Efficient Algorithm for Computing the Longest Common Prefix Array of a Labeled Graph

Conceptos Básicos

An efficient algorithm to compute the Longest Common Prefix (LCP) array of a labeled graph, which enables efficient pattern matching and navigation on the graph's paths.

Resumen

The paper presents an efficient algorithm for computing the Longest Common Prefix (LCP) array of a labeled graph G with n nodes and m edges.
The key steps are:

Pre-processing: The input graph G is transformed into a deterministic Wheeler pseudoforest Gis that compactly encodes the lexicographically smallest and largest strings entering each node of G. This step runs in O(min{m log n, m + n^2}) time on arbitrary labeled graphs, and in O(m) time on Wheeler semi-DFAs.

LCP Computation: A new compact-space algorithm is introduced to compute the reduced LCP array LCP*_Gis of the Wheeler pseudoforest Gis in O(n log σ) time and O(n log σ) bits of working space, where σ is the alphabet size.

Post-processing: The LCP array of the original graph G is derived from the LCP*_Gis array in O(m) time and O(m) words of space.

The overall algorithm computes the LCP array of the input graph G in O(n log σ + min{m log n, m + n^2}) time and O(m) words of space. If G is a Wheeler semi-DFA, the running time reduces to O(n log σ + m).
The authors also show that the natural generalization of a previous compact-space LCP-construction algorithm by Beller et al. runs in Ω(nσ) time on pseudoforests, motivating the need for their new algorithm.

Estadísticas

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Citas

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Ideas clave extraídas de

Computing the LCP Array of a Labeled Graph

by Jarno Alanko... a las arxiv.org 04-23-2024

https://arxiv.org/pdf/2404.14235.pdf

Consultas más profundas

How can the proposed algorithm be extended to handle dynamic updates to the input labeled graph

To extend the proposed algorithm to handle dynamic updates to the input labeled graph, we can incorporate techniques from dynamic data structures. One approach could be to maintain a data structure that tracks the changes in the graph, such as edge insertions or deletions. When a modification occurs, we can update the relevant data structures accordingly. For example, when an edge is added, we can update the bridge information and recompute the affected LCP values. By efficiently managing these updates, we can ensure that the LCP array remains accurate and up-to-date despite changes to the graph.

What are the potential applications of the LCP array of a labeled graph beyond pattern matching and navigation, and how could the algorithm be adapted to those use cases

The LCP array of a labeled graph has various potential applications beyond pattern matching and navigation. One such application could be in bioinformatics, specifically in DNA sequence analysis. By representing DNA sequences as labeled graphs, the LCP array can help identify common patterns or motifs in genetic data. This can be valuable in tasks such as sequence alignment, gene prediction, and evolutionary studies. To adapt the algorithm for these use cases, we would need to tailor the input graph representation and the specific queries or analyses performed on the LCP array to suit the requirements of genetic data analysis.

The algorithm assumes the input graph is deterministic. How could it be generalized to handle non-deterministic labeled graphs

To generalize the algorithm to handle non-deterministic labeled graphs, we would need to modify the data structures and algorithms to accommodate multiple possible transitions from a node based on the input label. This would involve considering all possible paths in the graph when computing the LCP array, taking into account the non-deterministic nature of the edges. By incorporating probabilistic or non-deterministic transitions into the algorithm, we can extend its applicability to a broader range of graph types, allowing for more flexibility in analyzing and processing labeled graphs with uncertain or variable outcomes.