## 2 Materials and Methods
### MK-Mediod Algorithm
#### 2.3.3 Collaborative Storage and Resolution based on Index Neighbor Structure
#### 3.2.1 Latency Measure Times

In order to compare the latency measurement cost of each algorithm, we counted the number of latency measurements of different index neighbor construction algorithms at different network sizes, and simulation results are shown in Figure 4.

As shown in Figure 4, the MK-Mediod algorithm and K-Mediod algorithm have the same latency measure times for each topology size--they require the most latency measurement cost. The Greedy algorithm and MGreedy algorithm have less latency measure times, and the MGreedy algorithm requires the least cost of latency measurements. The reason for this is that the clustering algorithm needs to perform latency measurements in each round with new cluster centers until the clustering algorithm obtains converged results. Thus, these two clustering algorithms need to measure the latency between every node to each other. The Greedy algorithm also traverses each resolution node, but the nodes traversed will definitely find their index neighbors and index neighbor groups, so there is no case of discarding the original traversal results and re-traversing, so the number of latency measurements required is less. The MGreedy algorithm requires fewer latency measurements because it firstly selects the children nodes nearest to the master node for traversal, and these nodes have a higher probability of being selected as index neighbors and building larger index neighbor groups. Furthermore, we found that latency measurement times of various index neighbor construction algorithms increases with increased network size, with MK-Mediod and K-Mediod algorithms showing a particularly significant increase in latency measurement times, while the other two greedy algorithms do not show a significant increase in the latency measurement times. #### 3.2.2 Computation Cost

Each algorithm involves multiple sorting operations, and the sorting operations are computationally intensive. We counted the number of sorting operation in different index neighbor construction algorithms at different network sizes, which reflects the computational consumption of each algorithm. The simulation results are shown in Figures 5 and 6, where the former figure shows the number of sorting operations performed in four index neighbor construction algorithms, Greedy, MGreedy, K-Mediod, and MK-Mediod, at different node sizes, and the latter figure shows detailed comparasion among Greedy, MGreedy, and MK-Mediod. Figure 4: Latency measure times of each algorithm with different network sizes. As shown in Figures 5 and 6, the K-Mediod algorithm involves the most number of sort operations; MK-Mediod and MGreedy algorithms were less, and Greedy algorithm was the least. The sort operation number in the MK-Mediod was 3.73% of that in K-Mediod. The reason for this is that the Greedy algorithm greedily traverses each resolution node without sort operations, so the sort operations in this algorithm are always 0. The MGreedy algorithm sorts the children at the beginning of the traversal based on the latency of each child node to the master node, so the MGreedy algorithm performs one sort operation. Both clustering methods sort the \(lat\) values of each node at each round of cluster center update operation, while the MK-Mediod algorithm performs fewer sort operations than the K-Mediod algorithm because it finish the construction with fewer rounds. ### Collaborative Storage and Resolution

To verify the impact on total system storage when using different index neighbor structures for inter-layer collaborative storage, we adopt the simplest static load balancing strategy; the master node stores a certain percentage of mapping records to index neighbors, and we compare the increase in total system storage load after collaborative storage as well as the average service latency and maximum service latency during collaborative resolution.