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...

Given a complete graph on n nodes with metric edge costs, the minimum-cost khop spanning tree (kHMST) problem asks for a spanning tree of minimum total cost such that the longest root-leaf-path in the tree has at most k edges. We present an algorithm that computes such a tree of total expected cost O(log n) times that of a minimum-cost k-hop spanning-tree.

The concept of the minimum spanning tree (MST) plays an important role in topological network design, because it models a cheapest connected network. In a tree, however, the failure of a vertex can disconnect the network. In order to tolerate such a failure, we generalize the MST to the concept of a cheapest biconnected network. For a set of points in the Euclidean plane, we show that it is NP-...

We are given a set P of points in the plane, together with a partition of P into classes of points; i.e., each point of P belongs to exactly one class. For a given network optimization problem, such as nding a minimum spanning tree or nding a minimum diameter spanning tree, we study the problem of choosing a subset P 0 of P that contains at least one point of each class and solving the network ...

A linear-time algorithm for the minimum-ratio spanning tree problem on planar graphs is presented. The algorithm is based on a new planar minimum spanning tree algorithm. The approach extends to other parametric minimum spanning tree problems on planar graphs and to other families of graphs having small separators.

We consider the minimum-weight path between any pair of nodes of the n-vertex complete graph in which the weights of the edges are i.i.d. exponentially distributed random variables. We show that the longest of these minimum-weight paths has about α logn edges where α ≈ 3.5911 is the unique solution of the equation α logα − α = 1. This answers a question left open by Janson [8].

We prove an O(nk 1=3) upper bound for planar k-sets. This is the rst considerable improvement on this bound after its early solutions approximately twenty seven years ago. Our proof technique also applies to improve the current bounds on the combinatorial complexities of k-levels in arrangements of line segments, k convex polygons in the union of n lines, parametric minimum spanning trees and p...

We prove an O(n(k + 1)1/3) upper bound for planar k-sets. This is the first considerable improvement on this bound after its early solution approximately 27 years ago. Our proof technique also applies to improve the current bounds on the combinatorial complexities of k-levels in the arrangement of line segments, k convex polygons in the union of n lines, parametric minimum spanning trees, and p...

An inverse spanning tree problem is to make the least modification on the edge weights such that a predetermined spanning tree is a minimum spanning tree. In this paper, based on the notion of fuzzy α-minimum spanning tree, the inverse spanning tree problem with fuzzy edge weights is discussed and formulated as a fuzzy programming model with some chance constraints. It shows that when all the e...