相关论文: Edge-Disjoint Spanning Trees on Star-Product Netwo…

Independent trees are used in building secure and/or fault-tolerant network communication protocols. They have been investigated for different network topologies including tori. Dense Gaussian networks are potential alternatives for…

Given a connected undirected graph G = [V; E] where |E| =2(|V| -1), we present two algorithms to check if G can be decomposed into two edge disjoint spanning trees, and provide such a decomposition when it exists. Unlike previous algorithms…

Spanning trees are fundamental for efficient communication in networks. For fault-tolerant communication, it is desirable to have multiple spanning trees to ensure resilience against failures of nodes and edges. To this end, various notions…

Let T1, T2,.... Tk be spanning trees in a graph G. If for any pair of vertices u and v of G, the paths between u and v in every Ti( 0 < i < k+1) do not contain common edges then T1, T2,.... Tk are called edge-disjoint spanning trees in G.…

Spanning trees are widely used in networks for broadcasting, fault-tolerance, and securely delivering messages. Hexagonal interconnection networks have a number of real life applications. Examples are cellular networks, computer graphics,…

The distribution of distances in the star graph $ST_n$, ($1<n\in\Z$), is established, and subsequently a threaded binary tree is obtained that realizes an orientation of $ST_n$ whose levels are given by the distances to the identity…

The minimum degree spanning tree (MDST) problem requires the construction of a spanning tree $T$ for graph $G=(V,E)$ with $n$ vertices, such that the maximum degree $d$ of $T$ is the smallest among all spanning trees of $G$. In this paper,…

We present time-efficient distributed algorithms for decomposing graphs with large edge or vertex connectivity into multiple spanning or dominating trees, respectively. As their primary applications, these decompositions allow us to achieve…

The minimum spanning tree (MST), a graph constructed from a distribution of points, draws lines between pairs of points so that all points are linked in a single skeletal structure that contains no loops and has minimal total edge length.…

Cartesian product networks are always regarded as a tool for ``combining'' two given networks with established properties to obtain a new one that inherits properties from both. For a graph $F=(V,E)$ and a set $S\subseteq V(F)$ of at least…

This paper makes two main contributions: The first is the construction of a near-minimum spanning tree with constant average distortion. The second is a general equivalence theorem relating two refined notions of distortion: scaling…

A network can contain numerous spanning trees. If two spanning trees $T_i,T_j$ do not share any common edges, $T_i$ and $T_j$ are said to be pairwisely edge-disjoint. For spanning trees $T_1, T_2, ..., T_m$, if every two of them are…

We study the problem of constructing universal Steiner trees for undirected graphs. Given a graph $G$ and a root node $r$, we seek a single spanning tree $T$ of minimum {\em stretch}, where the stretch of $T$ is defined to be the maximum…

In the Steiner Tree problem we are given an edge weighted undirected graph $G = (V,E)$ and a set of terminals $R \subseteq V$. The task is to find a connected subgraph of $G$ containing $R$ and minimizing the sum of weights of its edges. We…

Daily internet communication relies heavily on tree-structured graphs, embodied by popular data formats such as XML and JSON. However, many recent generative (probabilistic) models utilize neural networks to learn a probability distribution…

Given a spatio-temporal network (ST network) where edge properties vary with time, a time-sub-interval minimum spanning tree (TSMST) is a collection of minimum spanning trees of the ST network, where each tree is associated with a time…

Given a graph $G$ and a digraph $D$ whose vertices are the edges of $G$, we investigate the problem of finding a spanning tree of $G$ that satisfies the constraints imposed by $D$. The restrictions to add an edge in the tree depend on its…

We prove that any graph $G$ with $n$ points has a distribution $\mathcal{T}$ over spanning trees such that for any edge $(u,v)$ the expected stretch $E_{T \sim \mathcal{T}}[d_T(u,v)/d_G(u,v)]$ is bounded by $\tilde{O}(\log n)$. Our result…

Edge connectivity and vertex connectivity are two fundamental concepts in graph theory. Although by now there is a good understanding of the structure of graphs based on their edge connectivity, our knowledge in the case of vertex…

Geodesic distance, sometimes called shortest path length, has proven useful in a great variety of applications, such as information retrieval on networks including treelike networked models. Here, our goal is to analytically determine the…