Sign in to use this feature.

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline

Journals

Article Types

Countries / Regions

Search Results (2)

Search Parameters:
Keywords = greedoids

Order results
Result details
Results per page
Select all
Export citation of selected articles as:
10 pages, 262 KB  
Article
Greedoids and Violator Spaces
by Yulia Kempner and Vadim E. Levit
Axioms 2024, 13(9), 633; https://doi.org/10.3390/axioms13090633 - 17 Sep 2024
Viewed by 1428
Abstract
This research explores the interplay between violator spaces and greedoids—two distinct theoretical frameworks developed independently. Violator spaces were introduced as a generalization of linear programming, while greedoids were designed to characterize combinatorial structures where greedy algorithms yield optimal solutions. These frameworks have, until [...] Read more.
This research explores the interplay between violator spaces and greedoids—two distinct theoretical frameworks developed independently. Violator spaces were introduced as a generalization of linear programming, while greedoids were designed to characterize combinatorial structures where greedy algorithms yield optimal solutions. These frameworks have, until now, existed in isolation. This paper bridges the gap by showing that greedoids can be defined using a modified violator operator. The established connections not only deepen our understanding of these theories but also provide a new characterization of antimatroids. Full article
(This article belongs to the Section Algebra and Number Theory)
Show Figures

Figure 1

9 pages, 271 KB  
Article
A Note on Ultrametric Spaces, Minimum Spanning Trees and the Topological Distance Algorithm
by Jörg Schäfer
Information 2020, 11(9), 418; https://doi.org/10.3390/info11090418 - 28 Aug 2020
Cited by 1 | Viewed by 3090
Abstract
We relate the definition of an ultrametric space to the topological distance algorithm—an algorithm defined in the context of peer-to-peer network applications. Although (greedy) algorithms for constructing minimum spanning trees such as Prim’s or Kruskal’s algorithm have been known for a long time, [...] Read more.
We relate the definition of an ultrametric space to the topological distance algorithm—an algorithm defined in the context of peer-to-peer network applications. Although (greedy) algorithms for constructing minimum spanning trees such as Prim’s or Kruskal’s algorithm have been known for a long time, they require the complete graph to be specified and the weights of all edges to be known upfront in order to construct a minimum spanning tree. However, if the weights of the underlying graph stem from an ultrametric, the minimum spanning tree can be constructed incrementally and it is not necessary to know the full graph in advance. This is possible, because the join algorithm responsible for joining new nodes on behalf of the topological distance algorithm is independent of the order in which the nodes are added due to the property of an ultrametric. Apart from the mathematical elegance which some readers might find interesting in itself, this provides not only proofs (and clearer ones in the opinion of the author) for optimality theorems (i.e., proof of the minimum spanning tree construction) but a simple proof for the optimality of the reconstruction algorithm omitted in previous publications too. Furthermore, we define a new algorithm by extending the join algorithm to minimize the topological distance and (network) latency together and provide a correctness proof. Full article
(This article belongs to the Section Information and Communications Technology)
Show Figures

Figure 1

Back to TopTop