Eighty-four mature Norway spruce (Picea abies L. Karst), silver fir (Abies alba Mill) and Scots pine (Pinus sylvestris L.) trees were winched over to determine the maximum resistive turning moment (M(a)) of the root-soil system, the root-soil plate geometry, the azimuthal orientation of root growth, and the occurrence of root rot. The calculation of M(a), based on digital image tracking of stem...

Understanding tree growth as a function of tree size is important for a multitude of ecological and management applications. Determining what limits growth is of central interest, and forest inventory permanent plots are an abundant source of long-term information but are highly complex. Observation error and multiple sources of shared variation (spatial plot effects, temporal repeated measures...

Given a set P of points in the plane, a geometric minimum-diameter spanning tree (GMDST) of P is a spanning tree of P such that the longest path through the tree is minimized. In this paper, we present an approximation algorithm that generates a tree whose diameter is no more than (1+ ) times that of a GMDST, for any > 0. Our algorithm reduces the problem to several grid-aligned versions of the...

Let P be a set of n points in the plane. The geometric minimum-diameter spanning tree (MDST) of P is a tree that spans P and minimizes the Euclidian length of the longest path. It is known that there is always a monoor a dipolar MDST, i.e. a MDST whose longest path consists of two or three edges, respectively. The more difficult dipolar case can so far only be solved in O(n) time. This paper ha...

Most cut-to-length (CTL) harvesters provide sensors for measuring dtameter of trees as they are cut and processed. Among other uses, this capability provides a data collection tool for marketing of logs in real time. Logs can be sorted and stacked based on up-to-date market information, then transportation systems optimized to route wood to proper destinations at lowest cost. This capability do...

We point out a relation between the minimum diameter spanning tree of a graph and its absolute 1-center. We use this relation to solve the diameter problem and an extension of it eeciently.

This paper deals with the length of a Robertson–Seymour’s tree-decomposition. The tree-length of a graph is the largest distance between two vertices of a bag of a tree-decomposition, minimized over all tree-decompositions of the graph. The study of this invariant may be interesting in its own right because the class of bounded tree-length graphs includes (but is not reduced to) bounded chordal...

Given a set P of n points in a plane, the Geometric Minimum Diameter Spanning Tree (GMDST) of P is a tree that spans P and minimizes the Euclidian length of the longest path. The best known algorithm for this problem runs in slightly sub-cubic time. In this report, I have surveyed some algorithms and approximation schemes developed for this problem and investigated the relation between this pro...