The quadratic minimum spanning tree problem is to find a spanning tree on a graph that minimizes a quadratic objective function of the edge weights. In this paper, the quadratic minimum spanning tree problem is concerned on the graph with edge weights being assumed as uncertain variables. The notion of the uncertain quadratic -minimum spanning tree is introduced by using the uncertain chance co...

An inverse minimum spanning tree problem is to make the least modification on the edge weights such that a predetermined spanning tree is a minimum spanning tree with respect to the new edge weights. In this paper, the stochastic inverse minimum spanning tree problem is investigated. The concept of α-minimum spanning tree is initiated, and subsequently an α-minimum spanning tree model and a pro...

Given a 2-node connected, undirected graph G = (V,E), with n nodes and m edges with real weights, and given a minimum spanning tree (MST) T = (V, ET ) of G, we study the problem of finding, for every node v ∈ V , the MST of G− v = (V \ {v}, E \ Ev), where Ev is the set of edges incident to v in G. We show that this problem can be solved in O(min(m ·α(n, n),m+ n log n)) time and O(m) space. Our ...

An inverse minimum spanning tree problem is to make the least modification on the edge weights such that a predetermined spanning tree is a minimum spanning tree with respect to the new edge weights. In this paper, the inverse minimum spanning tree problem with stochastic edge weights is investigated. The concept of α-minimum spanning tree is initiated, and subsequently an α-minimum spanning tr...

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...

This paper considers the minimum spanning tree problem with uncertain random weights in an uncertain random network. The concept of uncertain random minimum spanning tree is initiated for minimum spanning tree problem with uncertain random edge weights. A model is presented to formulate a specific minimum spanning tree problem with uncertain random edge weights involving a distance chance distr...

Minimum spanning tree is a minimum-cost spanning tree connecting the whole network, but it couldn't be directly obtained on uncertain graph. In this paper, we define the reliability as the existence probability of all minimum spanning trees and present an algorithm for evaluating reliability of the minimum spanning tree on uncertain graph. The time complexity of the algorithm is O(Nmn), where n...