Charalampopoulos, Panagiotis and Gawrychowski, P. and Mozes, S. and Weimann, O. (2022) On the hardness of computing the edit distance of shallow trees. Lecture Notes in Computer Science 13617 , pp. 290-302. ISSN 0302-9743.
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Abstract
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(n^2 · d^2) and O(n^3), 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(n^{3−ϵ}) time (for any constant ϵ>0) under the APSP hypothesis. However, for small values of d, it is not known whether the O(n^2 · d^2) 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(n^2 · d^{1−ϵ}) (for any constant ϵ>0) when d=poly(n). Second, we show that there is no decomposition algorithm that runs in time o(min{n^2 · d^2,n^3}).
Metadata
| Item Type: | Article |
|---|---|
| Additional Information: | International Symposium on String Processing and Information Retrieval. SPIRE 2022: String Processing and Information Retrieval, Proceedings. ISBN: 9783031206429 |
| School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |
| Depositing User: | Panagiotis Charalampopoulos |
| Date Deposited: | 30 Nov 2022 06:38 |
| Last Modified: | 31 Oct 2023 01:10 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/49968 |
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