Fig. 7

Tuning time and access latency of four index approaches for kNN queries versus k. a Tuning time (OL). b Tuning time (SR). c Tuning time (CAL). d Tuning time (FL). e Access latency (OL). f Access latency (SR). g Access latency (CAL). h Access latency (FL). a–d The tuning time of four index methods on the four urban road network datasets of the OL, SR, CAL, and FLs in the case that the number of targets k to be queried is different. It can be seen from the figure that the tuning time increases linearly with the increase of the k value for the ISW index, especially on the FL large-scale data set; the tuning time of k = 20 is more than two times that of k = 1, which is related to the long broadcast period of the ISW index and the large number of frames. Both NPI index and IEI index have better performance, especially IEI index, considering the distributed mechanism. Tuning time is relatively stable; its performance is closer to the proposed DIM index in CAL and other small datasets, but in large-scale dataset FL, the advantage of DIM is reflected. e–h The access latency of four index methods on the four urban road network datasets of the OL, SR, CAL, and FL in the case where the number of targets k to be queried is different. As can be seen from the figure, access latency of ISW is increasing, the mobile client needs a lot of time to keep active mode, and access latency of ISW is three times as much as DIM. NPI, IEI, and DIM are relatively stable. For NPI, the absolute average of the road network results in expansion of the partition, and the broadcast cycle is longer. So access latency will continue to increase, but no ups and downs, which thanks to the pre-computation of NPI Index before querying, the pre-computation information consists of a large number of road network boundary points, each cell diameter, pairs of nodes of an edge