I'll start with some advice my advisor Amit Chakrabarti gave that I found quite useful: (1) Keep a research journal and write in it every day. Its easy to forget about the details of what I was ...

(1) The way I like to think about partial functions is by defining a total function with three outputs e.g, $f: \{0,1\}^n \times \{0,1\}^n \rightarrow \{0,1, *\}$. The $*$ values are where your ...

I'll start with answers to your general questions, then give one nice open problem with applications towards circuit complexity. It's hard to say what areas a new communication complexity researcher ...

There's a lot of real-world motivation for the study of streaming algorithms that comes from network intrusion detection. The paper below uses streaming algorithms for empirical entropy to detect ...

$N^1(DISJ_n) \geq n$. The fooling set technique actually provides lower bounds on the cover number. $C^1(f)$ is the minimum number of monochromatic rectangles needed to cover the $1$-inputs of $f$. ...

It's not possible. Consider the following 3x3 boolean matrix: 1 1 0 1 0 1 0 1 1 For every pair of rows {r,r'} , there exists a column c such that {r,r'} X {c} is a combinatorial rectangle. For ...

There are several flavors of communication complexity. It sounds like your "send once" model is uses one-way communication and private messages. For concreteness, I give short synopses of some ...