Description

Question 2 (E-Ievel)

Consider a setting when edges of the input graph G are divided between two

servers, called Alice and Bob: graph G1 = (V, E1) is given to Alice and graph

G2 = (V, E2) is given to Bob. The input graph G = (V, E1 u E2) is a union of

G1 and G2.

Your job is to design and analyze a randomized algorithm (protocol) that

requires O(log2° n) bits of communication between Alice and Bob with the

following property: in the end Alice and Bob output the same set A  V such

that the expected number of edges between A and V \ A is at least

E1 u E2 1/2.

Hint: You cannot assume that Alice and Bob have shared random string, but ¡t

maybe helpful to achieve an algorithm with shared random string first.