Leanness Computation: Small Values and Special Graph Classes

Let u and v be vertices in a connected graph G = (V, E). For any integer k such that 0 ≤ k ≤ dG (u, v), the k-slice Sk (u, v) contains all vertices x on a shortest uv-path such that dG (u, x) = k. The leanness of G is the maximum diameter of a slice. This metric graph invariant has been studied unde...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:Discrete Mathematics and Theoretical Computer Science Ročník 26:2; číslo Graph Theory; s. 1
Hlavní autoři: Coudert, David, Coulomb, Samuel, Ducoffe, Guillaume
Médium: Journal Article
Jazyk:angličtina
Vydáno: DMTCS 01.01.2024
Discrete Mathematics & Theoretical Computer Science
Témata:
[info.info-cc]computer science [cs]/computational complexity [cs.cc]
[info.info-ds]computer science [cs]/data structures and algorithms [cs.ds]
Algorithms
Analysis
Computational Complexity
Computer Science
Data Structures and Algorithms
geodetic graphs
graph algorithms
Graph theory
leanness
seth-based lower bounds
France
SETH-based lower bounds
Graph algorithms
Leanness
Geodetic graphs
ISSN:1365-8050, 1462-7264, 1365-8050
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:Let u and v be vertices in a connected graph G = (V, E). For any integer k such that 0 ≤ k ≤ dG (u, v), the k-slice Sk (u, v) contains all vertices x on a shortest uv-path such that dG (u, x) = k. The leanness of G is the maximum diameter of a slice. This metric graph invariant has been studied under different names, such as "interval thinness" and "fellow traveler property". Graphs with leanness equal to 0, a.k.a. geodetic graphs, also have received special attention in Graph Theory. The practical computation of leanness in real-life complex networks has been studied recently (Mohammed et al., COMPLEX NETWORKS'21). In this paper, we give a finer-grained complexity analysis of two related problems, namely: deciding whether the leanness of a graph G is at most some small value ℓ; and computing the leanness on specific graph classes. We obtain improved algorithms in some cases, and time complexity lower bounds under plausible hypotheses.
ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.12544