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A graph exemplifying merge sort. Two red arrows starting from the same node indicate a split, while two green arrows ending at the same node correspond to an execution of the merge algorithm. The merge algorithm plays a critical role in the merge sort algorithm, a comparison-based sorting algorithm. Conceptually, the merge sort algorithm ...
Join follows the right spine of t 1 until a node c which is balanced with t 2. At this point a new node with left child c, root k and right child t 2 is created to replace c. The new node may invalidate the balancing invariant. This can be fixed with rotations. The following is the join algorithms on different balancing schemes. The join ...
The classic merge outputs the data item with the lowest key at each step; given some sorted lists, it produces a sorted list containing all the elements in any of the input lists, and it does so in time proportional to the sum of the lengths of the input lists. Denote by A[1..p] and B[1..q] two arrays sorted in increasing order.
The sort-merge join (also known as merge join) is a join algorithm and is used in the implementation of a relational database management system. The basic problem of a join algorithm is to find, for each distinct value of the join attribute, the set of tuples in each relation which display that value. The key idea of the sort-merge algorithm is ...
A cut or split is trivial when one of its two sides has only one vertex in it; every trivial cut is a split. A graph is said to be prime (with respect to splits) if it has no nontrivial splits. [2] Two splits are said to cross if each side of one split has a non-empty intersection with each side of the other split.
A circular list can be split into two circular lists, in constant time, by giving the addresses of the last node of each piece. The operation consists in swapping the contents of the link fields of those two nodes. Applying the same operation to any two nodes in two distinct lists joins the two list into one.
Implementations of the fork–join model will typically fork tasks, fibers or lightweight threads, not operating-system-level "heavyweight" threads or processes, and use a thread pool to execute these tasks: the fork primitive allows the programmer to specify potential parallelism, which the implementation then maps onto actual parallel execution. [1]
If the running time (number of comparisons) of merge sort for a list of length n is T(n), then the recurrence relation T(n) = 2T(n/2) + n follows from the definition of the algorithm (apply the algorithm to two lists of half the size of the original list, and add the n steps taken to merge the resulting two lists). [5]