 Using quadtrees, we provide an alternative algorithm that runs in near linear time , although this second algorithm has a logarithmic dependence on either\big(\big(\big)\big) the ratio of the fastest speed to the slowest speed of disks or the spread of disk centers (the ratio of the maximum to the minimum distance between them). Our result improves the running times of previous algorithms by Funke, Krumpe, and Storandt [IWOCA 2016], Bahrdt et al.
<clarity>  Using quadtrees, we provide an alternative algorithm that runs in near linear time , although this second algorithm has a logarithmic dependence on either\big(\big(\big)\big) the ratio of the fastest speed to the slowest speed of disks or the spread of disk centers (the ratio of the maximum to the minimum distance between them). Our result improves the running times of previous algorithms by Funke, Krumpe, and Storandt [IWOCA 2016], Bahrdt et al.
 Using quadtrees, we provide an alternative algorithm that runs in near linear time , although this second algorithm has a logarithmic dependence on either\big(\big(\big)\big) the ratio of the fastest speed to the slowest speed of disks or the spread of disk centers (the ratio of the largest and the smallest distance between two disk centers. This improves the running times of previous algorithms by Funke, Krumpe, and Storandt [IWOCA 2016], Bahrdt et al.