaTeX">$m$</tex-math><alternatives><mml:math><mml:mi>m</mml:mi></mml:math><inline-graphic xlink:href="luo-ieq23-2906188.gif"/></alternatives></inline-formula> only deviates slightly from its current route. We present comprehensive studies on index-free and index-based algorithms for answering ROAM queries. Comprehensive experiments show that our algorithm runs up to 30 times faster than baseline algorithms.