This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Multiparty Equality Function Computation in Networks with PointtoPoint Links Guanfeng Liang and Nitin Vaidya Department of Electrical and Computer Engineering, and Coordinated Science Laboratory University of Illinois at UrbanaChampaign gliang2@illinois.edu, nhv@illinois.edu Technical Report October 26, 2010 This research is supported in part by Army Research Oce grant W911NF0710287 and National Science Foundation award 1059540. Any opinions, findings, and conclusions or recommendations ex pressed here are those of the authors and do not necessarily reect the views of the funding agencies or the U.S. government. 1 Introduction In this report, we study the multiparty communication complexity problem of the multiparty equality function (MEQ): EQ ( x 1 , ,x n ) = { 0 if x 1 = = x n 1 otherwise . (1) The input vector x = ( x 1 , ,x n ) is distributed among n 2 nodes, with x i known to node i , where x i is chosen from the set { 1 , ,M } , for some integer M > 0. 1.1 Communication Complexity The notion of communication complexity (CC) was introduced by Yao in 1979 [2], who investigated the following problem involving two separated parties (Alice and Bob) want to mutually compute a Boolean function that is defined on pairs of inputs. Formally, let f : X Y 7 { , 1 } be a Boolean function. The communication problem for f is the following twoparty game: Alice receives x X and Bob receives y Y , and the goal is for them to compute f ( x,y ), collaboratively. Alice and Bob have unlimited computational power and a full description of f , but they do not know each others input. They determine the output value by exchanging messages. The computation ends when either Alice or Bob has enough information to determine f ( x,y ), and sends a special symbol halt to the other party. A protocol P for computing f is an algorithm, according to which Alice and Bob send binary messages to each other. A protocol proceeds in rounds. In every round, the protocol specifies whose turn it is to send a message. Each party in his/her turn sends one bit that may depend on his/her input and the previous messages he/she has received. A correct protocol for f should terminate for every input pair ( x,y ) X Y , when either Alice or Bob knows f ( x,y ). The communication complexity of a protocol P is the number of bits exchanged for the worst case input pair. The communication complexity of a Boolean function f : X Y 7 { , 1 } , is that of the protocols for f with the least complexity. 1.2 Multiparty Communication Complexity There is more than one way to generalize communication complexity to a multiparty setting. The most commonly used model is the number on the forehead model introduced in [1]. Formally, there is some function f : n i =1 X i 7 { , 1 } , and the input is ( x 1 ,x 2 , ,x n ) where each x i X i . The ith party can see all the x j such that j = i . As in the 2party case, the....
View
Full
Document
This note was uploaded on 02/08/2012 for the course ECE 428 taught by Professor Hu during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Hu

Click to edit the document details