CS369E: Communication Complexity (for Algorithm Designers) Lecture #3: Lower Bounds for Compressive Sensing∗

We begin with an appetizer before starting the lecture proper — an example that demonstrates that randomized one-way communication protocols can sometimes exhibit surprising power. It won’t surprise you that the Equality function — with f(x,y) = 1 if and only if x = y — is a central problem in communication complexity. It’s easy to prove, by the Pigeonhole Principle, that its deterministic one-way communication complexity is n, where n is the length of the inputs x and y. What about its randomized communication complexity? Recall from last lecture that by default, our randomized protocols can use public coins and can have two-sided error , where is any constant less than 1 2 .