Karloff–Zwick algorithm: Difference between revisions

Revision as of 06:37, 26 July 2022

Revision as of 06:37, 26 July 2022

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The '''Karloff–Zwick algorithm''', in [[computational complexity theory]], is a [[randomized algorithm|randomised]] [[approximation algorithm]] taking an instance of [[MAX-3SAT]] [[Boolean satisfiability problem]] as input. If the instance is satisfiable, then the expected weight of the assignment found is at least 7/8 of optimal. There is strong evidence (but not a [[mathematical proof]]) that the algorithm achieves 7/8 of optimal even on unsatisfiable MAX-3SAT instances. [[Howard Karloff]] and [[Uri Zwick]] presented the algorithm in 1997.<ref name="Karloff">{{citation|last1=Karloff|first1= H.|title= Proceedings 38th Annual Symposium on Foundations of Computer Science|last2= Zwick|first2= U. |chapter=A 7/8-approximation algorithm for MAX 3SAT?|title-link=Symposium on Foundations of Computer Science|year=1997|pages=406–415|doi=10.1109/SFCS.1997.646129|isbn= 978-0-8186-8197-4|citeseerx= 10.1.1.51.1351|s2cid= 15447333}}.</ref>

The algorithm can be derandomized using, e.g., the techniques from <ref>{{citation|last1=Sivakumar |first1=D. |title=Algorithmic derandomization via complexity theory |journal=Proceedings of the ThiryThirty-fourthFourth Annual ACM Symposium on Theory of Computing |date=19 May 2002 |pages=619–626 |doi=10.1145/509907.509996|isbn=1581134959 |s2cid=94045 }}</ref> to yield a deterministic [[polynomial-time]] algorithm with the same approximation guarantees.

==Comparison to random assignment==