TY - GEN
T1 - On the Hardness of Computing the Edit Distance of Shallow Trees
AU - Charalampopoulos, Panagiotis
AU - Gawrychowski, Paweł
AU - Mozes, Shay
AU - Weimann, Oren
N1 - Publisher Copyright: © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.
PY - 2022
Y1 - 2022
N2 - We consider the edit distance problem on rooted ordered trees parameterized by the trees’ depth. For two trees of size at most n and depth at most d, the state-of-the-art solutions of Zhang and Shasha [SICOMP 1989] and Demaine et al. [TALG 2009] have runtimes O(n2d2) and O(n3), respectively, and are based on so-called decomposition algorithms. It has been recently shown by Bringmann et al. [TALG 2020] that, when d= Θ(n), one cannot compute the edit distance of two trees in O(n3-ϵ) time (for any constant ϵ> 0 ) under the APSP hypothesis. However, for small values of d, it is not known whether the O(n2d2) upper bound of Zhang and Shasha is optimal. We make the following twofold contribution. First, we show that under the APSP hypothesis there is no algorithm with runtime O(n2d1-ϵ) (for any constant ϵ> 0 ) when d= p oly(n). Second, we show that there is no decomposition algorithm that runs in time o(min { n2d2, n3} ).
AB - We consider the edit distance problem on rooted ordered trees parameterized by the trees’ depth. For two trees of size at most n and depth at most d, the state-of-the-art solutions of Zhang and Shasha [SICOMP 1989] and Demaine et al. [TALG 2009] have runtimes O(n2d2) and O(n3), respectively, and are based on so-called decomposition algorithms. It has been recently shown by Bringmann et al. [TALG 2020] that, when d= Θ(n), one cannot compute the edit distance of two trees in O(n3-ϵ) time (for any constant ϵ> 0 ) under the APSP hypothesis. However, for small values of d, it is not known whether the O(n2d2) upper bound of Zhang and Shasha is optimal. We make the following twofold contribution. First, we show that under the APSP hypothesis there is no algorithm with runtime O(n2d1-ϵ) (for any constant ϵ> 0 ) when d= p oly(n). Second, we show that there is no decomposition algorithm that runs in time o(min { n2d2, n3} ).
UR - http://www.scopus.com/inward/record.url?scp=85142756868&partnerID=8YFLogxK
U2 - https://doi.org/10.1007/978-3-031-20643-6_21
DO - https://doi.org/10.1007/978-3-031-20643-6_21
M3 - Conference contribution
SN - 9783031206429
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 290
EP - 302
BT - String Processing and Information Retrieval - 29th International Symposium, SPIRE 2022, Proceedings
A2 - Arroyuelo, Diego
A2 - Poblete, Barbara
PB - Springer Science and Business Media Deutschland GmbH
T2 - 29th International Symposium on String Processing and Information Retrieval, SPIRE 2022
Y2 - 8 November 2022 through 10 November 2022
ER -