Efficiently computing runs on a trie
Year: 2019
Type: preprint
Abstract: A maximal repetition, or run, in a string, is a maximal periodic substring whose smallest period is at most half the length of the substring. In this paper, we consider runs that correspond to a path on a trie, or in other words, on a rooted edge-labeled tree where the endpoints of the path must be a descendant/ancestor of the other. For a trie with $n$ edges, we show that the number of runs is less than $n$. We also show an asymptotic lower bound on the maximum density of runs in tries: $\lim_{n\rightarrow\infty}ρ_\mathcal{T}(n)/n \geq 0.993238$ where $ρ_{\mathcal{T}}(n)$ is the maximum number of runs in a trie with $n$ edges. Furthermore, we also show an $O(n\log \log n)$ time and $O(n)$ space algorithm for finding all runs.
Source: arXiv (Cornell University)
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Awards: G1244153478, G1666168458, Combinatorics of string lexicographic orders and their applications, G4245462952, G4383934419, Analysis of upper and lower bounds on string processing problems via advanced data structures, G7741065061, G7741475721, 情報爆縮に基づくIoTデータ処理基盤の構築, Simple and fast string algorithms by Lyndon words
OpenAlex ID: W3153057271