Proof of Concept: Fast Solutions to NP-problems by Using SAT and Integer Programming Solvers

In the last decade, the power of the state-of-the-art SAT and ILP (Integer Linear Programming) solvers has dramatically increased. They implement many new techniques and heuristics and since any NP problem can be converted to SAT or ILP instance, we could take advantage of these techniques in general by converting the instance of NP problem to SAT formula or Integer program. Cook-Levin theorem says that any NP problem can be reduced to SAT of polynomial size. However, to maximize the speed of our algorithms, we would like to get as short instance as possible (and with as least number of variables as possible). This concept of SAT complexity alone is worth more research in future. A problem we consider, in this proof of concept, is k-Clique problem.