Approximate Hamming Distance in a Stream
نویسندگان
چکیده
We consider the problem of computing a (1+ε)-approximation of the Hamming distance between a pattern of length n and successive substrings of a stream. We first look at the one-way randomised communication complexity of this problem. We show the following: If Alice and Bob both share the pattern and Alice has the first half of the stream and Bob the second half, then there is an O(ε−4 log2 n) bit randomised one-way communication protocol. If Alice has the pattern, Bob the first half of the stream and Charlie the second half, then there is an O(ε−2 √ n logn) bit randomised one-way communication protocol. We then go on to develop small space streaming algorithms for (1 + ε)-approximate Hamming distance which give worst case running time guarantees per arriving symbol. For binary input alphabets there is anO(ε−3 √ n log2 n) space andO(ε−2 logn) time streaming (1 + ε)-approximate Hamming distance algorithm. For general input alphabets there is an O(ε−5 √ n log4 n) space and O(ε−4 log3 n) time streaming (1 + ε)-approximate Hamming distance algorithm. 1998 ACM Subject Classification F.2 Analysis of algorithms and problem complexity
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تاریخ انتشار 2016