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.
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