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COCO
2011
Springer

Hardness of Max-2Lin and Max-3Lin over Integers, Reals, and Large Cyclic Groups

8 years 6 months ago
Hardness of Max-2Lin and Max-3Lin over Integers, Reals, and Large Cyclic Groups
—In 1997, H˚astad showed NP-hardness of (1 − , 1/q + δ)-approximating Max-3Lin(Zq); however it was not until 2007 that Guruswami and Raghavendra were able to show NP-hardness of (1 − , δ)approximating Max-3Lin(Z). In 2004, Khot–Kindler– Mossel–O’Donnell showed UG-hardness of (1 − , δ)approximating Max-2Lin(Zq) for q = q( , δ) a sufficiently large constant; however achieving the same hardness for Max-2Lin(Z) was given as an open problem in Raghavendra’s 2009 thesis. In this work we show that fairly simple modifications to the proofs of the Max-3Lin(Zq) and Max-2Lin(Zq) results yield optimal hardness results over Z. In fact, we show a kind of “bicriteria” hardness: even when there is a (1− )good solution over Z, it is hard for an algorithm to find a δ-good solution over Z, R, or Zm for any m ≥ q( , δ) of the algorithm’s choosing.
Ryan O'Donnell, Yi Wu, Yuan Zhou
Added 18 Dec 2011
Updated 18 Dec 2011
Type Journal
Year 2011
Where COCO
Authors Ryan O'Donnell, Yi Wu, Yuan Zhou
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