The matching problem has no small symmetric SDP

Braun, Gábor; Brown-Cohen, Jonah; Huq, Arefin; Pokutta, Sebastian; Raghavendra, Prasad; Roy, Aurko; Weitz, Benjamin; Zink, Daniel M.

doi:10.48550/arxiv.1504.00703

Cited by 2 publications

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“…Also, approximations of the slack matrix provide approximate programs for the optimization problem, as shown in Theorem 7.2. Our approach also immediately carries over to symmetric formulations (see Braun et al [2015a] for SDPs) and other conic programming paradigms; the details are left to the interested reader.…”

Section: Contributionmentioning

confidence: 99%

Affine reductions for LPs and SDPs

2018

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We define a reduction mechanism for LP and SDP formulations that degrades approximation factors in a controlled fashion. Our reduction mechanism is a minor restriction of classical reductions establishing inapproximability in the context of PCP theorems. As a consequence we establish strong linear programming inapproximability (for LPs with a polynomial number of constraints) for many problems. In particular we obtain a 3 2 − ε inapproximability for VertexCover answering an open question in Chan et al.[2013] and we answer a weak version of our sparse graph conjecture posed in Braun et al. [2014a] showing an inapproximability factor of 1 2 + ε for bounded degree IndependentSet. In the case of SDPs, we obtain inapproximability results for these problems relative to the SDP-inapproximability of MaxCUT. Moreover, using our reduction framework we are able to reproduce various results for CSPs from Chan et al.[2013] via simple reductions from Max-2-XOR.

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Section: Contributionmentioning

confidence: 99%

Affine reductions for LPs and SDPs

2018

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“…The actual factorization can be used to explicitly find the smallest reformulation. This line of research started with a seminal paper by Yannakakis [24], and has recently seen a flurry of research activity -see the surveys [15,7] and [10,9,21,6,16,22,17,5] for some of the most recent breakthroughs.…”

Section: Introductionmentioning

confidence: 99%

Computing approximate PSD factorizations

Basu,

Dinitz,

2016

Preprint

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We give an algorithm for computing approximate PSD factorizations of nonnegative matrices. The running time of the algorithm is polynomial in the dimensions of the input matrix, but exponential in the PSD rank and the approximation error. The main ingredient is an exact factorization algorithm when the rows and columns of the factors are constrained to lie in a general polyhedron. This strictly generalizes nonnegative matrix factorizations which can be captured by letting this polyhedron to be the nonnegative orthant.

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The matching problem has no small symmetric SDP

Cited by 2 publications

References 0 publications

Affine reductions for LPs and SDPs

Affine reductions for LPs and SDPs

Computing approximate PSD factorizations

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