## Theory of Combinatorial Algorithms

Prof. Emo Welzl and Prof. Bernd Gärtner

# Mittagsseminar (in cooperation with M. Ghaffari, A. Steger and B. Sudakov)

 Mittagsseminar Talk Information

Date and Time: Thursday, March 15, 2012, 12:15 pm

Duration: 30 minutes

Location: CAB G51

Speaker: Dominik Scheder (Aarhus University)

## A 29 Minutes Intro to Communication Complexity (Plus 1 Minute of Questions)

In romantic relationships, as well as in computer science, communication is important. While in a long-term relationship the partners, let's call them Alice and Bob, are typically encouraged to increase, or at least keep up, their amount of communication, in a computer science / complexity theory setting, they usually want to get things done communicating as little as possible. Computer science, it seems, is an unromantic business.

Suppose Alice and Bob each hold an n-bit string x and y, respectively, and jointly want to evaluate a function f(x,y). In communication complexity, we study the amount of bits Alice and Bob have to exchange to evaluate f. In my talk, which can of course only scratch the surface of this rich and active area, I will discuss the following topics:

1) If f(x,y) := [x = y] is the equality function, Alice cannot do anything smarter than sending Bob her input string x. This costs n bits.

2) If Alice and Bob have a common random source, and they accept some small error probability, they can do much better.

3) Even if they have only private randomness, i.e., they sit on different continents, and either one's computer has a device outputting random bits, they can be almost as good as in 2), if they know some basic number theory.

4) You might think shared randomness is more powerful than private randomness. Surprisingly, not much more. One can show that randomness can be privatized with little extra cost. The technique behind the proof is very versatile and will certainly enrich the toolbox of every theorist.

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