Towards using boolean operators on graphs to generate network topologies

Physical topology design (PTD) of networks is frequently accomplished by combining several solutions in a iterative way, specially if meta-heuristics are deployed. Suitable operators to recombine network topologies aiming at creating novel options for network design that preserve desired properties can improve the quality of algorithms developed to solve the PTD problem. In this paper we propose to deploy bitwise boolean operations to generate new physical topologies from two parent topologies. We assessed three different types of boolean bitwise operations: AND, OR and XOR. We generate networks that present different characteristics by using the generative procedures of Watts-Strogatz (WS) and Barabási-Albert (BA). Then we applied boolean-based operators to pairs of BA and WS networks in order to analyze the characteristics of the resulting network topologies. From our results, AND operations are not suitable to generate networks with combined information from the parents, since in general it generates disconnected networks. On the other hand, the OR and XOR operators can preserve some characteristics of parent networks and may be used as a recombination operator. XOR operator usually generates networks with lower link density than OR. We believe we can apply these operators as a crossover operator in evolutionary algorithms deployed for network planning in future works.