## 5 Experiments
### Algorithms Comparison
This clearly shows that for some favorable data locations integer solution may be found easily. The initial locations of data to be sent are depicted in Figure 4. In the case marked \"1\", the data are located close to the base station, and most of them may be sent in one hop. On the contrary, in the case marked \"2\", the nodes are located far from the base station and at such distance from each other that they can easily interfere. There are still several possible paths for the data. However, taken into account the radio range, they all require high power setting of the transmitter. Comparison of solution quality for both algorithms is not straightforward as they have different goals and performance indices. When comparing values of indices in Tables 6 and 7, two differences may be noticed. First, the spread of minimal and maximal values tends to be greater for algorithm minimizing total energy consumption. Next, values of the total energy consumption index tend to grow with the size of the network. In contrast, for algorithm minimizing maximal energy consumption, the performance index values are nearly constant. To make comparison easier, average values of the second index for both algorithms were computed and presented in Figure 5. The algorithm using the total energy consumption index minimizes the energy consumed by all network nodes in all frame slots. As the performance is a sum, it may be significantly lower for simpler  
Figure 4: Examples of initial location of data for network of 25 nodes. The case marked “1” may be solved significantly faster than “2”. Nodes having data to send are marked in red, base station is in the larger black one. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Number** & \multicolumn{3}{c}{**Average Solution**} & \multicolumn{2}{c}{**Average Branch**} \\ \cline{2-5}
**of Nodes** & **Root: Relaxed** & **Root: Upper Bound** & **Optimal** & **and Bound Iterations** \\ \hline
9 & 85.7 & 112 & 112 & 2351.5 \\ \hline
16 & 85 & 224.8 & 108.5 & 32,149 \\ \hline
25 & 85 & 160.25 * & 112 & 48,665.2 \\ \hline
36 & 86 & 112 ** & 110.4 & 26,929.3 \\ \hline
49 & 85 & 112 ** & 112 & 39,067.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Comparison of average relaxed solution and upper bounds in the root node for algorithm using maximal energy consumption index. The optimal solution is found after the number of branch and bound iterations presented in the last column. Value marked with (*) and (**) are means of 5 of 6 cases and 2 of 9 cases, respectively as CPLEX did not provide an initial approximation in the root node for all tasks. (e.g., having 3 sending nodes instead of 4 or having nodes located close to the base station) frames. On the contrary, the performance index of the second algorithm is equal to the power needed by the node transmitting the data with the highest power setting. As it is value for a single node, it does not grow with the size of the network, and there is also significantly less variability in it. Namely, it can take one of three values related to the three power levels of the sensor. The algorithm using maximal node energy index tries to maximize network life by using many nodes transmitting the data with low power settings. This way, the battery use is balanced among most sensors. Such a strategy typically, at least for small to medium networks, leads to solutions where the nodes transmit data no more than once--it may be clearly seen in Table 7 where the maximal value of performance index is 112 mW, which equals energy consumption for the highest transmission power. On the other hand, algorithm minimizing total energy allows multiple transmissions through the same node--this fact is reflected in the right graph of Figure 5.  
The overall network energy consumption for algorithm minimizing total energy may be significantly lower. However, it has two drawbacks. First, the resulting mathematical programming task is much harder to solve. It is necessary to take into consideration all nodes to minimize the total energy.