Parallel Solution of Covering Problems Super-Linear Speedup on a Small Set of Cores

This paper aims at better possibilities to solve problems of exponential complexity. Our special focus is the combination of the computational power of four cores of a standard PC with better approaches in the application domain. As the main example we selected the unate covering problem which must be solved, among others, in the process of circuit synthesis and for graph-covering (domination) problems. We introduce into the wide field of problems that can be solved using Boolean models. We explain the models and the classic solutions, and discuss the results of a selected model by using a benchmark set. Subsequently we study sources of parallelism in the application domain and explore improvements given by the parallel utilization of the available four cores of a PC. Starting with a uniform splitting of the problem, we suggest improvements by means of an adaptive division and an intelligent master. Our experimental results confirm that the combination of improvements of the application models and of the algorithmic domain leads to a remarkable speedup and an overall improvement factor of more than 35 millions in comparison with the improved basic approach. Keywords-covering; XBOOLE; ternary vector; parallel; message passing interface; unate SAT problems; Boolean models