# Communication Complexity (for Algorithm Designers)

arXiv: https://arxiv.org/abs/1509.06257 · HTML: https://mlsanity.com/paper/1509.06257/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Sep 2015.

## Built on by (most cited first, 5 of 5)

- [Subtractive Mixture Models via Squaring: Representation and Learning](https://mlsanity.com/paper/2310.00724/) (2023)
- [Coresets for Classification -- Simplified and Strengthened](https://mlsanity.com/paper/2106.04254/) (2021)
- [Lost in Transmission: When and Why LLMs Fail to Reason Globally](https://mlsanity.com/paper/2505.08140/) (2025)
- [Exponential Quantum Communication Advantage in Distributed Inference and Learning](https://mlsanity.com/paper/2310.07136/) (2023)
- [Context Compaction Theory](https://mlsanity.com/paper/2608.01326/) (2026)

## Abstract (arXiv)

This document collects the lecture notes from my course "Communication Complexity (for Algorithm Designers),'' taught at Stanford in the winter quarter of 2015. The two primary goals of the course are: 1. Learn several canonical problems that have proved the most useful for proving lower bounds (Disjointness, Index, Gap-Hamming, etc.). 2. Learn how to reduce lower bounds for fundamental algorithmic problems to communication complexity lower bounds. Along the way, we'll also: 3. Get exposure to lots of cool computational models and some famous results about them --- data streams and linear sketches, compressive sensing, space-query time trade-offs in data structures, sublinear-time algorithms, and the extension complexity of linear programs. 4. Scratch the surface of techniques for proving communication complexity lower bounds (fooling sets, corruption bounds, etc.).