Yi Wu 0002

SODA Conference 2013 Conference Paper

Local Distribution and the Symmetry Gap: Approximability of Multiway Partitioning Problems

• Alina Ene
• Jan Vondrák
• Yi Wu 0002

SODA Conference 2012 Conference Paper

Bypassing UGC from some optimal geometric inapproximability results

• Venkatesan Guruswami
• Prasad Raghavendra
• Rishi Saket
• Yi Wu 0002

SODA Conference 2012 Conference Paper

On the hardness of pricing loss-leaders

• Preyas Popat
• Yi Wu 0002

SODA Conference 2011 Conference Paper

Hardness Results for Agnostically Learning Low-Degree Polynomial Threshold Functions

• Ilias Diakonikolas
• Ryan O'Donnell
• Rocco A. Servedio
• Yi Wu 0002

SODA Conference 2009 Conference Paper

3-bit dictator testing: 1 vs. 5/8

• Ryan O'Donnell
• Yi Wu 0002

FOCS Conference 2009 Conference Paper

Agnostic Learning of Monomials by Halfspaces Is Hard

• Vitaly Feldman
• Venkatesan Guruswami
• Prasad Raghavendra
• Yi Wu 0002

We prove the following strong hardness result for learning: Given a distribution on labeled examples from the hypercube such that there exists a monomial (or conjunction) consistent with (1-¿)-fraction of the examples, it is NP-hard to find a halfspace that is correct on ( 1/2 + ¿)-fraction of the examples, for arbitrary constant ¿ > 0. In learning theory terms, weak agnostic learning of monomials by halfspaces is NP-hard. This hardness result bridges between and subsumes two previous results which showed similar hardness results for the proper learning of monomials and halfspaces. As immediate corollaries of our result, we give the first optimal hardness results for weak agnostic learning of decision lists and majorities. Our techniques are quite different from previous hardness proofs for learning. We use an invariance principle and sparse approximation of halfspaces from recent work on fooling halfspaces to give a new natural list decoding of a halfspace in the context of dictatorship tests/label cover reductions. In addition, unlike previous invariance principle based proofs which are only known to give Unique Games hardness, we give a reduction from a smooth version of Label Cover that is known to be NP-hard.

STOC Conference 2009 Conference Paper

Conditional hardness for satisfiable 3-CSPs

• Ryan O'Donnell
• Yi Wu 0002

STOC Conference 2008 Conference Paper

An optimal sdp algorithm for max-cut, and equally optimal long code tests

• Ryan O'Donnell
• Yi Wu 0002

Let G be an undirected graph for which the standard Max-Cut SDP relaxation achieves at least a c fraction of the total edge weight, 1/2 ≤ c ≤ 1. If the actual optimal cut for G is at most an s fraction of the total edge weight, we say that (c, s) is an SDP gap. We define the SDP gap curve GapSDP : [1/2,1] -> [1/2,1] by GapSDP(c) = inf{s : (c, s) is an SDP gap}. In this paper we complete a long line of work [15, 14, 20, 36, 19, 17, 13, 28] by determining the entire SDP gap curve; we show GapSDP(c) = S(c) for a certain explicit (but complicated to state) function S. In particular, our lower bound GapSDP(c) - S(c) is proved via a polynomial-time - RPR 2 ' algorithm. Thus we have given an efficient, optimal SDP-rounding algorithm for Max-Cut. The fact that it is RPR 2 confirms a conjecture of Feige and Langberg [17]. We also describe and analyze the tight connection between SDP gaps and Long Code tests (and the constructions of [25, 3, 4]). Using this connection, we give optimal Long Code tests for Max-Cut. Combining these with results implicit in [27, 29] and ideas from [19], we derive the following conclusions: - The Max-Cut SDP gap curve subject to triangle inequalities is also given by S(c). - No RPR 2 algorithm can be guaranteed to find cuts of value larger than S(c) in graphs where the optimal cut is c. (Contrast this with the fact that in the graphs exhibiting the c vs. S(c) SDP gap, our RPR 2 algorithm actually finds the optimal cut.) - Further, no polynomial-time algorithm of any kind can have such a guarantee, assuming P ≠ NP and the Unique Games Conjecture.