This paper deals with the recoverable robust spanning tree problem under interval uncertainty representations. A strongly polynomial time, combinatorial algorithm for the recoverable spanning tree problem is first constructed. This problem generalizes the incremental spanning tree problem, previously discussed in literature. The algorithm built is then applied to solve the recoverable robust sp...

The inverse spanning tree problem is to make a given spanning tree be a minimum spanning tree on a connected graph via a minimum perturbation on its edge weights. In this paper, a chance-constrained programming model is proposed to handle the inverse spanning tree problem where the edge weights are assumed to be uncertain variables. It is shown that such an uncertain minimum spanning tree can b...

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...

The minimum vertex ranking spanning tree problem is to find a spanning tree of G whose vertex ranking is minimum. This problem is NP-hard and no polynomial time algorithm for solving it is known for non-trivial classes of graphs other than the class of interval graphs. This paper proposes a polynomial time algorithm for solving the minimum vertex ranking spanning tree problem on outerplanar gra...

We present a distributed protocol for maintaining a maximum flow spanning tree in a network, with a designated node as the root of the tree. This maximum flow spanning tree can be used to route the allocation of new virtual circuits whose destination is the designated node. As virtual circuits are allocated and removed, the available capacity of the channels in the network changes, causing the ...

The paper aims at segmenting an image. The goal of image segmentation is to simplify and/or change the representation of an image into something that is more meaningful and simpler to analyze. In this paper we consider segmenting the image using the shortest spanning tree. To find the shortest spanning tree the image is first mapped into a graph. There have already been research conducted in th...

A formulation of a graph problem for scheduling parallel computations of multibody dynamic analysis is presented. The complexity of scheduling parallel computations for a multibody dynamic analysis is studied. The problem of finding a shortest critical branch spanning tree is described and transformed to a minimum radius spanning tree, which is solved by an algorithm of polynomial complexity. T...

Classic inverse minimum spanning tree problem is to make the least edge weight modification such that a predetermined spanning tree is a minimum spanning tree with respect to the new edge weights. Although many applications can be formulated into this problem, fuzzy parameters are met in some real-world applications. In this paper, a type of inverse minimum spanning tree problem with fuzzy edge...

A spanning tree of an unweighted graph is a minimum average stretch spanning tree if it minimizes the ratio of sum of the distances in the tree between the end vertices of the graph edges and the number of graph edges. We consider the problem of computing a minimum average stretch spanning tree in polygonal 2-trees, a super class of 2-connected outerplanar graphs. For a polygonal 2-tree on n ve...