Construction of Dual-CISTs on an Infinite Class of Networks

The main method to achieve fault-tolerant network systems is by exploiting and effectively utilizing the edge-disjoint and/or inner-vertex-disjoint paths between pairs of source and destination vertices. Completely independent spanning trees (CISTs for short) are powerful tools for reliable broadcasting/unicasting and secure message distribution. Particularly, it has been shown that two CISTs have an application on configuring a protection routing in IP networks, such as mobile ad hoc networks and relatively large (static) network topologies with scalability in [IEEE/ACM Trans. Netw., 27 (2019) 1112-1123]. Many results focus on CISTs in specific networks in the literature, however, few results are given on an infinite class of networks having common properties. In this article, we prove the existence of dual-CISTs in an infinite number of networks satisfying some Hamilton sufficient conditions. A unique algorithm to construct a CIST-partition is proposed, which can be applied to not only many kinds of networks, but our algorithm can also be implemented very easily in parallel or distributed systems satisfying the conditions. In addition, we make a comparative analysis between the proposed conditions and several known results on an infinite number of networks, the advantage of our result is significant. In particular, the bound in our conditions is sharp. The results will provide a powerful framework for the design of fault-tolerant network topologies and routing protocols for future networks.