Linear time algorithms for finding independent spanning trees on pyramid networks

The use of independent spanning trees (ISTs) has scientific applications in fault-tolerant requirement in network protocols and secure message distributions. Most of the designs of ISTs are for those interconnection networks with vertex symmetric property, implying that one can find ISTs rooted on a designated vertex, and, by the vertex symmetry property of the given network, hence have solved the ISTs problem on any arbitrary vertex. The existence of asymmetry makes the ISTs problem even harder than its symmetric counterpart. Cheriyan and Maheshwari (J Algorithms 9:507-537, 1988) showed that, for any 3-connected graph, 3-ISTs rooted at any vertex can be found in O(|V||E|) time. In this paper, we propose linear time algorithms that solved 3-ISTs rooted at an arbitrary vertex of pyramid networks.