Communication and Streaming Complexity of Approximate Pattern Matching

We consider the approximate pattern matching problem. Given a text T of length 2n and a pattern P of length n, the task is to decide for each prefix T [1, j] of T if it ends with a string that is at the edit distance at most k from P . If this is the case, we must output the edit distance and the corresponding edit operations. We first look at the communication complexity of the problem. We show the following: If Alice and Bob both share the pattern and Alice holds the first half of the text and Bob the second half, then the deterministic one-way communication complexity of the problem is Θ(k logn). If Alice holds the first half of the text, Bob the second half of the text, and Charlie the pattern, then there is a deterministic one-way communication protocol that uses O(k √ n logn) bits. We then develop the first sublinear-space streaming algorithm for the problem. There exists a streaming algorithm that solves the problem in O(k8 √ n log6 n) space. The worst-case time complexity of the algorithmO((k2 √ n+k13)·log4 n) per arrival. The algorithm is randomised with error probability at most 1/poly(n). 1998 ACM Subject Classification F.2 Analysis of Algorithms and Problem Complexity