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Randomized Meldable Heap
In computer science, a randomized meldable heap (also Meldable Heap or Randomized Meldable Priority Queue) is a priority queue based data structure in which the underlying structure is also a heap-ordered binary tree. However, there are no restrictions on the shape of the underlying binary tree. This approach has a number of advantages over similar data structures. It offers greater simplicity: all operations for the randomized meldable heap are easy to implement and the constant factors in their complexity bounds are small. There is also no need to preserve balance conditions and no satellite information within the nodes is necessary. Lastly, this structure has good worst-case time efficiency. The execution time of each individual operation is at most logarithmic with high probability.A. Gambin and A. Malinowski. 1998. Randomized Meldable Priority Queues. In Proceedings of the 25th Conference on Current Trends in Theory and Practice of Informatics: Theory and Practice of Infor ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Heap (data Structure)
In computer science, a heap is a specialized tree-based data structure which is essentially an almost complete tree that satisfies the heap property: in a ''max heap'', for any given node C, if P is a parent node of C, then the ''key'' (the ''value'') of P is greater than or equal to the key of C. In a ''min heap'', the key of P is less than or equal to the key of C. The node at the "top" of the heap (with no parents) is called the ''root'' node. The heap is one maximally efficient implementation of an abstract data type called a priority queue, and in fact, priority queues are often referred to as "heaps", regardless of how they may be implemented. In a heap, the highest (or lowest) priority element is always stored at the root. However, a heap is not a sorted structure; it can be regarded as being partially ordered. A heap is a useful data structure when it is necessary to repeatedly remove the object with the highest (or lowest) priority, or when insertions need to be intersper ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Priority Queue
In computer science, a priority queue is an abstract data-type similar to a regular queue or stack data structure in which each element additionally has a ''priority'' associated with it. In a priority queue, an element with high priority is served before an element with low priority. In some implementations, if two elements have the same priority, they are served according to the order in which they were enqueued; in other implementations ordering of elements with the same priority remains undefined. While coders often implement priority queues with heaps, they are conceptually distinct from heaps. A priority queue is a concept like a list or a map; just as a list can be implemented with a linked list or with an array, a priority queue can be implemented with a heap or with a variety of other methods such as an unordered array. Operations A priority queue must at least support the following operations: * ''is_empty'': check whether the queue has no elements. * ''insert_ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Data Structure
In computer science, a data structure is a data organization, management, and storage format that is usually chosen for Efficiency, efficient Data access, access to data. More precisely, a data structure is a collection of data values, the relationships among them, and the functions or operations that can be applied to the data, i.e., it is an algebraic structure about data. Usage Data structures serve as the basis for abstract data types (ADT). The ADT defines the logical form of the data type. The data structure implements the physical form of the data type. Different types of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks. For example, Relational database, relational databases commonly use B-tree indexes for data retrieval, while compiler Implementation, implementations usually use hash tables to look up identifiers. Data structures provide a means to manage large amounts of data efficiently for uses such a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binary Tree
In computer science, a binary tree is a k-ary k = 2 tree data structure in which each node has at most two children, which are referred to as the ' and the '. A recursive definition using just set theory notions is that a (non-empty) binary tree is a tuple (''L'', ''S'', ''R''), where ''L'' and ''R'' are binary trees or the empty set and ''S'' is a singleton set containing the root. Some authors allow the binary tree to be the empty set as well. From a graph theory perspective, binary (and K-ary) trees as defined here are arborescences. A binary tree may thus be also called a bifurcating arborescence—a term which appears in some very old programming books, before the modern computer science terminology prevailed. It is also possible to interpret a binary tree as an undirected, rather than a directed graph, in which case a binary tree is an ordered, rooted tree. Some authors use rooted binary tree instead of ''binary tree'' to emphasize the fact that the tree is roo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pat Morin
Patrick Ryan Morin is a Canadian computer scientist specializing in computational geometry and data structures. He is a professor in the School of Computer Science at Carleton University. Education and career Morin was educated at Carleton University, earning a bachelor's degree with highest honours in 1996, a master's degree in 1998, and a Ph.D. in 2001. His dissertation, ''Online Routing in Geometric Graphs'', was jointly supervised by Jit Bose and Jörg-Rüdiger Sack. After postdoctoral research at McGill University, he returned to Carleton University as a faculty member in 2002. Contributions Morin has published highly-cited work on geographic routing in geometric graphs, including unit disk graphs and triangulations, with coauthors including Jit Bose, Erik Demaine, Stefan Langerman, and Jorge Urrutia. With Joachim Gudmundsson, he co-founded the '' Journal of Computational Geometry'', and continues as its managing editor. He is the author of an open textbook on data structur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leftist Heap
In computer science, a leftist tree or leftist heap is a priority queue implemented with a variant of a binary heap. Every node x has an ''s-value'' which is the distance to the nearest leaf in subtree rooted at x. In contrast to a ''binary heap'', a leftist tree attempts to be very unbalanced. In addition to the heap property, leftist trees are maintained so the right descendant of each node has the lower s-value. The height-biased leftist tree was invented by Clark Allan Crane. The name comes from the fact that the left subtree is usually taller than the right subtree. A leftist tree is a mergeable heap. When inserting a new node into a tree, a new one-node tree is created and merged into the existing tree. To delete an item, it is replaced by the merge of its left and right sub-trees. Both these operations take O(log ''n'') time. For insertions, this is slower than Fibonacci heap In computer science, a Fibonacci heap is a data structure for priority queue operations, consi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Binomial Heap
In computer science, a binomial heap is a data structure that acts as a priority queue but also allows pairs of heaps to be merged. It is important as an implementation of the mergeable heap abstract data type (also called meldable heap), which is a priority queue supporting merge operation. It is implemented as a heap similar to a binary heap but using a special tree structure that is different from the complete binary trees used by binary heaps. Binomial heaps were invented in 1978 by Jean Vuillemin. Binomial heap A binomial heap is implemented as a set of binomial trees (compare with a binary heap, which has a shape of a single binary tree), which are defined recursively as follows: * A binomial tree of order 0 is a single node * A binomial tree of order k has a root node whose children are roots of binomial trees of orders k-1, k-2, ..., 2, 1, 0 (in this order). A binomial tree of order k has 2^k nodes, and height k. The name comes from the shape: a binomial tree of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fibonacci Heap
In computer science, a Fibonacci heap is a data structure for priority queue operations, consisting of a collection of heap-ordered trees. It has a better amortized running time than many other priority queue data structures including the binary heap and binomial heap. Michael L. Fredman and Robert E. Tarjan developed Fibonacci heaps in 1984 and published them in a scientific journal in 1987. Fibonacci heaps are named after the Fibonacci numbers, which are used in their running time analysis. For the Fibonacci heap, the find-minimum operation takes constant ('' O''(1)) amortized time. The insert and decrease key operations also work in constant amortized time. Deleting an element (most often used in the special case of deleting the minimum element) works in ''O''(log ''n'') amortized time, where ''n'' is the size of the heap. This means that starting from an empty data structure, any sequence of ''a'' insert and decrease key operations and ''b'' delete operations would take ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pairing Heap
A pairing heap is a type of heap data structure with relatively simple implementation and excellent practical amortized performance, introduced by Michael Fredman, Robert Sedgewick, Daniel Sleator, and Robert Tarjan in 1986. Pairing heaps are heap-ordered multiway tree structures, and can be considered simplified Fibonacci heaps. They are considered a "robust choice" for implementing such algorithms as Prim's MST algorithm, and support the following operations (assuming a min-heap): * ''find-min'': simply return the top element of the heap. * ''meld'': compare the two root elements, the smaller remains the root of the result, the larger element and its subtree is appended as a child of this root. * ''insert'': create a new heap for the inserted element and ''meld'' into the original heap. * ''decrease-key'' (optional): remove the subtree rooted at the key to be decreased, replace the key with a smaller key, then ''meld'' the result back into the heap. * ''delete-min'': remove ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Skew Heap
A skew heap (or self-adjusting heap) is a heap data structure implemented as a binary tree. Skew heaps are advantageous because of their ability to merge more quickly than binary heaps. In contrast with binary heaps, there are no structural constraints, so there is no guarantee that the height of the tree is logarithmic. Only two conditions must be satisfied: * The general heap order must be enforced * Every operation (add, remove_min, merge) on two skew heaps must be done using a special ''skew heap merge''. A skew heap is a self-adjusting form of a leftist heap which attempts to maintain balance by unconditionally swapping all nodes in the merge path when merging two heaps. (The merge operation is also used when adding and removing values.) With no structural constraints, it may seem that a skew heap would be horribly inefficient. However, amortized complexity analysis can be used to demonstrate that all operations on a skew heap can be done in O(log ''n''). In fact, with \varphi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
