iBet uBet web content aggregator. Adding the entire web to your favor.
iBet uBet web content aggregator. Adding the entire web to your favor.



Link to original content: https://doi.org/10.48550/arXiv.2306.16065
[2306.16065] Approximate Cartesian Tree Matching: an Approach Using Swaps
Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Computer Science > Data Structures and Algorithms

arXiv:2306.16065 (cs)
[Submitted on 28 Jun 2023 (v1), last revised 18 Oct 2024 (this version, v2)]

Title:Approximate Cartesian Tree Matching: an Approach Using Swaps

Authors:Bastien Auvray, Julien David, Richard Groult, Thierry Lecroq
View PDF HTML (experimental)
Abstract:Cartesian tree pattern matching consists of finding all the factors of a text that have the same Cartesian tree than a given pattern. There already exist theoretical and practical solutions for the exact case. In this paper, we propose the first algorithm for solving approximate Cartesian tree pattern matching. We consider Cartesian tree pattern matching with one swap: given a pattern of length m and a text of length n we present two algorithms that find all the factors of the text that have the same Cartesian tree of the pattern after one transposition of two adjacent symbols. The first algorithm uses a characterization of a linear representation of the Cartesian trees called parent-distance after one swap and runs in time Theta(mn) using Theta(m) space. The second algorithm generates all the parent-distance tables of sequences that have the same Cartesian tree than the pattern after one swap. It runs in time O((m^2 + n)log m) and has O(m^2) space complexity.
Comments: Submitted to SPIRE 2023
Subjects: Data Structures and Algorithms (cs.DS)
Cite as: arXiv:2306.16065 [cs.DS]
  (or arXiv:2306.16065v2 [cs.DS] for this version)
  https://doi.org/10.48550/arXiv.2306.16065

Submission history

From: Bastien Auvray [view email]
[v1] Wed, 28 Jun 2023 10:00:23 UTC (274 KB)
[v2] Fri, 18 Oct 2024 12:26:41 UTC (208 KB)
Full-text links:

Access Paper:

view license
Current browse context:
cs.DS
< prev   |   next >
new | recent | 2023-06
Change to browse by:
cs

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)