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A planar graph and its minimum spanning tree. Each edge is labeled with its weight, which here is roughly proportional to its length. A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all the vertices together, without any cycles and with the minimum possible total edge weight. [1]
Growth charts have been constructed by observing the growth of large numbers of healthy children over time. The height, weight, and head circumference of a child can be compared to the expected parameters of children of the same age and sex to determine whether the child is growing appropriately. Growth charts can also be used to predict the ...
The 2000 CDC growth charts - a revised version of the 1977 NCHS growth charts - are the current standard tool for health care providers and offer 16 charts (8 for boys and 8 for girls), of which BMI-for-age is commonly used for aiding in the diagnoses of childhood obesity. [1]
In graph theory, Edmonds' algorithm or Chu–Liu/Edmonds' algorithm is an algorithm for finding a spanning arborescence of minimum weight (sometimes called an optimum branching). [1] It is the directed analog of the minimum spanning tree problem.
By doing this, doctors can track a child's growth over time and monitor how a child is growing in relation to other children. There are different charts for boys and girls because their growth rates and patterns differ. For both boys and girls there are two sets of charts: one for infants ages 0 to 36 months and another for ages 2 and above.
The diagnosis of FTT relies on plotting the child's height and weight on a validated growth chart, such as the World Health Organization (WHO) growth charts [62] for children younger than two years old or the U.S. Centers for Disease Control and Prevention (CDC) growth charts [63] for patients between the ages of two and twenty years old. [3]
Alternatively, if the edges of the graph have positive weights, the minimum weight cycle basis may be constructed in polynomial time. In planar graphs, the set of bounded cycles of an embedding of the graph forms a cycle basis. The minimum weight cycle basis of a planar graph corresponds to the Gomory–Hu tree of the dual graph.
These algorithms find the minimum spanning forest in a possibly disconnected graph; in contrast, the most basic form of Prim's algorithm only finds minimum spanning trees in connected graphs. However, running Prim's algorithm separately for each connected component of the graph, it can also be used to find the minimum spanning forest. [9]