# A Community-Based Construct Method for an Inter-Satellite Communication Network of Satellite Swarm
## 4 Optimized Constructions of ICNS
### Dynamic-Connectivity-Oriented Construction Method of ICNS  
The dynamic-connectivity-oriented construction method of ICNS is illustrated in Algorithm 2, which is also the process of constructing an ICNS in this study. We employed the Jaccard distance and the blacklist in Algorithm 2. The Jaccard distance is a measure of the similarity of two sets. For two non-empty finite sets, \(Y\) and \(Z\), their Jaccard coefficient is the ratio of the cardinality of their intersection to the cardinality of their union [25], as shown in Equation (16):  
\[J(Y,Z)=\frac{|Y\cap Z|}{|Y\cup Z|} \tag{16}\]  
The greater \(J(Y,Z)\) is, the more similar \(Y\) and \(Z\) are. The blacklist is the set shown in Equation (17):  
\[B=\{\widetilde{e}_{ij}|\widetilde{e}_{ij}\in\overline{M}_{\zeta}\cap\cdots \cap\overline{M}_{\rho}\} \tag{17}\]  
where \(\kappa\) is the maximum number of times that one CLC is permitted to repeat. The blacklist collects those CLCs that have occurred frequently in selected CCLCs. Any CCLC with even one element of the blacklist should be removed from the subset of all CCLCs \(\mathcal{M}_{k}\) obtained by Algorithm 1. Figure 3: Binary tree showing dynamic paths. ```
0:\(A_{k}\), \(D_{k}\), \(W_{k}\), \(\mathcal{S}=\{\overline{M}_{1},\cdots,\overline{M}_{k-1}\}\), \(\hat{E}=E_{1}\cup\cdots\cup E_{k-1}\)
0:\(E_{k}\)
1: Establish three matrices: \(A^{\prime}=\left({a^{\prime}}_{ij}\right)_{\Theta\times\Theta^{\prime}}\), \(D^{\prime}=\left({d^{\prime}}_{ij}\right)_{\Theta\times\Theta}\) and \(W^{\prime}=\left({w^{\prime}}_{ij}\right)_{\Theta\times\Theta}\); \(A^{\prime}\gets A_{k}\), \(D^{\prime}\gets D_{k}\), \(W^{\prime}\gets W_{k}\)
2: Obtain \(\mathcal{M}^{\prime}_{k}\) based on \(A^{\prime}\) using Algorithm 1
3: Obtain the MSE-CCLC in \(\mathcal{M}^{\prime}_{k}\), denoted by \(\overline{M}_{k}\), based on \(D^{\prime}\) and \(W^{\prime}\)
4:if\(\overline{M}_{k}\
otin\mathcal{S}\)then
5:\(E_{k}=\{\varepsilon_{\lambda\mu}|\vec{e}_{\lambda\mu}\in\overline{M}_{k}\}\)
6:else
7: For each \(\epsilon_{ij}\in\hat{E}\): \({a^{\prime}}_{ij}\leftarrow 0\), \({a^{\prime}}_{ji}\leftarrow 0\), \({w^{\prime}}_{ij}\leftarrow 0\), \({w^{\prime}}_{ji}\leftarrow 0\), \({d^{\prime}}_{ij}\leftarrow{d^{\prime}}_{ij}-1\), \(d^{\prime}_{ji}\leftarrow{d^{\prime}}_{ji}-1\)
8: Obtain \(\mathcal{M}^{\prime}_{k}\) based on new \(A^{\prime}\) using Algorithm 1
9:if\(\mathcal{M}^{\prime}_{k}\
eq\varnothing\)do
10: Obtain the MSE-CCLC in \(\mathcal{M}^{\prime}_{k}\), denoted by \(\overline{M}_{k}\), based on new \(D^{\prime}\) and new \(W^{\prime}\)
11:\(E_{k}=\{\varepsilon_{\lambda\mu}|\vec{e}_{\lambda\mu}\in\overline{M}_{k}\}\), \(\mathcal{S}\leftarrow\mathcal{S}\cup\{\overline{M}_{k}\}\), \(\hat{E}\leftarrow\hat{E}\cup E_{k}\)
12:else
13: Obtain \(\mathcal{M}_{k}\) based on \(A_{k}\) using Algorithm 1
14:\(\mathcal{M}_{k}\leftarrow\mathcal{M}_{k}-\left(\mathcal{M}_{k}\cap\mathcal{S}\right)\)
15: Establish the matrix \(Y=\left(y_{\varepsilon\tau}\right)_{|\mathcal{M}_{k}|\times|\mathcal{S}|}\), where \(y_{\varepsilon\tau}=\left(M_{k}(\epsilon),E_{\tau}\right)\), \(1\leq\varepsilon\leq\mid\mathcal{M}_{k}\mid\), \(1\leq\tau\leq k-1\)
16: Establish the sequence: \(\overline{y}_{1},\cdots,\overline{y}_{\sigma},\cdots,\overline{y}_{|\mathcal{ M}_{k}|}\), where \(\overline{y}_{\epsilon}=\frac{1}{F-1}\sum\limits_{\tau=1}^{k-1}y_{\varepsilon\tau}\) ; sort the sequence from small to large, which creates the new sequence: \(y^{\prime}_{1},\cdots,y^{\prime}_{\sigma},\cdots,y^{\prime}_{|\mathcal{M}_{k}|}\); define the mapping \(f(\cdot)\) and let \(f(y^{\prime}_{\sigma})=\varepsilon\)
17:for\(\sigma=1\)to\(|\mathcal{M}_{k}|\)do
18:if\(M_{k}[f(y^{\prime}_{\sigma})]\cap B\
eq\varnothing\)and\(M_{k}[f(y^{\prime}_{\sigma})]\
otin S\)then
19:\(E_{k}=\left\{\varepsilon_{\lambda\mu}\Big{|}\vec{e}_{\lambda\mu}\in M_{k}[f(y^{ \prime}_{\sigma})]\right\}\), \(S\gets S\cup\{M_{k}[f(y^{\prime}_{\sigma})]\}\), \(\hat{E}\leftarrow\hat{E}\cup E_{k}\)
20:break
21:endif
22:endfor
23:endif
```  
**Algorithm 2** Dynamic-connectivity-oriented construction method of ICNS.