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An Improved Sketching Algorithm for Edit Distance

Authors Ce Jin , Jelani Nelson , Kewen Wu

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  • Theory of computation → Sketching and sampling
Keywords
  • edit distance
  • sketching

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Abstract

We provide improved upper bounds for the simultaneous sketching complexity of edit distance. Consider two parties, Alice with input x ∈ Σⁿ and Bob with input y ∈ Σⁿ, that share public randomness and are given a promise that the edit distance ed(x,y) between their two strings is at most some given value k. Alice must send a message sx and Bob must send sy to a third party Charlie, who does not know the inputs but shares the same public randomness and also knows k. Charlie must output ed(x,y) precisely as well as a sequence of ed(x,y) edits required to transform x into y. The goal is to minimize the lengths |sx|, |sy| of the messages sent. 
The protocol of Belazzougui and Zhang (FOCS 2016), building upon the random walk method of Chakraborty, Goldenberg, and Koucký (STOC 2016), achieves a maximum message length of Õ(k⁸) bits, where Õ(⋅) hides poly(log n) factors. In this work we build upon Belazzougui and Zhang’s protocol and provide an improved analysis demonstrating that a slight modification of their construction achieves a bound of Õ(k³).

Cite As Get BibTex

Ce Jin, Jelani Nelson, and Kewen Wu. An Improved Sketching Algorithm for Edit Distance. In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 45:1-45:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.STACS.2021.45

Author Details

Ce Jin
  • MIT, Cambridge, MA, USA
Jelani Nelson
  • University of California at Berkeley, CA, USA
Kewen Wu
  • University of California at Berkeley, CA, USA

Funding

  • Jin, Ce: Supported by Akamai Presidential Fellowship.
  • Nelson, Jelani: Supported by NSF award CCF-1951384, ONR grant N00014-18-1-2562, ONR DORECG award N00014-17-1-2127, an Alfred P. Sloan Research Fellowship, and a Google Faculty Research Award.

Acknowledgements

We thank Qin Zhang for answering several questions about [Djamal Belazzougui and Qin Zhang, 2016]. C. J. thanks Virginia Vassilevska Williams for several helpful discussions. We thank anonymous reviewers for their helpful comments.

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