# Computer Science and Discrete Mathematics (CSDM)

Theoretical Computer Science and Discrete Mathematics

## New insights on the (non)-hardness of circuit minimization and related problems

Eric Allender
Rutgers University
February 27, 2017
The Minimum Circuit Size Problem (MCSP) and a related problem (MKTP) that deals with time-bounded Kolmogorov complexity are prominent candidates for NP-intermediate status. We present new results relating the complexity of various approximation problems related to MCSP and MKTP. We show that, under modest cryptographic assumptions, some of these approximation problems must have intermediate complexity: they have no solution in P/poly and are not NP-hard under P/poly reductions.

## A unified duality-based approach to Bayesian mechanism design

Matt Weinberg
Princeton University
February 14, 2017

We provide a duality framework for Bayesian Mechanism Design. Specifically, we show that the dual problem to revenue maximization is a search over virtual transformations. This approach yields a unified view of several recent breakthroughs in algorithmic mechanism design, and enables some new breakthroughs as well. In this talk, I'll:

1) Provide a brief overview of the challenges of multi-dimensional mechanism design.

2) Construct a duality framework to resolve these problems.

## Nearest neighbor search for general symmetric norms via embeddings into product spaces

Ilya Razenshteyn
Massachusetts Institute of Technology
February 13, 2017
I will show a new efficient approximate nearest neighbor search (ANN) algorithm over an arbitrary high-dimensional *symmetric* norm. Traditionally, the ANN problem in high dimensions has been studied over the $\ell_1$ and $\ell_2$ distances with a few exceptions. Thus, the new result can be seen as a (modest) step towards a "unified theory" of similarity search.