License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2021.45
URN: urn:nbn:de:0030-drops-136905
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Jin, Ce ; Nelson, Jelani ; Wu, Kewen

An Improved Sketching Algorithm for Edit Distance

LIPIcs-STACS-2021-45.pdf (0.8 MB)


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).

BibTeX - Entry

  author =	{Jin, Ce and Nelson, Jelani and Wu, Kewen},
  title =	{{An Improved Sketching Algorithm for Edit Distance}},
  booktitle =	{38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)},
  pages =	{45:1--45:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-180-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{187},
  editor =	{Bl\"{a}ser, Markus and Monmege, Benjamin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-136905},
  doi =		{10.4230/LIPIcs.STACS.2021.45},
  annote =	{Keywords: edit distance, sketching}

Keywords: edit distance, sketching
Collection: 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)
Issue Date: 2021
Date of publication: 10.03.2021

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