# Area Division Using Affinity Propagation for Multi-Robot Coverage Path Planning
## 6 Discussion  
### Limitations  
While this paper proposed an innovative application of AP in the field of multi-robot CPP, it is not without limitations. A clear understanding of these potential constraints is essential for refining the algorithm, enhancing its applicability, and identifying areas for future research.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Environment** & **Importance Factors (\(E_{uv}\), \(F_{W}\))** & **Height Homogeneity** & **Floor Homogeneity** \\ \hline
100 \(\times\) 100 & (0, 0) & 0.61 & 0.49 \\
100 \(\times\) 100 & (0.8, 0) & 0.75 & 0.45 \\
100 \(\times\) 100 & (0.8, 0.8) & 0.59 & 0.53 \\
100 \(\times\) 100 & (0, 0.8) & 0.53 & 0.78 \\ \hline \end{tabular}
\end{table}
Table 2: Experimental results from the execution of the proposed algorithm in the same environment using different elevation \(E_{w}\) and floor type \(F_{W}\) weight factors. These values range from 0 to 1 and describe how important the preservation of elevation or floor type within a generated sub-area is. Increasing or decreasing both values at the same time reduces the importance of both variables within the clustering process.  
Figure 6: The initial environment as depicted in (**a**) contains two layer types (green and gray). The second image (**b**) shows the output clusters of the algorithm (blue and yellow) with an importance factor \(T_{W}=0\). The third image (**c**) shows the output of the algorithm for the same input environment where the importance factor \(T_{W}\) is equal to 0.8. Increasing the importance factor of floor type increases the likelihood that the algorithm will consider two cells of the same type to be more similar.  
Figure 7: An example environment with dimensions \(24\times 24\). The initial environment (**a**) contains two layer types (green and gray). The second image (**b**) shows the output clusters of the algorithm (blue and yellow) with an importance factor \(T_{W}=0.3\).  
The primary limitation arises from the AP's inherent computational complexity. With a time complexity of O(N\({}^{2T}\)), where N represents the number of data points and T denotes the number of iterations, AP can be computationally expensive for large-scale environments. This computational cost is primarily due to the calculation of the similarity matrix and the iterative exchange of \"responsibility\" and \"availability\" messages. This renders the algorithm less practical for real-time operations, particularly for larger environments, as it may lead to increased latency in area division and subsequent path planning.  
Another important limitation is the static nature of the AP algorithm, which is very hard if not impossible to adjust for dynamic environments. The AP algorithm, as applied in this context, assumes a static environment where the position of obstacles and the type of each cell are known beforehand. In scenarios where the environment changes over time, the algorithm would need to be rerun, potentially leading to delays and inefficiencies. The ability to adapt to dynamic environments remains a significant challenge in the field of multi-robot CPP and represents a key area for future research.