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Computer science concept
computer science, an optimal binary search tree (Optimal BST), sometimes called a weight-balanced binary tree, is a binary search tree which provides the
Optimal_binary_search_tree
Rooted binary tree data structure
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
Binary_search_tree
Any node-based binary search tree that automatically keeps its height the same
In computer science, a self-balancing binary search tree (BST) is any node-based binary search tree that automatically keeps its height (maximal number
Self-balancing binary search tree
Self-balancing_binary_search_tree
Self-adjusting binary search tree
splay tree is a binary search tree with the additional property that recently accessed elements are quick to access again. Like self-balancing binary search
Splay_tree
Limited form of tree data structure
Huffman tree K-ary tree Kraft's inequality Merkle tree Optimal binary search tree Random binary tree Recursion (computer science) Red–black tree Rope (computer
Binary_tree
Search algorithm finding the position of a target value within a sorted array
In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position
Binary_search
Type of binary search tree
online binary search tree that achieves an O ( log log n ) {\displaystyle O(\log \log n)} competitive ratio relative to the offline optimal binary search
Tango_tree
Sorting algorithm
Mehlhorn's algorithm for computing nearly optimal binary search trees with low overhead, thereby achieving optimal adaptivity up to an additive linear term
Powersort
computer science, one approach to the dynamic optimality problem on online algorithms for binary search trees involves reformulating the problem geometrically
Geometry of binary search trees
Geometry_of_binary_search_trees
algorithm is an efficient method for computers to construct optimal binary search trees and alphabetic Huffman codes, in linearithmic time. It is named
Garsia–Wachs_algorithm
Binary search variation with simplified midpoint calculation
multiplicative binary search makes it suitable for out-of-core search on block-oriented storage as an alternative to B-trees and B+ trees. For optimal performance
Multiplicative_binary_search
Self-balancing binary search tree data structure
tree is a self-balancing binary search tree data structure noted for fast storage and retrieval of ordered information. The nodes in a red-black tree
Red–black_tree
Algorithm to search the nodes of a graph
Breadth-first search (BFS) is an algorithm for searching a tree data structure for a node that satisfies a given property. It starts at the tree root and explores
Breadth-first_search
Type of sorting algorithm
A tree sort is a sort algorithm that builds a binary search tree from the elements to be sorted, and then traverses the tree (in-order) so that the elements
Tree_sort
Multidimensional search tree for points in k dimensional space
neighbor searches) & Creating point clouds. k-d trees are a special case of binary space partitioning trees. The k-d tree is a binary tree in which every
K-d_tree
Algorithm used for pathfinding and graph traversal
used in many fields of computer science due to its completeness, optimality, and optimal efficiency. Given a weighted graph, a source node and a goal node
A*_search_algorithm
and their processing power. Tree (data structure) Search tree Binary search tree Tree traversal Monte Carlo tree search Parallel computing Colbrook A
Distributed_tree_search
Tree data structure to hold intervals
nodes of the binary search tree, but since binary heap query is optimum, this is acceptable (a 2- dimensional problem can not be optimum in both dimensions)
Interval_tree
Computer science data structure
sequence for an in-order traversal (as there would be in, e.g., a binary search tree). The heap relation mentioned above applies only between nodes and
Heap_(data_structure)
Binary tree derived from a sequence of numbers
used in the definition of the treap and randomized binary search tree data structures for binary search problems, in comparison sort algorithms that perform
Cartesian_tree
Search algorithm
pruning is a search algorithm that seeks to decrease the number of nodes that are evaluated by the minimax algorithm in its search tree. It is an adversarial
Alpha–beta_pruning
Branching diagram of evolutionary relationships between organisms
finding optimal phylogenetic tree in the phylogenetic landscape. Phylogenetic trees may be rooted or unrooted. In a rooted phylogenetic tree, each node
Phylogenetic_tree
Any algorithm which solves the search problem
only in a probabilistic sense, many of these tree-search methods are guaranteed to find the exact or optimal solution, if given enough time. This is called
Search_algorithm
Algorithm for finding shortest paths
graph in the form of adjacency lists and using a self-balancing binary search tree, binary heap, pairing heap, Fibonacci heap or a priority heap as a priority
Dijkstra's_algorithm
Technique to compress data
comparisons in the same total time bound. These optimal alphabetic binary trees are often used as binary search trees. If weights corresponding to the alphabetically
Huffman_coding
Method for recursively subdividing a space into two subsets using hyperplanes
also developed an optimal rate-distortion (RD) image compression framework and image manipulation approaches using BSP trees. Binary space partitioning
Binary_space_partitioning
Mathematician
conjecture. He is also the namesake of the Garsia–Wachs algorithm for optimal binary search trees, which he published with his student Michelle L. Wachs in 1977
Adriano_Garsia
Method for efficiently balancing binary search trees
binary search trees – that is, decreasing their height to O(log n) nodes, where n is the total number of nodes. Unlike a self-balancing binary search
Day–Stout–Warren_algorithm
Search algorithm
random tree (RRT) is an algorithm designed to efficiently search nonconvex, high-dimensional spaces by randomly building a space-filling tree. The tree is
Rapidly_exploring_random_tree
Self-balancing binary search tree data structure
red–black (LLRB) tree is a type of self-balancing binary search tree, introduced by Robert Sedgewick. It is a variant of the red–black tree and guarantees
Left-leaning_red–black_tree
In computer science, join-based tree algorithms are a class of algorithms for self-balancing binary search trees. This framework aims at designing highly-parallelized
Join-based_tree_algorithms
Tree in which each node has at most three children
4,5]. Optimal radix choice: Hayes suggests a ternary tree system is the optimal branching factor for a telephone menu system Binary tree Tree structure
Ternary_tree
Least-weight tree connecting graph vertices
decision trees. The runtime of this step is unknown, but it has been proved that it is optimal - no algorithm can do better than the optimal decision tree. Thus
Minimum_spanning_tree
Machine learning algorithm
1016/S0304-3975(01)00011-1. Hyafil, Laurent; Rivest, RL (1976). "Constructing Optimal Binary Decision Trees is NP-complete". Information Processing Letters. 5 (1): 15–17
Decision_tree_learning
Optimization problem in computer science
analysis for region and partial region searches in multidimensional binary search trees and balanced quad trees". Acta Informatica. 9 (1): 23–29. doi:10
Nearest_neighbor_search
Data structure holding key/value pairs
hash tables and search trees. It is sometimes also possible to solve the problem using directly addressed arrays, binary search trees, or other more specialized
Associative_array
Taiwanese-American computer scientist
for scheduling tree-structured tasks,[H61a] the widest path problem,[H61b] optimal binary search trees,[HT71] linear layouts of trees and graphs,[AH73]
T._C._Hu
Computer science data structure
a set I of intervals, or segments, a segment tree T for I is structured as follows: T is a binary tree. Its leaves correspond to the elementary intervals
Segment_tree
Overview of and topical guide to algorithms
Circular buffer Tree (data structure) Binary tree Binary search tree AVL tree Red–black tree B-tree B+ tree Trie Segment tree Fenwick tree Heap (data structure)
Outline_of_algorithms
Variant of heap data structure
binary heap is a heap data structure that takes the form of a binary tree. Binary heaps are a common way of implementing priority queues. The binary heap
Binary_heap
Self-balancing binary search tree
In computer science, weight-balanced binary trees (WBTs) are a type of self-balancing binary search trees that can be used to implement dynamic sets, dictionaries
Weight-balanced_tree
Family of cache algorithms
The algorithm works as follows: consider a binary search tree for the items in question. Each node of the tree has a one-bit flag denoting "go left to insert
Pseudo-LRU
Algorithm for searching sorted, infinite lists
lists, such as binary search, when the element being searched for is near the beginning of the array. This is because exponential search will run in O
Exponential_search
O(m+z)} time, which is asymptotically optimal (assuming the size of the alphabet is constant). When constructing such a tree, each string should be padded with
Generalized_suffix_tree
Algorithm to search the nodes of a graph
Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures. The algorithm starts at the root node (selecting some
Depth-first_search
Set of basic shapes which assemble into a polygon
Christos; Lingas, Andrzej; Sack, Jörg-R. (1989). "Heuristics for optimum binary search trees and minimum weight triangulation problems". Theoretical Computer
Polygon_partition
entropy coding that is optimal for alphabets following geometric distributions Rice coding: form of entropy coding that is optimal for alphabets following
List_of_algorithms
Abstract data type in computer science
self-balancing binary search tree is used, insertion and removal also take O ( log n ) {\displaystyle O(\log n)} time, although building trees from existing
Priority_queue
space and performs searches in O(logw n) time, which is asymptotically faster than a traditional self-balancing binary search tree, and also better than
Fusion_tree
Canadian computer scientist
fundamental contributions to algorithms and data structures (including optimal binary search trees, priority queues, hashing, and space-efficient data structures)
Ian Munro (computer scientist)
Ian_Munro_(computer_scientist)
American mathematician
Adriano Garsia are the namesakes of the Garsia–Wachs algorithm for optimal binary search trees, which they published in 1977.[A] She is also known for her research
Michelle_L._Wachs
Algorithmic optimization method
actually equal to the optimal solution value. When this happens, the decision algorithm can detect the equality and save the optimal solution value for later
Parametric_search
theory of optimal binary search trees, the interleave lower bound is a lower bound on the number of operations required by a Binary Search Tree (BST) to
Interleave_lower_bound
Graphics structure
holds for a high-degree tree: although the tree will be of smaller height, more work is spent at each node. In practice, binary trees (degree = 2) are by
Bounding_volume_hierarchy
Data structure
A top tree is a data structure based on a binary tree for unrooted dynamic trees that is used mainly for various path-related operations. It allows simple
Top_tree
Number of digits needed to express a number in a particular base
In mathematics and computer science, optimal radix choice is the problem of choosing the base, or radix, that is best suited for representing numbers
Optimal_radix_choice
Mathematical optimization problem restricted to integers
estimate of how far from optimality the returned solution is. Finally, branch and bound methods can be used to return multiple optimal solutions. Suppose A
Integer_programming
Probabilistic data structure
implement than the deterministic balancing schemes used in balanced binary search trees. Skip lists are also useful in parallel computing, where insertions
Skip_list
Computer science algorithm
network; serialization/deserialization of a binary tree vs serialization in sorted order (allows the tree to be re-constructed in an efficient manner);
Graph_traversal
Maximal biconnected subgraph
to run a depth-first search while maintaining the following information: the depth of each vertex in the depth-first-search tree (once it gets visited)
Biconnected_component
Decision tree algorithm
iteration. The algorithm's optimality can be improved by using backtracking during the search for the optimal decision tree at the cost of possibly taking
ID3_algorithm
Numerical invariant of graphs
binary search strategy, which guarantees that at most ⌈ log 2 ( n + 1 ) ⌉ {\displaystyle \lceil \log _{2}(n+1)\rceil } pebbles are needed. The tree-depth
Tree-depth
Use of multiple antennas in radio
introduced: The modified best-first (MBF) tree search transforms the M-ary search tree into a binary tree using a first-child/next-sibling structure
MIMO
Auxiliary data structure to the suffix array in computer science
during binary search. So there are exactly N distinct ranges ( L … M … R ) {\displaystyle (L\dots M\dots R)} that can possibly play a role during binary search
LCP_array
Data structure for priority queues
and using only type A skew links results in a perfectly balanced binary tree. Search the list of roots to find the node containing the minimum key. This
Skew_binomial_heap
Key-independent optimality is a property of some binary search tree data structures in computer science proposed by John Iacono. Suppose that key-value
Key-independent_optimality
Sweep line algorithm
recently processed event. The binary search tree may be any balanced binary search tree data structure, such as a red–black tree; all that is required is that
Bentley–Ottmann_algorithm
Technique in parallel algorithms
ISBN 0-262-03293-7 . Section 10.4: Representing rooted trees, pp. 214–217. Chapters 12–14 (Binary Search Trees, Red-Black Trees, Augmenting Data Structures), pp. 253–320
Tree_contraction
Query of largest element in a set less than an element
structures used to solve the problem include balanced binary search trees, van Emde Boas trees, and fusion trees. In the static predecessor problem, the set of
Predecessor_problem
Measure of similarity between two graphs
computation of the optimal edit path is cast as a pathfinding search or shortest path problem, often implemented as an A* search algorithm. In addition
Graph_edit_distance
can achieve O(log d) expected search time. A treap is a randomized binary search tree (BST). Searching in a treap is the same as searching for an element
Finger_search
Tree data structure
asymptotically faster than a B-tree. Like a B-tree, a fractal tree index is a generalization of a binary search tree in that a node can have more than
Fractal_tree_index
Searching algorithm
between key values are sensible. By comparison, binary search always chooses the middle of the remaining search space, discarding one half or the other, depending
Interpolation_search
viewing the variables as vertices and the (binary) constraints as edges, the resulting graph is required to be a tree or a forest. In order for the new problem
Decomposition method (constraint satisfaction)
Decomposition_method_(constraint_satisfaction)
Process in machine learning and statistics
Y.; Wang, S.; Phillips, P. (2014). "Binary PSO with Mutation Operator for Feature Selection using Decision Tree applied to Spam Detection". Knowledge-Based
Feature_selection
Sequence of operations for a task
programming When a problem shows optimal substructures—meaning the optimal solution can be constructed from optimal solutions to subproblems—and overlapping
Algorithm
Directed graph with no directed cycles
with one fewer element; the tree formed in this way for a set of strings is called a trie. Similarly, a binary search tree can be viewed as a rooted DAG
Directed_acyclic_graph
Application of computational algorithms, methods and programs to phylogenetic analyses
of searching for the optimal phylogenetic tree is known as phylogeny search space. Maximum Likelihood (also likelihood) optimality criterion is the process
Computational_phylogenetics
Data structure for approximate set membership
other data structures for representing sets, such as self-balancing binary search trees, tries, hash tables, or simple arrays or linked lists of the entries
Bloom_filter
Equivalence of average-case and expected complexity
principle, proved it in this way. The optimal mixed strategy for Alice (a randomized algorithm) and the optimal mixed strategy for Bob (a hard input distribution)
Yao's_principle
Permutation that reverses binary numbers
{\displaystyle 0} and n − 1 {\displaystyle n-1} , inclusive, in any binary search tree holding those values, is Ω ( n log n ) {\displaystyle \Omega (n\log
Bit-reversal_permutation
Optimization algorithm
programming and binary search. To attempt to avoid getting stuck in local optima, one could use restarts (i.e. repeated local search), or more complex
Hill_climbing
Optimality criterion in phylogeny
changes) is constructed. Under the maximum-parsimony criterion, the optimal tree will minimize the amount of homoplasy (i.e., convergent evolution, parallel
Maximum_parsimony
Methodological basis for 3D CAD/CAM solid modeling and image rendering
composition tree, the exhaustive search for a ray-solid intersection resembles an efficient binary search. The brute force algorithm does an exhaustive search because
Ray_casting
Optimization problem
Optimal job scheduling is a class of optimization problems related to scheduling. The inputs to such problems are a list of jobs (also called processes
Optimal_job_scheduling
worst case. This shows that a sorted table together with binary search for queries is an optimal scheme, in this restricted setting. It is worth noting
Cell-probe_model
Description of limiting behavior in probabilistic algorithms
deterministic algorithms WHP. Treap: a randomized binary search tree. Its height is logarithmic WHP. Fusion tree is a related data structure. Online codes: randomized
With_high_probability
Overview of and topical guide to machine learning
cortex basal ganglia working memory PVLV Q-learning Quadratic unconstrained binary optimization Query-level feature Quickprop Radial basis function network
Outline_of_machine_learning
Data structure and types for evolutionary computation
represent all the individuals of a population using binary encoding, permutational encoding, encoding by tree, or any one of several other representations.
Genetic_representation
Type of computer memory
longest prefix match searches as required in internet routing tables. Binary CAM is the simplest type of CAM and uses data search words consisting entirely
Content-addressable_memory
Data structure for a string
'72. pp. 125–136. doi:10.1145/800152.804905. Farach, M. (1997). Optimal suffix tree construction with large alphabets. Proceedings 38th Annual Symposium
Suffix_array
Categorization of data using statistics
can be thought of as two separate problems – binary classification and multiclass classification. In binary classification, a better understood task, only
Statistical_classification
Method for speeding related binary searches
to speed up a sequence of binary searches for the same value in a sequence of related data structures. The first binary search in the sequence takes a logarithmic
Fractional_cascading
Hybrid sorting algorithm based on insertion sort and merge sort
overhead and smaller space overhead than N. First, Timsort performs a binary search to find the location where the first element of the second run would
Timsort
Data structure which is efficient to both store in memory and query
representation techniques, including binary trees, k {\displaystyle k} -ary trees and multisets, as well as suffix trees and arrays. The basic problem is
Succinct_data_structure
NP-complete problem in computer science
Algorithm (CGA) considers all partitions by constructing a binary tree. Each level in the tree corresponds to an input number, where the root corresponds
Partition_problem
Competitive algorithm for searching a problem space
range of possible solutions (the search space). Occasionally, the solutions may be "seeded" in areas where optimal solutions are likely to be found or
Genetic_algorithm
Subset of a graph's vertices, including at least one endpoint of every edge
cover – including an optimal vertex cover – must contain u or v (or both); otherwise the edge e is not covered. That is, an optimal cover contains at least
Vertex_cover
Comparison-based sorting algorithm
Heapsort maps the binary tree to the array using a top-down breadth-first traversal of the tree; the array begins with the root of the tree, then its two
Smoothsort
Problem in combinatorial optimization
algorithm is optimal for 2D knapsack (packing squares into a two-dimensional unit size square): when there are at most five squares in an optimal packing.
Knapsack_problem
OPTIMAL BINARY-SEARCH-TREE
OPTIMAL BINARY-SEARCH-TREE
Surname or Lastname
English
English : unexplained. Compare Scarce.
Surname or Lastname
English (chiefly South Yorkshire)
English (chiefly South Yorkshire) : topographic name for someone who lived on land enclosed by a bend in a river, from Old English binnan ēa ‘within the river’, or a habitational name from places in Kent called Binney and Binny, which have this origin.Scottish : habitational name from Binney or Binniehill near Falkirk, named in Gaelic as Beinnach, from beinn ‘hill’ + the locative suffix -ach.
Surname or Lastname
English
English : unexplained. It may be a variant of Sears or Sayers.
Male
Irish
Variant spelling of Irish Bearach, BERACH means "sharp."
Male
English
Variant spelling of English Piers, PEARCE means "rock, stone."
Female
Turkish
Turkish name PINAR means "spring."
Male
Hindi/Indian
(विनय) Hindi name VINAY means "leading asunder."
Male
Irish
Irish name derived from the Gaelic word biorach, BEARACH means "sharp."
Male
Hindi/Indian
Variant spelling of Hindi Vijay, BIJAY means "victory."
Surname or Lastname
English
English : variant of Searle.
Female
English
English pet form of German Belinda, possibly BINDY means "bright serpent" or "bright linden tree."
Surname or Lastname
English or Irish
English or Irish : variant of Searcy.
Male
English
English surname transferred to forename use, from the Norman French word march, MARCH means "boundary." Compare with other forms of March.
Female
Gaelic
(pron. Lee-shock) Gaelic name LUÃSEACH means "light-bringer."Â
Male
Scandinavian
Scandinavian form of Old Norse Einarr, EINAR means "lone warrior."
Female
Hebrew
Variant spelling of Hebrew Bina, BINAH means "intelligence, wisdom."Â
Boy/Male
American, Australian, French, German, Greek, Latin, Polish, Swedish
Cheerful; Happy; Joyful; Similar to Hilary
Surname or Lastname
English (Oxfordshire)
English (Oxfordshire) : habitational name from Stirch in Warwickshire.
Surname or Lastname
English
English : variant of Surridge 1.
Male
English
English unisex form of Latin Hilarius and Hilaria, HILARY means "joyful; happy."Â Originally, this was strictly a masculine name.
OPTIMAL BINARY-SEARCH-TREE
OPTIMAL BINARY-SEARCH-TREE
Boy/Male
Danish, Finnish, German
Lovely
Boy/Male
Hindu
Worship
Girl/Female
Indian, Tamil
God's Presence
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
Merciful Lord Shiva
Boy/Male
Welsh American
Cried over.
Boy/Male
Arabic, Muslim
A Place in Arab; One who Lives in Tihamah
Girl/Female
Arthurian Legend
A princess who dresses as a man.
Boy/Male
German
Peaceful Hun.
Surname or Lastname
English
English : habitational name from either of two places called Bowley, near Leominster in Herefordshire and in Devon. The first is named with Old English bula ‘bull’, perhaps a byname (see Bull) + lēah ‘woodland clearing’. The second is from Old English boga ‘bow’, ‘river bend’ + lēah.
Girl/Female
Muslim/Islamic
Well-known
OPTIMAL BINARY-SEARCH-TREE
OPTIMAL BINARY-SEARCH-TREE
OPTIMAL BINARY-SEARCH-TREE
OPTIMAL BINARY-SEARCH-TREE
OPTIMAL BINARY-SEARCH-TREE
n.
A canary bird.
a.
Consisting of starch; resembling starch; stiff; precise.
v. i.
To perform the canary dance; to move nimbly; to caper.
a.
Relating to the science of optics; as, optical works.
n.
A pale yellow color, like that of a canary bird.
v. t.
To make search after; to investigate or examine; to ensearch.
a.
Of or pertaining to the Canary Islands; as, canary wine; canary birds.
v. t.
To examine or explore by feeling with an instrument; to probe; as, to search a wound.
a.
Of a pale yellowish color; as, Canary stone.
v. t.
To search again; to examine anew.
v. t.
To search for.
a.
Of or pertaining to the urine; as, the urinary bladder; urinary excretions.
n.
See Perch.
v. t.
To look over or through, for the purpose of finding something; to examine; to explore; as, to search the city.
a.
Relating or belonging to bile; conveying bile; as, biliary acids; biliary ducts.
imp. & p. p.
of Search
v. t.
To stiffen with starch.
n.
Wine made in the Canary Islands; sack.
a.
Involving an option; depending on the exercise of an option; left to one's discretion or choice; not compulsory; as, optional studies; it is optional with you to go or stay.
n.
See Finery.