The decades-old Pattern Matching with Edits problem, given a length-n string T (the text), a length-m string P (the pattern), and a positive integer k (the threshold), asks to list all fragments of T that are at edit distance at most k from P. The one-way communication complexity of this problem is the minimum amount of space needed to encode the answer so that it can be retrieved without accessing the input strings P and T.
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Kociumaka et al. (2024) studied this question.
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