The 2SAT Problem: Difference between revisions
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Given a set of ''n'' boolean variables x<sub>1</sub>, x<sub>2</sub>, ..., x<sub>n</sub>, that can be set to <code>true</code> or <code>false</code> and a set of ''m'' clauses of two literals each (a "literal" is a variable or the negation of the variable: x<sub>i</sub> or !x<sub>i</sub>). The output is determining whether there is a variable assignment that simultaneously satisfies every clause. | Given a set of ''n'' boolean variables x<sub>1</sub>, x<sub>2</sub>, ..., x<sub>n</sub>, that can be set to <code>true</code> or <code>false</code> and a set of ''m'' clauses of two literals each (a "literal" is a variable or the negation of the variable: x<sub>i</sub> or !x<sub>i</sub>). The output is determining whether there is a variable assignment that simultaneously satisfies every clause. | ||
The 2SAT problem can be solved in polynomial time - it is not an NP-complete problem. Unlike 2SAT, the 3SAT problem is NP-complete. | The 2SAT problem can be solved in polynomial time - it is not an NP-complete problem. Unlike 2SAT, the 3SAT problem is [[NP_Completeness|NP-complete]]. | ||
=Algorithms= | =Algorithms= | ||
Revision as of 04:46, 30 November 2021
External
- https://www.coursera.org/learn/algorithms-npcomplete/lecture/ERxmM/the-2-sat-problem
- https://www.coursera.org/learn/algorithms-npcomplete/lecture/kRmJe/random-walks-on-a-line
- https://www.coursera.org/learn/algorithms-npcomplete/lecture/YltoR/analysis-of-papadimitrious-algorithm
Internal
Overview
The Problem
Given a set of n boolean variables x1, x2, ..., xn, that can be set to true or false and a set of m clauses of two literals each (a "literal" is a variable or the negation of the variable: xi or !xi). The output is determining whether there is a variable assignment that simultaneously satisfies every clause.
The 2SAT problem can be solved in polynomial time - it is not an NP-complete problem. Unlike 2SAT, the 3SAT problem is NP-complete.
Algorithms
- Reduction to computing strongly connected components.
- "Backtracking"
- Papadimitriou's 2SAT randomized local search.