Approximation Resistance by Disguising Biased Distributions
Peng Cui
TL;DR
This paper demonstrates that certain 3-XOR problems are NP-hard yet solvable with a specific SDP algorithm, ultimately claiming to prove P=NP, which challenges existing computational complexity assumptions.
Contribution
It introduces a method to disguise biased distributions in 3-XOR problems, leading to an NP-hardness result and a breakthrough claim that P equals NP.
Findings
NP-hardness of some 3-XOR gap problems
SDP algorithm solves these problems in two rounds
Claimed proof that P=NP
Abstract
In this short note, the author shows that the gap problem of some 3-XOR is NP-hard and can be solved by running Charikar\&Wirth's SDP algorithm for two rounds. To conclude, the author proves that .
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Computational Geometry and Mesh Generation · Machine Learning and Algorithms