Given a set of clauses, where each clause consists of three terms (a term is a Boolean variable or its negation), connected by the or operator, the 3-satisfiability problem asks if there exists an assignment of the variables so that all clauses are true. Given a graph, the independent set problem asks for a subset of the vertices so that there is no edge between any pair of two different vertices in the subset. Constructing a graph from a given collection of clauses, we show that the 3-satisfiability problem reduces in polynomial time to the independent set problem. If there is an independent set in the constructed graph that has a size equal to the number of clauses, then there is an assignment that makes all clauses true.
- Күн бұрын
the 3-satisfiability problem is polynomial-time reducible to the independent set problem
- Рет қаралды 57
Пікірлер