Fault Tolerant Routing in Star Graphs Using Fault Vector

In this paper a fault tolerant routing algorithm for unicasting on star graph is proposed. The routing algorithm does not involve back tracking and uses fault-vectors. Each node in an n-star has a fault-vector of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lfloor\frac{3(n-1)}{2}\rfloor$\end{document} bits. The kth bit of a node’s fault-vector is a measure of its routing ability to nodes which are at distance k from itself. The fault-vector of each node can easily be calculated through \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\lfloor\frac{3(n-1)}{2}\rfloor$\end{document} rounds of information exchanges among neighbor nodes. For a given source destination pair (u,v), the routing algorithm finds a path of length d + h where d is the length of the shortest path between u and v in a fault-free star graph and h = 0, 2 or 4. The space requirement for storing the fault vector is O(n) in each node. Simulation results show that the proposed algorithm far outperforms the routing algorithm based on safety vectors [13].