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The most common formulation of a branching process is that of the Galton–Watson process.Let Z n denote the state in period n (often interpreted as the size of generation n), and let X n,i be a random variable denoting the number of direct successors of member i in period n, where X n,i are independent and identically distributed random variables over all n ∈{ 0, 1, 2, ...} and i ∈ {1 ...
In computer science, a binary decision diagram (BDD) or branching program is a data structure that is used to represent a Boolean function. On a more abstract level, BDDs can be considered as a compressed representation of sets or relations. Unlike other compressed representations, operations are performed directly on the compressed ...
The Galton–Watson process is a branching stochastic process arising from Francis Galton's statistical investigation of the extinction of family names. [ 1 ] [ 2 ] The process models family names as patrilineal (passed from father to son), while offspring are randomly either male or female, and names become extinct if the family name line dies ...
In probability theory, a branching random walk is a stochastic process that generalizes both the concept of a random walk and of a branching process. At every generation (a point of discrete time ), a branching random walk's value is a set of elements that are located in some linear space , such as the real line .
If this process is stopped at any fixed time, the result is a binary tree of a random size (depending on the stopping time), distributed according to the random permutation model for that size. Devroye and Robson use this model as part of an algorithm to quickly generate trees in the random permutation model, described by their numbers of nodes ...
Historically, branch prediction took statistics, and used the result to optimize code. A programmer would compile a test version of a program, and run it with test data. The test code counted how the branches were actually taken. The statistics from the test code were then used by the compiler to optimize the branches of released code.
Branch predictors play a critical role in achieving high performance in many modern pipelined microprocessor architectures. Figure 1: Example of 4-stage pipeline. The colored boxes represent instructions independent of each other. Two-way branching is usually implemented with a conditional jump instruction. A conditional jump can either be ...
The following is the skeleton of a generic branch and bound algorithm for minimizing an arbitrary objective function f. [3] To obtain an actual algorithm from this, one requires a bounding function bound, that computes lower bounds of f on nodes of the search tree, as well as a problem-specific branching rule.