Independent Spanning Trees in Networks: A Survey

The problem of constructing independent spanning trees (ISTs) dates back to as early as the late 1980s. Given a network G of a certain topology, the question is whether we can, as well as how to, construct a set of ISTs in G. ISTs have proven to be of great importance in many network tasks. The past decade has seen a particularly remarkable increase in the literature on ISTs, manifesting a significant growth of interest. ISTs can be classified into edge-independent spanning trees (edge-ISTs), node-independent spanning trees (node-ISTs), and completely independent spanning trees (CISTs). For a network G, node-ISTs (edge-ISTs) rooted at u are a set of spanning trees rooted at u in G such that there are no common internal nodes (edges) between u and any other node among the paths in these spanning trees. If every node in a set of node-ISTs can act as a root node, the set of trees is called CISTs. This survey aims at bringing together important works on ISTs that have been reported in the literature. It provides a historical perspective of how the field has evolved, and can serve as an integrated useful resource of references for future research on ISTs.