The Communication Complexity of Pattern Matching with Edits Revisited
Tomasz Kociumaka, Jakob Nogler, Philip Wellnitz

TL;DR
This paper improves the understanding of the communication complexity for pattern matching with edits, providing tighter bounds and matching lower bounds for the problem, especially over constant-sized alphabets.
Contribution
It refines the encoding size to match lower bounds and establishes a new tight lower bound for reporting edit sequences in pattern matching with edits.
Findings
Improved encoding size to O(n/m · k log(m|Σ|/k))
Established a new tight lower bound matching the encoding size
Matching the communication complexity for pattern matching with mismatches in streaming contexts
Abstract
In the decades-old Pattern Matching with Edits problem, given a length- string (the text), a length- string (the pattern), and a positive integer (the threshold), the task is to list the -error occurrences of in , that is, all fragments of whose edit distance to is at most . The one-way communication complexity of Pattern Matching with Edits is the minimum number of bits that Alice, given an instance of the problem, must send to Bob so that Bob can reconstruct the answer solely from that message. For the natural parameter regime of , our recent work [STOC'24] yields that bits are necessary and bits are sufficient for Pattern Matching with Edits. More generally, for strings over an alphabet , our recent work [STOC'24] gives an $O(n/m \cdot k \log m…
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