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Approximate Hamming distance in a stream
We consider the problem of computing a -approximation of the
Hamming distance between a pattern of length and successive substrings of a
stream. We first look at the one-way randomised communication complexity of
this problem, giving Alice the first half of the stream and Bob the second
half. We show the following: (1) If Alice and Bob both share the pattern then
there is an bit randomised one-way communication
protocol. (2) If only Alice has the pattern then there is an
bit randomised one-way communication protocol.
We then go on to develop small space streaming algorithms for
-approximate Hamming distance which give worst case running time
guarantees per arriving symbol. (1) For binary input alphabets there is an
space and
time streaming -approximate Hamming distance algorithm. (2) For
general input alphabets there is an
space and time streaming
-approximate Hamming distance algorithm.Comment: Submitted to ICALP' 201
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