Investigations of graph properties in terms of wireless sensor network optimization

Wireless Sensor Networks (WSNs) serve as the basis for today's Internet of Things applications. A WSN consists of a number of spatially distributed sensor nodes, which cooperatively monitor physical or environmental conditions. In order to ensure the dependability of WSN functionalities, several reliability and security requirements have to be fulfilled. By applying a Satisfiability Modulo Theories (SMT) formalization for WSNs, a sleep/wake-up scheduling that respects those requirements can be generated by using SMT solvers. It is also important to prolong the lifetime of a WSN as much as possible. The recent success of Optimization Modulo Theories (OMT) approaches makes us able to generate for a WSN a sleep/wake-up scheduling that is optimal in terms of energy efficiency. In our previous work, we reported experiments on WSN benchmarks with different OMT solvers and it turned out that several such benchmarks were not challenging enough in terms of OMT. In this paper, we address this problem by proposing certain graph criteria for WSNs and investigate their correlation with the degree of challenge for OMT solvers. We will also discuss why the examination of those criteria helps in a real-world environment to plan the physical distribution of sensor nodes in order to prolong the WSN's lifetime as much as possible.