Recursive and parallel constructions of independent spanning trees in alternating group networks

Abstract

In this paper, we propose a recursive algorithm and a parallel algorithm for constructing independent spanning trees in ANn. The main ideas of the recursive algorithm are to construct large trees from small trees, use triangle breadth-first search (TBFS) to build a frame of an IST, and use breadth-first search (BFS) to link the rest of the nodes. The main ideas of the parallel algorithm are to build frames through TBFS in parallel, and to use the specific rules to link the rest of the nodes in parallel. We prove the correctness of both algorithms for constructing ISTs in AN_n. Both algorithms are accurate; furthermore, the parallel algorithm is more ecient than the recursive algorithm. (An extended abstract of this paper appeared in: Jie-Fu Huang and Sun-Yuan Hsieh ‘Two methods for constructing independent spanning trees in alternating group networks’ Proceedings of International Conference on Creative Lifestyle Computing (ICCLC), 2020.)

Keywords:

• Independent spanning trees
• alternating group networks
• Cayley graph
• recursive algorithm
• parallel algorithm

2010 Mathematics Subject Classifications:

• 05C05
• 68R10

Disclosure statement

No potential conflict of interest was reported by the authors.