
AlternationTrading Proofs, Linear Programming, and Lower Bounds
A fertile area of recent research has demonstrated concrete polynomial t...
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Size, Cost, and Capacity: A Semantic Technique for Hard Random QBFs
As a natural extension of the SAT problem, an array of proof systems for...
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New Competitiveness Bounds for the Shared Memory Switch
We consider one of the simplest and best known buffer management archite...
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Distributed and Streaming Linear Programming in Low Dimensions
We study linear programming and general LPtype problems in several big ...
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Bridging between 0/1 and Linear Programming via Random Walks
Under the Strong Exponential Time Hypothesis, an integer linear program ...
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Checking Phylogenetic Decisiveness in Theory and in Practice
Suppose we have a set X consisting of n taxa and we are given informatio...
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SOS lower bounds with hard constraints: think global, act local
Many previous SumofSquares (SOS) lower bounds for CSPs had two deficie...
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Extended Formulation Lower Bounds for Refuting Random CSPs
Random constraint satisfaction problems (CSPs) such as random 3SAT are conjectured to be computationally intractable. The average case hardness of random 3SAT and other CSPs has broad and farreaching implications on problems in approximation, learning theory and cryptography. In this work, we show subexponential lower bounds on the size of linear programming relaxations for refuting random instances of constraint satisfaction problems. Formally, suppose P : {0,1}^k →{0,1} is a predicate that supports a t1wise uniform distribution on its satisfying assignments. Consider the distribution of random instances of CSP P with m = Δ n constraints. We show that any linear programming extended formulation that can refute instances from this distribution with constant probability must have size at least Ω(((n^t2/Δ^2)^1ν/k)) for all ν > 0. For example, this yields a lower bound of size (n^1/3) for random 3SAT with a linear number of clauses. We use the technique of pseudocalibration to directly obtain extended formulation lower bounds from the planted distribution. This approach bypasses the need to construct SheraliAdams integrality gaps in proving general LP lower bounds. As a corollary, one obtains a selfcontained proof of subexponential SheraliAdams LP lower bounds for these problems. We believe the result sheds light on the technique of pseudocalibration, a promising but conjectural approach to LP/SDP lower bounds.
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