Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, September 15, 2005, 12:15 pm

Duration: This information is not available in the database

Location: This information is not available in the database

Speaker: Elias Vicari

Communication Complexity in the Algebraic Model

In this talk I will survey some results and future goals of the project I am currently working on. The problem is the following: two players are given two private vectors as input and their aim is to compute the value of a multivariate rational function f: kⁿ x k^m -> k (k a field) depending on them, exchanging some messages. The issue is to develop techniques to prove lower bounds on the number of messages required according to how the function f "looks like".

The question is not really new, since the boolean counterpart with a bits-model is already well developed thanks to its high applicability in VLSI design. Distributed Algorithmic Mechanism Design problems are our motivation to change point of view and switching to an algebraic setting, where players can perform the four basic algebraic operations {+, -, x, /} over k.

I will present results on the one-way case, where only a player is allowed to send messages, two-way case and some generalizations, namely introducing the ability to perform equality tests and extending the problem to more players communicating over a given graph.

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