Before revision:  ^{ 1/2 } /\varepsilon^3 )\big(}{\eps^2}}\big) ^{ d(k+1) } ) and can answer the \big\}\big)  \textsc{(1+ \varepsilon \eps )\delta-ANNS} queries in O(kd) query time \D  . Considering k as part of the query slightly changes the space to O( n ( 64d^{1/2/\varepsilon^3} )^{md\big({\eps}}\big) with O(kd) query time within  5 (1 + \varepsilon) approximation factor . We also \eps show that our data structure could give an alternative treatment of the approximate subtrajectory range counting (\textsc{ASRC ) problem studied by de Berg et al.
After revision:  ^{ 1/2 } /\varepsilon^3 )\big(}{\eps^2}}\big) ^{ d(k+1) } ) and can answer the \big\}\big) \textsc{(1+ \varepsilon \eps )\delta-ANNS} queries in O(kd) query time \D . Considering k as part of the query slightly changes the space to O( n ( 64d^{1/2/\varepsilon^3} )^{md\big({\eps}}\big) with O(kd) query time within 5 (1 + \eps show that our data structure could give an alternative treatment of the approximate subtrajectory range counting (\textsc{ASRC ) problem studied by de Berg et al.