An almost optimal edit distance oracle

Panagiotis Charalampopoulos, Paweł Gawrychowski, Shay Mozes, Oren Weimann

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We consider the problem of preprocessing two strings S and T, of lengths m and n, respectively, in order to be able to efficiently answer the following queries: Given positions i, j in S and positions a, b in T, return the optimal alignment score of S[i..j] and T[a..b]. Let N = mn. We present an oracle with preprocessing time N1+o(1) and space N1+o(1) that answers queries in log2+o(1) N time. In other words, we show that we can efficiently query for the alignment score of every pair of substrings after preprocessing the input for almost the same time it takes to compute just the alignment of S and T. Our oracle uses ideas from our distance oracle for planar graphs [STOC 2019] and exploits the special structure of the alignment graph. Conditioned on popular hardness conjectures, this result is optimal up to subpolynomial factors. Our results apply to both edit distance and longest common subsequence (LCS). The best previously known oracle with construction time and size O(N) has slow Ω(√ N) query time [Sakai, TCS 2019], and the one with size N1+o(1) and query time log2+o(1) N (using a planar graph distance oracle) has slow Ω(N3/2) construction time [Long & Pettie, SODA 2021]. We improve both approaches by roughly a √ N factor.

Original languageEnglish
Title of host publication48th International Colloquium on Automata, Languages, and Programming, ICALP 2021
EditorsNikhil Bansal, Emanuela Merelli, James Worrell
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959771955
StatePublished - 1 Jul 2021
Event48th International Colloquium on Automata, Languages, and Programming, ICALP 2021 - Virtual, Glasgow, United Kingdom
Duration: 12 Jul 202116 Jul 2021

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs


Conference48th International Colloquium on Automata, Languages, and Programming, ICALP 2021
Country/TerritoryUnited Kingdom
CityVirtual, Glasgow


  • Edit distance
  • Longest common subsequence
  • Planar graphs
  • Voronoi diagrams

All Science Journal Classification (ASJC) codes

  • Software


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