Portfolio SAT and SMT Solving of Cardinality Constraints in Sensor Network Optimization

Abstract

Wireless Sensor Networks (WSNs) serve as the basis for 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. In previous work, we applied OMT (Optimization Modulo Theories) solvers to maximize a WSN's lifetime, i.e., to generate an optimal sleep/wake-up scheduling for the sensor nodes. We discovered that the bottleneck for the underlying SMT (Satisfiability Modulo Theories) solvers was typically to solve satisfiable instances. In this paper, we encode the WSN verification problem as a set of Boolean cardinality constraints, therefore SAT solvers can also be applied as underlying solvers. We have experimented with different SAT solvers and also with different SAT encodings of Boolean cardinality constraints. Based on our experiments, the SAT-based approach is very powerful on satisfiable instances, but quite poor on unsatisfiable ones. In this paper, we apply both SAT and SMT solvers in a portfolio setting. Based on our experiments, the MiniCARD+Z3 setting can be considered to be the most powerful one, which outperforms OMT solvers by 1-2 orders of magnitude.