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The sequential merge sort procedure can be described in two phases, the divide phase and the merge phase. The first consists of many recursive calls that repeatedly perform the same division process until the subsequences are trivially sorted (containing one or no element). An intuitive approach is the parallelization of those recursive calls. [19]
The difference in performance between the two situations may be enormous: for example, when n = 1,000,000, the minimum height is ⌊ (,,) ⌋ =. If the data items are known ahead of time, the height can be kept small, in the average sense, by adding values in a random order, resulting in a random binary search tree .
Fig. 1: A binary search tree of size 9 and depth 3, with 8 at the root. In computer science, a binary search tree (BST), also called an ordered or sorted binary tree, is a rooted binary tree data structure with the key of each internal node being greater than all the keys in the respective node's left subtree and less than the ones in its right subtree.
In this model, each process is modeled as a node of a graph. Each communication channel between two processes is an edge of the graph. Two commonly used algorithms for the classical minimum spanning tree problem are Prim's algorithm and Kruskal's algorithm. However, it is difficult to apply these two algorithms in the distributed message ...
In computer science, an optimal binary search tree (Optimal BST), sometimes called a weight-balanced binary tree, [1] is a binary search tree which provides the smallest possible search time (or expected search time) for a given sequence of accesses (or access probabilities). Optimal BSTs are generally divided into two types: static and dynamic.
A multiway merge allows for the files outside of memory to be merged in fewer passes than in a binary merge. If there are 6 runs that need be merged then a binary merge would need to take 3 merge passes, as opposed to a 6-way merge's single merge pass.
Join: The function Join is on two red–black trees t 1 and t 2 and a key k, where t 1 < k < t 2, i.e. all keys in t 1 are less than k, and all keys in t 2 are greater than k. It returns a tree containing all elements in t 1, t 2 also as k. If the two trees have the same black height, Join simply creates a new node with left subtree t 1, root k ...
A polyphase merge sort is a variation of a bottom-up merge sort that sorts a list using an initial uneven distribution of sub-lists (runs), primarily used for external sorting, and is more efficient than an ordinary merge sort when there are fewer than eight external working files (such as a tape drive or a file on a hard drive).