# The communication complexity of the two list problem

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## Abstract

Let L and R be processors, each containing the *n* numbers x_{1},..., x_{n} and y_{1},..., y_{n} respectively, where each number consists of *n* bits. Their task is to determine whether there exists an *i* such that x_{i}=y_{i}. This problem requires Ω(n^{2}) bits for deterministic algorithms [7]. Here a simple O(*n*) expected bit randomized (Las Vegas) algorithm is suggested. Its properties depend on the properties of universal hash functions, not on prime numbers or finite fields. Then the number of random bits is reduced by a general construction. Finally, practical algorithms using almost independent strings are presented.

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© Springer-Verlag Berlin Heidelberg 1992