## 2 Materials and Methods
### Random Tree Pruning Based Search
The following criteria are present for the creation of a tree of mutually acceptable interfering line sets:

* Mutually acceptable line sets calculation is independent for every line. * For each node, the creation of the candidate set is independent. * The creation of candidate set for one node is sequential. * The creation of a successor set is based on each element in the candidate set and is independent. * To check if the element in the candidate set can be promoted to the successor set, we need to perform mutual interference check for the set of lines. Estimating interference is independent for each line in the set. * Choosing which nodes to prune in the next layer is sequential. For the random and GA search, the creation of the initial population and solution estimation is independent for each solution; crossover and mutation of the solution are independent for the pairs of solutions. Sorting the solutions and searching for the best one in the current iteration can be parallel. Each iteration of the random search is parallel, and for the GA each iteration is sequential. Minimal set cover search can be parallel depending on the algorithm. ## 3 Results

The results of the proposed algorithm evaluation are described in this section. There are two extreme cases of topologies. The first one is when lines are too separated from each other, so that cumulative interference is negligible irrespective of the number of lines; then all lines can transmit together. The second one is a fully connected network when all lines are close together; then only one line at a time can transmit. The more interesting topology is an intermediate case, when nodes are uniformly distributed in the space, and their transmission ranges only slightly overlap with some closest nodes. Also, there are two extreme cases of SNR values. If the SNR value is chosen only to combat receiver thermal noise, than all lines must transmit separately. If the SNR is chosen to be quite large, we, essentially, neglect the thermal noise, and only the interference from other lines places the limit on the simultaneous line transmission; we obtain the case with the largest number of line sets to choose from. Irrespective of how large the SNR is, relative interferes will be the same, if all lines' SNR is equal, and transmission power is chosen considering the space propagation signal decay to reach exactly the given SNR. For modeling, we have chosen the SNR to be equal to 30 dB (received signal power is 1000 times more than thermal noise power), which is reachable in many wireless communication systems and allows for low bit error rates for many modulation types. To obtain the intermediate case of topology, we generate the following random network topologies (Figure 6). On the Figure 6, nodes are depicted as red cirles, the radius of circle is proportional to the number of lines coming from the node. We use the maximal connection distance approach: if nodes are separated for less than the maximal connection distance, then they have bi-directional lines. To create a random topology, we create randomly distributed points inside the circle of diameter 1. Firstly, we create the points with the coordinates uniformly distributed in the range from \(-0.5\) to \(0.5\) and then reject points outside of the circle. We set the maximal connection distance equal to the estimated minimal one until the network is still connected. To do that, we start with the maximal connection distance equal to 1 and, with 30 iterations of dichotomy search, gradually reduce it up until the point where the network splits into the subcomponents. We have chosen the target bit error rate for the modeling based on the following assumptions. The most widespread packet size in the Internet is 1500 bytes. The packet error rate is quite often required to be equal to 0.01. We can calculate the packet bit error rate using the following equation: \(packetBitErrorRate)^{1/packetSizeInBits}\). The target bit error rate is then equal to the \(8.375\times 10^{-7}\).