Õ(n+poly(k))-time Algorithm for Bounded Tree Edit Distance

Debarati Das, Jacob Gilbert, Mohammad Taghi Hajiaghayi, Tomasz Kociumaka, Barna Saha, Hamed Saleh

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Abstract

    Computing the edit distance of two strings is one of the most basic problems in computer science and combinatorial optimization. Tree edit distance is a natural generalization of edit distance in which the task is to compute a measure of dissimilarity between two (unweighted) rooted trees with node labels. Perhaps the most notable recent application of tree edit distance is in NoSQL big databases, such as MongoDB, where each row of the database is a JSON document represented as a labeled rooted tree and finding dissimilarity between two rows is a basic operation. Until recently, the fastest algorithm for tree edit distance ran in cubic time (Demaine, Mozes, Rossman, Weimann; TALG'10); however, Mao (FOCS'21) broke the cubic barrier for the tree edit distance problem using fast matrix multiplication.Given a parameter k as an upper bound on the distance, an O(n+k2)-time algorithm for edit distance has been known since the 1980s due to works of Myers (Algorithmica'86) and Landau and Vishkin (JCSS'88). The existence of an O(n+poly(k))-time algorithm for tree edit distance has been posed as open question, e.g., by Akmal and Jin (ICALP'21), who give a stateof-the-art O(nk2)-time algorithm. In this paper, we answer this question positively.

    Original languageEnglish (US)
    Title of host publicationProceedings - 2022 IEEE 63rd Annual Symposium on Foundations of Computer Science, FOCS 2022
    PublisherIEEE Computer Society
    Pages686-697
    Number of pages12
    ISBN (Electronic)9781665455190
    DOIs
    StatePublished - 2022
    Event63rd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2022 - Denver, United States
    Duration: Oct 31 2022Nov 3 2022

    Publication series

    NameProceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
    Volume2022-October
    ISSN (Print)0272-5428

    Conference

    Conference63rd IEEE Annual Symposium on Foundations of Computer Science, FOCS 2022
    Country/TerritoryUnited States
    CityDenver
    Period10/31/2211/3/22

    All Science Journal Classification (ASJC) codes

    • Computer Science(all)

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