Algorithm 1: Distributed PQ-index Construction

Input: Set of taxi trips T  Output: PQ-index $PQI$  // information extraction   1: Taxi trip information $TI$←$\mathtt{informationExtraction}$(T);  // grouping by area or route   2: Initialize $AG$ as a tuple of (pair ($ar$,$tp$), a list of taxi trip information);   3: Initialize $RG$ as a tuple of (pair ($rt$,$tp$), a list of taxi trip information);   4: $AG$ ← $\mathtt{groupByAreaTP}$($TI$);   5: $RG$ ← $\mathtt{groupByRouteTP}$($TI$);  // construct basic summaries   6: Initialize $ASP$ for an area summary;   7: Initialize $RSP$ for a route summary;   8: $ASP$ ← $\mathtt{BuildAreaSummary}$($AG$); // Algorithm 2   9: $RSP$ ← $\mathtt{BuildRouteSummary}$($RG$); // Algorithm 3  // PQ-index construction 10: An extended route summary $ERSP$ ← $\mathtt{BuildExtendedRouteSummary}$($RSP$); // Algorithm 4 11: $PQI$ ← $\mathtt{mergeByKey}$($ASP$,$ERSP$); 12: return $PQI$;