# Efficient Mobile Sink Routing in Wireless Sensor Networks Using Bipartite Graphs
## 4 Proposed Mobility Model  
The work proposed in this paper relies on randomly deployed W.S.N.s made up of N stationary sensor nodes and one additional node that can move to serve as a mobile sink node. Following network deployment, the base station receives the locations of the mobile sink and the stationary sensor nodes. Consequently, the base station calculates a bipartite graph, and the stationary sensor nodes are grouped into two disjoint sets, as explained in Section 2. It is worth noting that the mobile sink is not included in this calculation because it is supposed to visit stationary sensor nodes and collect information. To clarify, a bipartite graph is derived by the base station using the locations of the static sensor nodes as a point of reference and the neighborhood data of the static sensor nodes. Thus, the stationary sensor nodes are grouped into two disjoint sets. The based station will also calculate the breadth-first traversal for the nodes in each subset based on the Euclidean distance between the static sensor nodes within each set. After that, based on the locations of the stationary sensor nodes, the mobile sink will choose one of the sets to start visiting stationary sensor nodes that are members of that set. In other words, the mobile sink will choose the nearest node to it and start visiting it; thus, it selects the set with the nearest member nodes to the mobile sink. Consequently, the mobile sink will deal with the nodes in the selected set as a subgraph. The stationary sensor nodes within the set are visited according to the breadth-first traversal algorithm calculated based on the Euclidean distance between the nodes that are members of the selected set. After visiting all the nodes in the first set, the mobile sink node will start moving towards the nearest member of the other set, and the static sensor nodes within that set will be visited according to the breadth-first algorithm that is calculated based on the Euclidean distance between the nodes that are a member of the new set. This process continues until a recalculation of the bipartite graph is triggered or required based on changes in the topology of the W.S.N. that might occur because of the death of static sensor nodes caused by energy depletion. It is worth noting that when the mobile sink is visiting stationary sensor nodes in one set, it will be within the range of communication of other stationary sensor nodes that are members of the other set but are neighbors of the node being visited; thus, these neighbor nodes can send data to the mobile sink before being visited. Consequently, we can ensure that the nodes will not suffer from buffer overflow and that the sensed information will promptly be communicated to the mobile sink. Furthermore, the mobile sink's movement will follow the breadth traversal of the nodes in the selected set and is divided into sojourn periods and movement periods. In the sojourn period, the mobile sink will pause in its current location for a specific period. After that, it will begin moving toward a new location at a set pace. When the mobile sink arrives at the new location, the sojourn period begins again and stays in the new place for the same period. A flowchart of the mobility model suggested in this paper is shown in Figure 2.  
Consider the networks shown in Figure 1a that were processed to deduce the bipartite graph in Figure 1b. Based on the Euclidian distance, the mobile sink will choose the nearest node to it to start its journey. For example, the mobile sink selected node 1, which belongs to V\({}_{1}\), as the starting node of its journey. As a result, the mobile sink must visit all the nodes in V\({}_{1}\) based on the breadth-first traversal algorithm. After visiting all the nodes in V\({}_{1}\), the mobile sink will move to the nearest node in V\({}_{2}\) and will visit all the nodes of V\({}_{2}\) using the breadth-first traversal algorithm. Thus, the mobile sink will keep switching between the nodes of the two sets.