Fig. 1. The distribution of the cover time on as an histogram from 10,000 runs.

Fig. 2. The load balance at cover time for random geometric graph .

Fig. 3. An example of (a) r=1.5r_con (b) r=2r_con (c) r=2.5r_con.

Fig. 4. The cover time of for increasing radius and choice: (a) full cover time; (b) time to cover 80% of the nodes.

Fig. 5. The improvement ratio (SRW/RWC(2)) of for increasing radius.

Fig. 6. Cover Time as a function of radius, size and choice.

Fig. 7. Eighty percent of cover time as a function of radius, size and choice.

Fig. 8. The expected cover time progress on a grid (normalized by grid size) for the simple random walk, and choice of 2 and 3: (a) 400 nodes; (b) 900 nodes.

Fig. 9. The cover time and 50% cover time for different grid sizes: (a) cover time; (b) 50% cover time.

Fig. 10. The improvement ratio of cover time for the choices of 2 and 3 for different grid sizes.

Fig. 11. The distribution of the cover time on a grid as an histogram from 10,000 runs for the simple random walk, and choice of 2 and 3: (a) 400 nodes; (b) 900 nodes.

Fig. 12. The expected load balance as number of visits at cover time on a grid. Average over 10,000 runs for the simple random walk, and choice of 2 and 3: (a) 400 nodes; (b) 900 nodes.

Fig. 13. The improvement ratios, L₂(n) and L₃(n), of the most visited node in SRW, RWC(2) and RWC(3) for different grid sizes.

Fig. 14. The variation distance progress until cover time on a grid average over 10,000 runs for the simple random walk, and choice of 2 and 3: (a) 400 nodes; (b) 900 nodes.

Fig. 15. The cover time of the different sizes cube and grid.

Fig. 16. The improvement ratio of cover time for the choice of 2 in the hyper-cube and grid for different sizes.

Statistical data for the cover time distribution of (normalized by n)

Mean and variance of cover times on grids (normalized by n)