A symmetric representation for a set of objects requires the same amount of space for the set as for its complement. Complexity classifications that are based on the length of the input can depend on whether the representation is symmetric. In this article we describe a symmetric representation scheme for ... more >>>

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.). ... more >>>

The {\em Unique Coverage} problem, given a universe $V$ of elements and a collection $E$ of subsets of $V$, asks to find $S \subseteq V$ to maximize the number of $e \in E$ that intersects $S$ in {\em exactly one} element. When each $e \in E$ has cardinality at most ... more >>>