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Depending on the application on hand, one can prefer better approximation ratio, or better dependence in the running time from the size of the input or the treewidth. The table below provides an overview of some of the treewidth algorithms. Here k is the treewidth and n is the number of vertices of an input graph G.
On sloping ground, the "above ground" reference point is usually taken as the highest point on the ground touching the trunk, but some use the average between the highest and lowest points of ground. If the DBH point falls on a swelling in the trunk it is customary to measure the girth below the swelling at the point where the diameter is smallest.
Equations used to describe plant size over time are then often expolinear [15] or sigmoidal. [16] [17] Agronomic studies often focus on the above-ground part of plant biomass, and consider crop growth rates rather than individual plant growth rates. Nonetheless there is a strong corollary between the two approaches.
Single trunk trees can also pose measurement problems. Consider trees with very large girths, such as some of the sequoias growing the western United States. If they are growing on even a gentle slope, if girth is measured at 4.5 feet above where the pith of the tree emerges from the ground, the upside of the tape could easily be below ground ...
The girth measurement should then be taken at the narrowest point below the odd growth and the height of the girth measurement noted. In some cases a girth taken just above the odd growth will be more representative of the actual girth of the tree. In these cases the measurement should be taken there and the height above the base of the tree noted.
Note that this more general concept of boundedness does not correspond to a notion of "size". A subset S of a partially ordered set P is called bounded above if there is an element k in P such that k ≥ s for all s in S. The element k is called an upper bound of S. The concepts of bounded below and lower bound are defined similarly.
Diameter at breast height (DBH) – measurement of a tree's girth standardized with different countries having different standards they are often at 1.3 meters (about 4.5 feet) above the ground Form factor – the shape of the tree, based on recorded trees and commonly then given for calculating tree volumes for a given species.
A set with an upper (respectively, lower) bound is said to be bounded from above or majorized [1] (respectively bounded from below or minorized) by that bound. The terms bounded above ( bounded below ) are also used in the mathematical literature for sets that have upper (respectively lower) bounds.