*5.1. Comparison to Other Algorithms*

We compare CODB with other three competing algorithms (i.e., Brushfire, Dynamic Brushfire, and algorithms proposed by Boris Lau et al. [23] (we abbreviate it as BL below)) which are discussed in Section 2 in four typical scenarios as shown in Figure 9.

**Figure 9.** The grid maps used to compare performance of different algorithms. (**a**) Full reconstruction; (**b**) 75% changed; (**c**) 50% changed; (**d**) 25% changed. Within these figures, the obstacles marked in black and blue are static, while the obstacles marked in yellow randomly change their positions or shapes.

We set aside four grid maps (from Figure 9a to Figure 9d) which have the same size (100 × 100) while allowing different proportions of the obstacles (i.e., fully reconstruction, 75%, 50%, and 25% respectively) to randomly change their positions or shapes. After each set of changes, we use the above mentioned four algorithms to construct or reconstruct the DMs. We run each algorithm on each scenario 100 times, and the comparisons of the performances among these algorithms are shown in Table 7 and Figure 10 (i.e., the average computation time scaled in milliseconds and its variance) and Table 8 and Figure 11 (i.e., the maximal size of the priority queue *OPEN* during construction and its variance).



\* Dynamic algorithms that only repair the affected portions.

**Table 8.** Comparison of themaximal size of the priority queue*OPEN*(Onlydynamic algorithms are compared).


**Figure 10.** The average computation time provided by the four algorithms for updating DMs. The algorithms prefixed with "\*" are dynamic algorithms and only update the affected areas.

**Figure 11.** The average cell visits provided by the three dynamic algorithms.

For the first scenario in which full reconstructions are inevitable since all the obstacles are moved or reshaped, the extra operations that enable local repairs make Dynamic Brushfire (8.61 ms) and BL (7.22 ms) slower than their static counterpart, Brushfire (6.34 ms). However, due to the integration of Canonical Ordering strategy, CODB can substantially prune the search space; thus, it still maintains an obvious advantage over the other three algorithms in time efficiency (4.26 ms), even in the case of full reconstructions. As for the other three scenarios, as the proportion of the dynamic obstacles decreases, dynamic algorithms gradually manifest their superiority in speed. Among the three dynamic algorithms, CODB is also faster than the others due to fewer cell visits, reducing the computation time by at least 50%.
