Sanjeev Khanna, Madhu Sudan, David P. Williamson

In this paper we study the approximability of boolean constraint

satisfaction problems. A problem in this class consists of some

collection of ``constraints'' (i.e., functions

$f:\{0,1\}^k \rightarrow \{0,1\}$); an instance of a problem is a set

of constraints applied to specified subsets of $n$ boolean

variables. Schaefer earlier ...
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Joseph Swernofsky

We prove that approximating the rank of a 3-tensor to within a factor of $1 + 1/1852 - \delta$, for any $\delta > 0$, is NP-hard over any finite field. We do this via reduction from bounded occurrence 2-SAT.

more >>>Orr Paradise

Probabilistically checkable proofs (PCPs) can be verified based only on a constant amount of random queries, such that any correct claim has a proof that is always accepted, and incorrect claims are rejected with high probability (regardless of the given alleged proof). We consider two possible features of PCPs:

- ...
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Per Austrin, Jonah Brown-Cohen, Johan HÃ¥stad

The factor graph of an instance of a constraint satisfaction problem (CSP) is the bipartite graph indicating which variables appear in each constraint. An instance of the CSP is given by the factor graph together with a list of which predicate is applied for each constraint. We establish that many ... more >>>

Elena Grigorescu, Brendan Juba, Karl Wimmer, Ning Xie

Determinantal Point Processes (DPPs) are a widely used probabilistic model for negatively correlated sets. DPPs have been successfully employed in Machine Learning applications to select a diverse, yet representative subset of data. In these applications, the parameters of the DPP need to be fitted to match the data; typically, we ... more >>>