Independent Spanning Trees in Networks – A Survey
نویسندگان
چکیده
The problem of constructing independent spanning trees (ISTs) dates back to as early the late 1980s. Given a network G certain topology, question is whether we can, well how to, construct set ISTs in . have proven be great importance many tasks. past decade has seen particularly remarkable increase literature on ISTs, manifesting significant growth interest. can classified into edge-independent (edge-ISTs), node-independent (node-ISTs), and completely (CISTs). For , node-ISTs (edge-ISTs) rooted at u are such that there no common internal nodes (edges) between any other node among paths these trees. If every act root node, called CISTs This survey aims bringing together important works been reported literature. It provides historical perspective field evolved, serve an integrated useful resource references for future research ISTs.
منابع مشابه
Node-Independent Spanning Trees in Gaussian Networks
Gaussian network is known to be an alternative to toroidal network since it has the same number of nodes with less diameter, which makes it perform better than toroidal network. Spanning trees are said to be independent if all trees are rooted at the same node r and for any other node u, the nodes of the paths from r to u in all trees are distinct except the nodes r and u. In this paper, we inv...
متن کاملCompletely Independent Spanning Trees in Some Regular Networks
Let k ≥ 2 be an integer and T1, . . . , Tk be spanning trees of a graph G.If for any pair of vertices (u, v) of V (G), the paths from u to v in each Ti,1 ≤ i ≤ k, do not contain common edges and common vertices, except thevertices u and v, then T1, . . . , Tk are completely independent spanningtrees in G. For 2k-regular graphs which are 2k-connected, such as theCartesian pro...
متن کاملNetworks and Spanning Trees
In 1857 Arthur Cayley (1821–1895) published a paper [9] that introduces the term “tree” to describe the logical branching that occurs when iterating the fundamental process of (partial) differentiation. When discussing the composition of four symbols that involve derivatives, Cayley writes “But without a more convenient notation, it would be difficult to find [their] corresponding expressions ....
متن کاملIndependent spanning trees in crossed cubes
A set of spanning trees in a graph is said to be independent (ISTs for short) if all the trees are rooted at the same node r and for any other node v(6= r), the paths from v to r in any two trees are nodedisjoint except the two end nodes v and r. For an n-connected graph, the independent spanning trees problem asks to construct n ISTs rooted at an arbitrary node of the graph. Recently, Zhang et...
متن کاملCompletely independent spanning trees in (partial) k-trees
Two spanning trees T1 and T2 of a graph G are completely independent if, for any two vertices u and v, the paths from u to v in T1 and T2 are internally disjoint. For a graph G, we denote the maximum number of pairwise completely independent spanning trees by cist(G). In this paper, we consider cist(G) when G is a partial k-tree. First we show that ⌈k/2⌉ ≤ cist(G) ≤ k − 1 for any k-tree G. Then...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ACM Computing Surveys
سال: 2023
ISSN: ['0360-0300', '1557-7341']
DOI: https://doi.org/10.1145/3591110