Hamiltonian Connectivity of Twisted Hypercube-Like Networks under the Large Fault Model

TL;DR

This paper proves that twisted hypercube-like networks maintain Hamiltonian connectivity under large fault conditions, enhancing their reliability for parallel computing systems.

Contribution

It establishes fault-tolerant Hamiltonian connectivity in THLNs with up to 2n-10 faults, extending their known robustness in large-scale networks.

Findings

Hamiltonian or near-Hamiltonian paths exist under specified fault conditions.

Fault-tolerance extends the embedding capabilities of THLNs.

Results apply to various hypercube variants like crossed and twisted cubes.

Abstract

Twisted hypercube-like networks (THLNs) are an important class of interconnection networks for parallel computing systems, which include most popular variants of the hypercubes, such as crossed cubes, M\"obius cubes, twisted cubes and locally twisted cubes. This paper deals with the fault-tolerant hamiltonian connectivity of THLNs under the large fault model. Let $G$ be an $n$-dimensional THLN and $F \subseteq V(G)\bigcup E(G)$, where $n \geq 7$ and $|F| \leq 2n - 10$. We prove that for any two nodes $u,v \in V(G - F)$ satisfying a simple necessary condition on neighbors of $u$ and $v$, there exists a hamiltonian or near-hamiltonian path between $u$ and $v$ in $G-F$. The result extends further the fault-tolerant graph embedding capability of THLNs.