Top-Down Construction of Independent Spanning Trees in Alternating Group Networks
| Autor: | Shih-Shun Kao, Sun-Yuan Hsieh, Jie Fu Huang, Ralf Klasing |
|---|---|
| Přispěvatelé: | National Cheng Kung University (NCKU), Université de Bordeaux (UB) |
| Rok vydání: | 2020 |
| Předmět: |
Vertex (graph theory)
alternating group networks General Computer Science Computer science triangle breadth-first search 0102 computer and information sciences 02 engineering and technology 01 natural sciences Cayley graph [INFO.INFO-NI]Computer Science [cs]/Networking and Internet Architecture [cs.NI] 0202 electrical engineering electronic engineering information engineering General Materials Science Time complexity interconnection networks Discrete mathematics Interconnection Spanning tree General Engineering Alternating group Telecommunications network Graph Independent spanning trees Vertex (geometry) 010201 computation theory & mathematics 020201 artificial intelligence & image processing lcsh:Electrical engineering. Electronics. Nuclear engineering lcsh:TK1-9971 |
| Zdroj: | IEEE Access IEEE Access, IEEE, 2020, 8, pp.112333-112347. ⟨10.1109/access.2020.2999421⟩ IEEE Access, Vol 8, Pp 112333-112347 (2020) |
| ISSN: | 2169-3536 |
| DOI: | 10.1109/access.2020.2999421 |
| Popis: | International audience; A set of spanning trees in a graph G is called independent spanning trees (ISTs) if they are rooted at the same vertex r, and for each vertex v(= r) in G, the two paths from v to r in any two trees share no common vertex expect for v and r. ISTs can be applied in many research fields, such as fault-tolerant broadcasting and secure message distribution in reliable communication networks. Since Cayley graphs have been widely used to design interconnection networks, constructing ISTs on cayley graphs is worth studying. The alternating group network is a subclass of Cayley graphs, and the approach of constructing ISTs in alternating group networks is still unknown. In this paper, we propose a novel and simple top-down approach for constructing ISTs in alternating group networks. The main ideas of the algorithm are to use induction to develop small trees to big trees, to use a triangle breadth-first search (TBFS) process to create a backbone of an IST, and to use breadth-first search (BFS) process to connect the rest of nodes. Compared to other methods of different interconnection networks in the literature, the uniqueness of our method is that it does not need to determine the parent of one node by any rule, on the contrary others determine that by rules. The time complexity in n-dimensional alternating group network AN n is O(n 2 × n!), where n! is twice the number of nodes of AN n ; hence it is polynomial time. We implement the algorithm in PHP and run cases from AN 3 to AN 10. The results reveal that all spanning trees of AN 3 to AN 10 are independent and that our algorithm is accurate and efficient. INDEX TERMS Independent spanning trees, alternating group networks, triangle breadth-first search, interconnection networks, Cayley graph. |
| Databáze: | OpenAIRE |
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