On Finding Optimal (Dynamic) Arborescences

Let G=(V,E) be a directed and weighted graph with a vertex set V of size n and an edge set E of size m such that each edge (u,v)∈E has a real-valued weight w(u,c). An arborescence in G is a subgraph T=(V,E′) such that, for a vertex u∈V, which is the root, there is a unique path in T from u to any ot...

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Bibliographic Details
Published in:Algorithms Vol. 16; no. 12; p. 559
Main Authors: Espada, Joaquim, Francisco, Alexandre P., Rocher, Tatiana, Russo, Luís M. S., Vaz, Cátia
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.12.2023
Subjects:
algorithm engineering
Algorithms
Design optimization
dynamic algorithm
Edmonds’ algorithm
Graph theory
Graphs
Inference
Minimum weight
Network design
optimal arborescences
Phylogenetics
Phylogeny
Traveling salesman problem
Vertex sets
Portugal
ISSN:1999-4893, 1999-4893
Online Access:Get full text
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Summary:Let G=(V,E) be a directed and weighted graph with a vertex set V of size n and an edge set E of size m such that each edge (u,v)∈E has a real-valued weight w(u,c). An arborescence in G is a subgraph T=(V,E′) such that, for a vertex u∈V, which is the root, there is a unique path in T from u to any other vertex v∈V. The weight of T is the sum of the weights of its edges. In this paper, given G, we are interested in finding an arborescence in G with a minimum weight, i.e., an optimal arborescence. Furthermore, when G is subject to changes, namely, edge insertions and deletions, we are interested in efficiently maintaining a dynamic arborescence in G. This is a well-known problem with applications in several domains such as network design optimization and phylogenetic inference. In this paper, we revisit the algorithmic ideas proposed by several authors for this problem. We provide detailed pseudocode, as well as implementation details, and we present experimental results regarding large scale-free networks and phylogenetic inference. Our implementation is publicly available.
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ISSN:1999-4893
1999-4893
DOI:10.3390/a16120559