## 4 Main Tools of the WSN-DPCM Platform
### Tool for WSN Application Planning and RF Simulation
#### 4.1.3 Topology Reduction
Starting from the initial network that is usually created with maximum transmission power, we perform link reduction by targeting the following parameters: predefined number of neighbors, predefined n-connected topology and transmission power reduction. These approaches and mainly their relative integration effort in WSN-DPCM Planning Tool are described next. It is noted that the core algorithms have been presented and evaluated in [41] under various cases of controllable network topological scenarios in MATLAB. K-ROUTE: MST-based link reduction algorithm [38]. Given a connected, undirected graph, a spanning tree of that graph is a sub-graph comprising a tree that connects all vertices. A graph can have many different spanning trees. We can also assign a weight to each edge, which is a number representing how unfavorable this edge is, and use this to compute the sum of the weights of the edges in that spanning tree. A minimum spanning tree (MST), or minimum weight spanning tree, is then a spanning tree with weight less than or equal to the weight of every other spanning tree. If each edge has a distinct weight, then the MST is unique. From a more abstract point of view, any undirected graph has a minimum spanning forest, which is a union of minimum spanning trees for its connected components. Figure 8 shows the effect of the respective integrated algorithm to the same topology scenario assuming a requirement of 2-route connected graph. So effectively, and with respect to Figure 7 topology, in this case initially the optimal minimum spanning tree is identified (_i.e._, the MST with the minimum cost edges which represents the most robust connections). Then, the identified MST is excluded and the second best MST topology is identified. Finally, the two identified MST topologies are merged to provide the final alternative topology. As indicated, the number of links and average neighbors are significantly reduced (from 166 to 38 and from 15 to 4), which can enhance networks efficiency and resource conservation. However, as expected, the number of hops to ROOT nodes is also increased (from 0 to 6), which indicates the need for multi-hop communication and routing protocols. Figure 8: WSN-DPCM K-Route Link Reduction Integrated Algorithm (power in dBm): graphical results (**a**) and statistics (**b**). N-NEIGHB: Neighbor-based link reduction algorithm. The algorithm attempts to ensure a specific number of neighbors. Actually, the minimum number of nodes is bounded, hence for some nodes the number of neighbors could be slightly increased. The process starts from the node with the smallest number of neighbors. The first n-neighbors with the strongest RSS are added in the new neighbor table for this node. The algorithm continues by processing all nodes in ascending order of their number of neighbors. Before adding a new neighbor to the table, its number of neighbors is checked. If this number is equal or larger than required, this neighbor is discarded and the next neighbor in the list is evaluated. If all neighbors of a node have more than the required number of neighbors, but this node has not reached the required number of neighbors, then the first n-neighbors with the strongest RSS are added in the nodes neighbor table even through these neighbors exceed the required number of neighbors. Figure 9 shows an example integrated in WSN-DPCM planning tool. Comparing the extracted metrics with the respective measurements shown in Figure 7, it is shown that the proposed algorithm enables the developer to find the optimum trade-off between the number of neighbors/links and the number of hops to the ROOT node. TxPR: Transmission power-based link reduction algorithm. Instead of transmitting with the maximal power, the nodes can collaboratively reduce their transmitted power and define network topology by forming neighbor relations with specific criteria.