Algorithm 4: Build an Extended Route Summary

Input: $RSP$: tuple (key k, area $ar$, first time period $t{p}_{min}$, second time period $t{p}_{max}$, route summary $rs$)  Output: $ERSP$: pair (spatio-temporal hash-key $key$, Extended Route Summary $ERS$) 1 Initialize $ERS$ as Extended Route Summary;  // Assign a route summary 2 $ERS.RS$ ← $RSP.rs$; 3 $ERS.t{p}_{min}$ ← $RSP.t{p}_{min}$; 4 $ERS.t{p}_{max}$ ← $RSP.t{p}_{max}$;  // augmenting a route summary with area summries 5 $ERS.A{S}_{min}$ ← GetAreaSummary $RSP.ar$, $t{p}_{min}$; 6 $ERS.A{S}_{max}$ ← GetAreaSummary $RSP.ar$, $t{p}_{max}$;  // combine a spatio-temporal hashkey with an extended route summary 7 $ERSP$ ← a pair of ($key$, $ERS$); 8 return $ERSP$;