# Intersection and Complement Set (IACS) Method to Reduce Redundant Node in Mobile WSN Localization
## 3 Problem Analysis  
The simulation details of MSL\({}^{\star}\) and LCC are explained in this section. For this research, Netbeans (netbeans.org) is used for the simulation of MSL\({}^{\star}\), LCC and IACS. Netbeans is an Integrated Development Environment (IDE) for Java language. The base source codes for the simulation have been acquired from the original author.  
Sensor nodes \(N\) are arbitrarily scattered throughout the 2-dimensional Euclidean space (2E) to create the WSN environment. The parameters of our experimental setup are shown as in Table 1. LCC [4] reduces the communication and computation cost of the localization process in MSL by reducing the number of nodes used during the localization process. Figure 1a,b shows the comparison of overall computation and communication costs between MSL\({}^{\star}\) and LCC. Based on these results, reducing the number of neighbor nodes used for the localization process contributes to a significant reduction of computation and communication costs.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Time Slot & 200 \\ Iteration & 50 \\ _maxv_ & 0.2\(r\) \\ \(r\) & 50 unit \\ Environment & Square bordered area of 500 unit \(\times\) 500 unit \\ Maximum sample number & 50 samples \\ Mobility model & Modified Random Waypoint with 0 pause time \\ Base Density & 32 \\ Sd & 1.0 \\ Nd & 10.0 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Experimental Setup Parameters.  
Further study on LCC is done to detect any research gaps. As a start, a simulation to detect redundancy on the LCC node selection method is performed. The simulation is based on the experimental setup in Table 1 including the list of all the intersection sets of each blind node neighbors.  
LCC [4] filters the neighbor for each node based on intersection sets. Table 2 shows the examples of the filtered neighbor nodes (Id), selected based on their respective list of neighbor sets and intersection sets. Based on the table, there are duplicated intersection between node 8 and node 9. This shows that node 8 and 9 share the same information for the filtering method in LCC. Therefore, a simulation to detect these duplicates is done using the experimental setup in Table 1.  
In term of information sharing, even though the sampling process requires the data from both first and second hop neighbors, LCC only considers the total intersected neighbors between the blind node and its neighbors. Therefore, by also considering the total non-intersected neighbors shared between the blind nodes and their neighbors, more nodes for the localization process can be filtered. For these reasons, IACS is proposed to safely discard these redundant data in order to minimize the localization cost. IACS considers both intersection and non-intersection sets to further reduce the redundancy (Section 4). The complement set is included in the proposed method to remove the redundant data from the neighboring node that is outside of the blind node signal range.  
Table 3 shows the tabulated version of duplicate intersection sets in Figure 2. Based on the simulation, the basic statistics of duplicated intersection sets detected for 320 nodes within 200 time slots are summarized in Table 4. The maximum duplication can reach up to 20, while zero (no duplicate) is the minimum. Each node has approximately an average of 5 duplicate intersection sets while the total duplication in each node that frequently occurred is 3.  
\begin{table}
\begin{tabular}{c c c} \hline
**Id** & **Neighbor Set** & **Intersection Set** \\ \hline
0 & \{1, 2, 3, 5, 7, 8, 9\} & \{1, 7, 8, 9\} \\
1 & \{0, 3, 5, 6, 7, 8, 9\} & \{0, 6, 7, 8, 9\} \\
6 & \{1, 3, 4, 5, 8, 9\} & \{1, 8, 9\} \\
7 & \{0, 1, 3, 5, 8, 9\} & \{0, 1, 8, 9\} \\
8 & \{0, 1, 2, 3, 4, 5, 6, 7\} & \{0, 1, 6, 7\} \\
9 & \{0, 1, 2, 4, 5, 6, 7\} & \{0, 1, 6, 7\} \\ \hline \end{tabular}
\end{table}
Table 2: LCC Intersection set example.  
Figure 1: (a) Average computation cost of MSL\({}^{*}\) and LCC. (b) Average communication cost of MSL\({}^{*}\) and LCC.