Dynamic Reconfiguration of Complete Binary Trees in Faulty Locally Twisted Cubes

Abstract

The complete binary tree is an important network structure for parallel and distributed computing, which has many nice properties and is often used to be embedded into other interconnection architectures. The locally twisted cube LTQn is an important variant of the hypercube Qn. It has many better properties than Qn with the same number of edges and vertices. In this paper, we prove that the complete binary tree CBTn can be embedded with dilation 2 and congestion 1 into LTQn. Furthermore, it is proven that if there exists an arbitrary faulty node in LTQn, then both the dilation and congestion values will become 2 after reconfiguring CBTn, while if there are two arbitrary faulty nodes in LTQn, then both the dilation and congestion values will become 3 after reconfiguration.