# Value of Information Based Data Retrieval in UWSNs
## 4 Path Planning Algorithms
### Greedy Path Planner-GPP  
GPP and its variants are reactive path planning algorithms. This path planner provides a visitation sequence of nodes in descending order of their VoI aggregate profiles, i.e., the AUV will visit the node with maximum VoI available first and then other nodes in decreasing order of VoI at offer by them. The VoI is determined as the value available at the time instant when the AUV visits the sensor node. This is a greedy approach as the algorithm tries to maximize the VoI accumulated by determining which node has the highest amount to offer and then visit it. A potential path planned using the GPP algorithm is shown with the red colored trail in Figure 1.  
VoI accumulation is dependent on the final time-stamps \(\tau_{f}\) as suggested by Equation (17). The lesser the value of \(\tau_{f}\), the higher the VoI accumulated, i.e., the earlier the data is retrieved from a node, the more quickly the value decay is locked down, hence, resulting in greater value dividends. It would, therefore, make more sense to lock down VoI at nodes that have higher values to offer. Otherwise, more VoI would be potentially lost.  
If there is a scenario where high-priority events are being reported because of a catastrophe, then it is imperative that it be reported at the earliest. The more the delay in reporting catastrophic data, the more would be the losses incurred. Moreover, as the UWSN has been deployed to report of catastrophic events, therefore, it is necessary that the AUV visits the nodes reporting the catastrophe first.  
Algorithm 2 details the steps for the greedy approach. The algorithm maintains a history of nodes that it has already visited and the ones that it has yet to visit. From the nodes not visited yet, it selects the ones that give it the maximum VoI at its time of arrival. Once it selects a node as its next destination, it takes a direct euclidean route to it. The complexity of GPP is \(\mathcal{O}(n^{2})\) where n is the number of sensor nodes.  
```
1:procedureGPP(\(S\), \(s_{o}\))
2:\(S\leftarrow\{s_{1},s_{2},...,s_{n}\}\)\(\triangleright\) Set of sensor nodes
3:\(V\leftarrow\emptyset\)\(\triangleright\) Visitation sequence
4:\(i\gets s_{o}\)\(\triangleright\) Tour starting node
5:while\(S\
eq\emptyset\)do
6:\(j\leftarrow\textsc{GetNodeThatHasMaxVoi(S)}\)
7:\(\textsc{tourEuclidean(}i,j\texttt{)}\)
8:\(V\gets V+j\)
9:\(S\gets S-j\)
10:endwhile
11:return\(V\)
12:endprocedure
13:procedureGetNodeThatHasMaxVoi(\(S_{r}\))
14:\(\forall s_{x}\in S_{r}\) determine \(\textsc{Y}_{s_{x}}\) using \(\textsc{DetermineNodeVoi}(D_{s_{x}},t)\)
15:\(k\gets s_{x}\in S_{r}\) such that \(\textsc{Y}_{s_{x}}\) is \(\max\sum Ae^{-B(t-\tau_{o})}\)
16:return\(k\)
17:endprocedure
18:procedureDetermineNodeVoi(\(D,t\))
19:\(D\leftarrow\{d_{1},d_{2},...,d_{k}\}\)\(\triangleright\) Data reports at node
20:\(\textsc{Y}\gets 0\)
21:\(\tau_{f}\gets t\)\(\triangleright\) AUV arrival time at node
22:while\(D\
eq\emptyset\)do
23:\(j\leftarrow\textsc{GetNextDataReport(}D\texttt{)}\)
24:\(\alpha\leftarrow\textsc{Get}A_{x}(j)\)
25:\(\beta\leftarrow\textsc{Get}B_{x}(j)\)
26:\(\tau_{o}\leftarrow\textsc{Get}\tau_{o}(j)\)
27:\(\textsc{Y}\mathrel{+}=\alpha e^{-\beta(\tau_{f}-\tau_{o})}\)
28:\(D\gets D-j\)
29:endwhile
30:endprocedure
```  
**Algorithm 2** Greedy Path Planner-**G**PP.