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The Communication Complexity of Pattern Matching with Edits Revisited

Authors Tomasz Kociumaka , Jakob Nogler , Philip Wellnitz

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ACM Subject Classification
  • Theory of computation → Pattern matching
  • Theory of computation → Communication complexity
  • Mathematics of computing → Combinatorics on words
Keywords
  • Edit distance
  • Pattern matching
  • Communication complexity

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Abstract

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 the k-error occurrences of P in T, that is, all fragments of T whose edit distance to P is at most k. The one-way communication complexity of this problem is the minimum number of bits that Alice, given an instance (P,T,k) of the problem, must send to Bob so that Bob can reconstruct the answer solely from that message.
In recent work [STOC'24], we showed that, in the natural parameter regime 0 < k < m < n/2, Ω(n/m ⋅ k log(m/k)) bits are necessary and 𝒪(n/m ⋅ k log² m) bits are sufficient for this problem. More generally, for strings over an alphabet Σ, we gave an 𝒪(n/m ⋅ k log m log(m|Σ|))-bit encoding that allows one to recover a shortest sequence of edits for every k-error occurrence of P in T.
In this paper, we revisit the original proof and improve the encoding size to 𝒪(n/m ⋅ k log (m|Σ|/k)), which matches the lower bound for constant-sized alphabets. We further establish a new tight lower bound of Ω(n/m ⋅ k log(m|Σ|/k)) for the edit sequence reporting variant we solve. Our encoding size also matches the communication complexity established for the simpler Pattern Matching with Mismatches problem in the context of streaming algorithms [Clifford, Kociumaka, Porat; SODA'19].

Cite As Get BibTex

Tomasz Kociumaka, Jakob Nogler, and Philip Wellnitz. The Communication Complexity of Pattern Matching with Edits Revisited. In 37th Annual Symposium on Combinatorial Pattern Matching (CPM 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 369, pp. 26:1-26:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.CPM.2026.26

Author Details

Tomasz Kociumaka
  • Max Planck Institute for Informatics, Saarland Informatics Campus, Saarbrücken, Germany
Jakob Nogler
  • Massachusetts Institute of Technology, Cambridge, MA, USA
Philip Wellnitz
  • National Institute of Informatics, Tokyo, Japan
  • The Graduate University for Advanced Studies, SOKENDAI, Tokyo, Japan

References

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