# Towards Collaborative and Dynamic Spectrum Sharing via Interpretation of Spectrum Access Policies
## 5 Policies
### Planner
#### 6.4.2 Rendezvous Channels  
The objective here is to define the Rendezvous Channels Selection as an optimization problem. In other words, the idea is to first formalize the problem and then try to figure out whether this problem is possibly a case of a known problem already formulated (and possibly solved) somewhere else. We are considering a scenario in which \(r\) wireless radio nodes distributed over some geographical 2D space are trying to find a number of channels on which they could communicate while not violating any of the policies that the radios must obey. For every two radios to communicate at the same time, assuming every pair needs a separate channel (i.e., every pair tuned to the same frequency, while all of the other pairs use different frequencies), we need \(f\) frequencies, where \(f\) is defined as:  
\[f=r(r-1)/2\]  
We can think of the value of \(f\) as the minimal requirement. The Controller will need more frequencies to choose from. This requirement makes the problem complex since if there are \(r\) radios and \(f\) frequencies, there are \(f^{r}\) selection options, of which only \(f\) selections satisfy the requirement of tuning to the same frequency. While a full formalization of this problem would require a definition of the tuning precision, conceptually they must be on _the same frequency_ in order to communicate. The policies are known to all the radios, however, the radios know only their own locations but not the locations of the other nodes. Moreover, it is assumed that all the nodes must obey the policies, i.e., they can transmit only if there is a policy that allows them to transmit in a given location at a specified time on a given frequency, and there is no disallowing policy. The rendezvous algorithm will be executed on all the radios with the same input data (i.e., the same set of policies), and thus, the result should be the same for all the radios. We are considering a scenario in which any two wireless radio nodes distributed over some geographical 2D space are trying to find common channels on which they could communicate. The objective here is to define the Rendezvous Channels Selection as an optimization problem. The rules (pertaining to the currently active policy) are known to all the radios; however, the radios know only their own locations but not the locations of the other nodes. Moreover, it is assumed that all the nodes must obey the rules, i.e., they can only transmit if there is a policy (rule) that allows them to transmit in a given location at a specified time on a given frequency. The rendezvous algorithm will be executed on all the radios with the same input data (i.e., the same set of rules) and is designed to guarantee some number of common channels between any two radios, even though the locations of radios are different. **Problem Formulation:**  
**Given:**  
* A collection of \"primary\" policies, \(P\) (policies that cover all other \"allow\" policies geographically, e.g., D, E and F in Figure 8);
* A collection of \"secondary\" policies \(S\) (all?allow? rules, e.g., A, B, D, E and F in Figure 8);
* A ratio, \(r\), of the number of selections of center frequencies from the policies \(F_{P}\) vs. the frequencies selected from the policies \(F_{S}\), \(r=|F_{P}|/|F|\), where \(F=F_{P}\cup F_{S}\);
* The number of maximum communication channels, \(n\);
* One half of the width of each channel, \(b\);
* A set of sub-bands \(R=\{R_{1},\ldots,R_{k}\}\) (derived by the opportunities algorithm);
* Allowed frequency multiplier, \(\Delta\).