Communication complexity of composed functions

Contents The Stretch Factor of L 1 - and L ∞ - Delaunay Triangulations 3 The NOF Multiparty Communication Complexity of Composed Functions 3 Spectral Norm of Symmetric Functions

Raz-McKenzie simulation with the inner product gadget

In this note we show that the Raz-McKenzie simulation algorithm which lifts deterministic query lower bounds to deterministic communication lower bounds can be implemented for functions f composed with the Inner Product gadget 1ip(x, y) = ∑ i xiyi mod 2 of logarithmic size. In other words, given a function f : {0, 1}n → {0, 1} with deterministic query complexity D( f ), we show that the determi...

Composition Theorems in Communication Complexity

A well-studied class of functions in communication complexity are composed functions of the form (f ◦ g)(x, y) = f(g(x, y), . . . , g(x, y)). This is a rich family of functions which encompasses many of the important examples in the literature. It is thus of great interest to understand what properties of f and g affect the communication complexity of (f ◦ g), and in what way. Recently, Shersto...

A multi agent method for cell formation with uncertain situation, based on information theory

This paper assumes the cell formation problem as a distributed decision network. It proposes an approach based on application and extension of information theory concepts, in order to analyze informational complexity in an agent- based system, due to interdependence between agents. Based on this approach, new quantitative concepts and definitions are proposed in order to measure the amount of t...

Randomized Query Complexity of Sabotaged and Composed Functions

We study the composition question for bounded-error randomized query complexity: Is R(f ◦ g) = Ω(R(f)R(g)) for all Boolean functions f and g? We show that inserting a simple Boolean function h, whose query complexity is only Θ(logR(g)), in between f and g allows us to prove R(f ◦ h ◦ g) = Ω(R(f)R(h)R(g)). We prove this using a new lower bound measure for randomized query complexity we call rand...