Optimal prefix-suffix queries with applications
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917829601656832 |
|---|---|
| author | Pissis, Solon P. |
| author_facet | Pissis, Solon P. |
| contents | We revisit the classic border tree data structure [Gu, Farach, Beigel, SODA 1994] that answers the following prefix-suffix queries on a string $T$ of length $n$ over an integer alphabet $Σ=[0,σ)$: for any $i,j \in [0,n)$ return all occurrences of $T$ in $T[0\mathinner{.\,.} i]T[j\mathinner{.\,.} n-1]$. The border tree of $T$ can be constructed in $\mathcal{O}(n)$ time and answers prefix-suffix queries in $\mathcal{O}(\log n + \textsf{Occ})$ time, where $\textsf{Occ}$ is the number of occurrences of $T$ in $T[0\mathinner{.\,.} i]T[j\mathinner{.\,.} n-1]$. Our contribution here is the following. We present a completely different and remarkably simple data structure that can be constructed in the optimal $\mathcal{O}(n/\log_σn)$ time and supports queries in the optimal $\mathcal{O}(1)$ time. Our result is based on a new structural lemma that lets us encode the output of any query in constant time and space. We also show a new direct application of our result in pattern matching on node-labeled graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03784 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimal prefix-suffix queries with applications Pissis, Solon P. Data Structures and Algorithms We revisit the classic border tree data structure [Gu, Farach, Beigel, SODA 1994] that answers the following prefix-suffix queries on a string $T$ of length $n$ over an integer alphabet $Σ=[0,σ)$: for any $i,j \in [0,n)$ return all occurrences of $T$ in $T[0\mathinner{.\,.} i]T[j\mathinner{.\,.} n-1]$. The border tree of $T$ can be constructed in $\mathcal{O}(n)$ time and answers prefix-suffix queries in $\mathcal{O}(\log n + \textsf{Occ})$ time, where $\textsf{Occ}$ is the number of occurrences of $T$ in $T[0\mathinner{.\,.} i]T[j\mathinner{.\,.} n-1]$. Our contribution here is the following. We present a completely different and remarkably simple data structure that can be constructed in the optimal $\mathcal{O}(n/\log_σn)$ time and supports queries in the optimal $\mathcal{O}(1)$ time. Our result is based on a new structural lemma that lets us encode the output of any query in constant time and space. We also show a new direct application of our result in pattern matching on node-labeled graphs. |
| title | Optimal prefix-suffix queries with applications |
| topic | Data Structures and Algorithms |
| url | https://arxiv.org/abs/2411.03784 |