Tree Accumulation

	Tree Accumulation In computer science, tree accumulation is the process of accumulating data placed in tree nodes according to their tree structure. Formally, this operation is a catamorphism. Upward accumulation refers to accumulating on each node information about all descendants. Downward accumulation refers to accumulating on each node information of every ancestor. One application would be calculating national election results. Construct a tree with the root node as the entire nation and each level representing refined geographical areas such as states/provinces, counties/parishes, cities/townships, and polling districts as the leaves. By accumulating the vote totals from the polling districts, one can compute the vote totals for each of the larger geographic areas. Formal analysis Gibbons et al. formally define binary tree accumulation as iterative application of a ternary operator \otimes(A,B,A); where A are descendant labels and B is a junction label. References {{Reflist Trees (data ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Computer Science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (including the design and implementation of hardware and software). Computer science is generally considered an area of academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing security vulnerabilities. Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of repositories ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Tree (data Structure) In computer science, a tree is a widely used abstract data type that represents a hierarchical tree structure with a set of connected nodes. Each node in the tree can be connected to many children (depending on the type of tree), but must be connected to exactly one parent, except for the ''root'' node, which has no parent. These constraints mean there are no cycles or "loops" (no node can be its own ancestor), and also that each child can be treated like the root node of its own subtree, making recursion a useful technique for tree traversal. In contrast to linear data structures, many trees cannot be represented by relationships between neighboring nodes in a single straight line. Binary trees are a commonly used type, which constrain the number of children for each parent to exactly two. When the order of the children is specified, this data structure corresponds to an ordered tree in graph theory. A value or pointer to other data may be associated with every node in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Catamorphism In category theory, the concept of catamorphism (from the Ancient Greek: "downwards" and "form, shape") denotes the unique homomorphism from an initial algebra into some other algebra. In functional programming, catamorphisms provide generalizations of ''folds'' of lists to arbitrary algebraic data types, which can be described as initial algebras. The dual concept is that of anamorphism that generalize ''unfolds''. A hylomorphism is the composition of an anamorphism followed by a catamorphism. Definition Consider an initial F-algebra (A, in) for some endofunctor F of some category into itself. Here in is a morphism from FA to A. Since it is initial, we know that whenever (X, f) is another F-algebra, i.e. a morphism f from FX to X, there is a unique homomorphism h from (A, in) to (X, f). By the definition of the category of F-algebra, this h corresponds to a morphism from A to X, conventionally also denoted h, such that h \circ in = f \circ Fh. In the context of F-algebra, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]