Near-Optimal Alphabet Soundness Tradeoff PCPs

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• Kai Zhe Zheng (MIT)
• Tuesday 21 January 2025, 14:00-15:00
• Computer Laboratory, William Gates Building, FW26.

If you have a question about this talk, please contact Tom Gur.

We show a nearly optimal alphabet-soundness tradeoff for NP-hardness of 2-Prover-1-Round Games (2P1R). More specifically, we show that for all \eps > 0, for sufficiently large M, it is NP-hard to decide whether a 2P1R instance of alphabet size M has value nearly 1 or at most M^{-1+\eps}. 2P1R are equivalent to 2-Query PCP , and are widely used in obtaining hardness of approximation results. As such, our result implies the following: 1) hardness of approximating Quadratic Programming within a factor of nearly log(n), 2) hardness of approximating d-bounded degree 2-CSP within a factor of nearly d/2, and 3) improved hardness of approximation results for various k-vertex connectivity problems. For the first two applications, our results nearly match the performance of the best known algorithms.

Joint work with Dor Minzer.

This talk is part of the Algorithms and Complexity Seminar series.

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