# Adaptive Multi-Channel Clustering in IEEE 802.11s Wireless Mesh Networks +
## 4 The CHaChA Clustering Approach
### Metrics, Messages, and Parameters
It denotes the number of mesh neighbors that are currently also in the PCH role due to the same degree of connectivity (NC metric) and competition for becoming final CH. NC-to-PCHNC Ratio (NPR):The NPR is part of the metric Weighted NC-to-PCHNC Ratio (WNPR) and is calculated as the ratio of NC and PCHNC. All PCHs calculate it according to the rule \(NPR=\frac{NC}{(1+PCHNC)\cdot N}\). To guarantee a range of values between 0 and 1, the metric is also normalized to the network size \(N\). In the course of their competition, PCHs with higher NPR should be given priority since they are located in regions with fewer CH candidates. However, if NPR alone were used as a criterion, PCHs in the immediate vicinity of the outermost edge nodes of the network would be particularly preferred. Since these edge nodes usually have a lower connectivity degree (NC metric) than their neighbors located further within the network, they are not PCH candidates themselves. To compensate for an uncontrolled shift of final CHs towards the network edge, a centrality weight is added to the NPR in the form of the WNPR. Weighted NC-to-PCHNC Ratio (WNPR):All PCHs compete for the CH role with this metric and compute it according to the rule \(WNPR=NPR\cdot\frac{CENT}{CENT_{max}}\). Hence, it is obtained as the product of NPR and centrality of a PCH. For WNPR comparability between different PCHs, their own centrality is normalized to that of the MCH node (\(CENT_{max}\)), which was determined in phase 0. By means of the centrality weight, the competition finds a trade-off between favoring PCHs in underpopulated regions and keeping proximity to the MCH at the center of the network. On the one hand, this compensates for the dominance of PCHs close to the network edge, which is inherently sparse with PCH candidates as a result of the NPR metric. On the other hand, distributed applications can benefit from a proximity of CHs to the MCH, e.g., when the MCH acts as administrative synchronization point and central data sink on the base channel. Integer value of MAC address:In case of a tie (two compared metric values are identical), the node with larger integer value of its MAC address wins. This allows for quick and clear decision-making in the different competitive phases of CHaChA. An exception is the NC metric, where a tie is explicitly allowed. As a result, several CH candidates are initially created, which are subsequently thinned out using the WNPR. All CHaChA control messages are listed in Table 4. These include unicast messages, which are primarily exchanged between neighboring nodes, and broadcast messages for disseminating information throughout the network. Unlike unicast frames, the WLAN link layer transmits broadcast frames unacknowledged and thus without retransmissions in case of failure. To increase reliability, the CHaChA concept is to always send broadcast messages multiple times at the application layer. This concerns the CENT messages, carrying the CENT metric, as well as the PHASE_X messages of the MCH for announcing phase transitions. The cluster announcement messages of the CH nodes are already generated periodically. Various time interval and threshold parameters also allow for customization in terms of reliability and timing. Table 5 gives an overview of the CHaChA parameters.