A fundamental problem in wireless networks is the minimum spanning tree (MST) problem: given a set V of wireless nodes, compute a spanning tree T , so that the total cost of T is minimized. In recent years, there has been a lot of interest in the physical interference model based on SINR constraints. Distributed algorithms are especially challenging in the SINR model, because of the non-localit...

The robust spanning tree problem is a variation, motivated by telecommunications applications, of the classic minimum spanning tree problem. In the robust spanning tree problem edge costs lie in an interval instead of having a fixed value. Interval numbers model uncertainty about the exact cost values. A robust spanning tree is a spanning tree whose total cost minimizes the maximum deviation fr...

A directed spanning tree in a directed graph G = (V,A) is a spanning tree such that no two arcs share their tails. In this paper, we propose an algorithm for listing all directed spanning trees of G. Its time and space complexities are O(|A| + ND(|V |, |A|)) and O(|A|+DS(|V |, |A|)), where D(|V |, |A|) and DS(|V |, |A|) are the time and space complexities of the data structure for updating the ...

We present a deterministic linear time algorithm for the Tree Path Maxima problem. As a corollary, we obtain a deterministic linear time algorithm for checking whether a given spanning tree T of a weighted graph is a minimum spanning tree.

In this paper, the minimum spanning tree problem is investigated on the graph with fuzzy edge weights. The notion of fuzzy α-minimum spanning tree is presented based on the credibility measure, and then the solutions of the fuzzy α-minimum spanning tree problem are discussed under different assumptions. First, we respectively assume that all the edge weights are triangular fuzzy numbers and tra...

In a connected graph, spanning tree centralities of a vertex and an edge measure how crucial they are for the graph to be connected. In this paper, we propose efficient algorithms for estimating spanning tree centralities with theoretical guarantees on their accuracy. We experimentally demonstrate that our methods are orders of magnitude faster than previous methods. Then, we propose a novel ce...

A spanning tree of an infinite graph is normal if the endvertices of any chord are comparable in the tree order defined by some arbitrarily chosen root. (In finite graphs, these are their ‘depth-first search’ trees; see [3] for precise definitions.) Normal spanning trees are perhaps the most important single structural tool for analysing an infinite graph (see [4] for a good example), but they ...

The Minimal Spanning Tree (MST) problem is a classical graph problem which has many applications in various areas. In this paper we discuss a concurrent MST algorithm derived from Prim’s algorithm presented by Setia et al. in 2009, targeting symmetric multiprocessing (SMP) with a shared address space. The pseudocode of the algorithm is presented, combined with three interesting heuristics in or...

We consider a model of communication in a network, where multiple sources have messages to disseminate among the network membership. We propose that all the messages (one from each source) be disseminated along the same spanning tree of the network and consider the problem of constructing such a tree. One evaluative measure for suitability of the construction is the sum of distances from each s...

Attribute clustering has been previously employed to detect statistical dependence between subsets of variables. We propose a novel attribute clustering algorithm motivated by research of complex networks, called the Star Discovery algorithm. The algorithm partitions and indirectly discards inconsistent edges from a maximum spanning tree by starting appropriate initial modes, therefore generati...