Papadimitriou's 2SAT Algorithm

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

• Local Search
• The 2SAT Problem

Overview

The algorithm performs a randomized local search. Generally, local search heuristics are not guaranteed to run in polynomial time. The randomized local search algorithm for the 2SAT problem is one of the rare cases when we can prove it is guaranteed to converge with the correct answer quickly.

Algorithm

Repeat log2n times:
  Choose random initial assignment
  Repeat 2n2 times:
     If current assignment satisfies all clauses, halt and report.
     Else pick arbitrary unsatisfied clause and flip the value of one of its variables # choose between the two uniformly at random.
Report "unsatisfiable".

Playground Implementation

https://github.com/ovidiuf/playground/blob/master/learning/stanford-algorithms-specialization/19-2SAT/src/main/java/playground/stanford/twosat/TwoSATInstance.java

Running Time

Runs in polynomial time.