Worst-Case to Average-Case Reductions via Additive Combinatorics

Worst-Case to Average-Case Reductions via Additive Combinatorics (via Zoom)

Abstract: We present a new framework for designing worst-case to average-case reductions. For a large class of problems, it provides a transformation of algorithms running in time T that are only correct on a small (subconstant) fraction of their inputs into algorithms running in time O-tilde(T) that are correct on all inputs.

Using  our framework, we obtain efficient worst-case to average-case reductions for fundamental problems in a variety of computational models: algorithms for matrix multiplication, streaming algorithms for the online matrix-vector multiplication problem, and  static data structures for all linear problems.

Our techniques rely on results from additive combinatorics. In particular, we  show a local correction lemma that relies on a new probabilistic version of the quasi-polynomial Bogolyubov-Ruzsa lemma.

To appear in STOC 2022.

Bio: Igor Shinkar is an Assistant Professor in the School of Computing Science at Simon Fraser University.  He received his PhD in 2014 from Weizmann Institute of Science in Israel. Igor is broadly interested in theoretical computer science, discrete mathematics, probability, and the interplay between them.