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Numerical invariant of graphs
tree-depth of a connected undirected graph G {\displaystyle G} is a numerical invariant of G {\displaystyle G} , the minimum height of a Trémaux tree
Tree-depth
Type of data structure
hash tree size is a prerequisite of some formal security proofs, and helps in making some proofs tighter. Some implementations limit the tree depth using
Merkle_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
Topics referred to by the same term
depth, or coverage, in genetic sequencing Depth (coordinate), a type of vertical distance Tree depth Depth (video game), an asymmetrical multiplayer video
Depth
Class of algorithms
canonically traversed in linear order, trees may be traversed in multiple ways. They may be traversed in depth-first or breadth-first order. There are
Tree_traversal
Tree searching strategy
depth limits until the goal is found. IDDFS is optimal, meaning that it finds the shallowest goal. Since it visits all the nodes in the search tree down
Iterative deepening depth-first search
Iterative_deepening_depth-first_search
Generalization of depth-first search trees
theory, a Trémaux tree of an undirected graph G {\displaystyle G} is a type of spanning tree, generalizing depth-first search trees. They are defined
Trémaux_tree
Perennial woody plant with elongated trunk
botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be
Tree
Tree-based computer data structure
carrying the data objects/chunks. A B-tree of depth n+1 can hold about U times as many items as a B-tree of depth n, but the cost of search, insert, and
B-tree
Machine learning technique
separate validation data set. Another regularization parameter for tree boosting is tree depth. The higher this value the more likely the model will overfit
Gradient_boosting
Data structure in tree form sorted for fast lookup
tree Depth-first search Black, Paul and Pieterse, Vreda (2005). "search tree". Dictionary of Algorithms and Data Structures Toal, Ray. "(a,b) Trees"
Search_tree
Visual ability to perceive the world in 3D
Depth perception is the ability to perceive distance to objects in the world using the visual system and visual perception. It is a major factor in perceiving
Depth_perception
Undirected, connected, and acyclic graph
The depth of a tree is the maximum depth of any vertex. Depth is commonly needed in the manipulation of the various self-balancing trees, AVL trees in
Tree_(graph_theory)
Mathematical optimization problem restricted to integers
A {\displaystyle A} is the minimum of the tree-depth of the graph of A {\displaystyle A} and the tree-depth of the graph of the transpose of A {\displaystyle
Integer_programming
In applied mathematics, a technique to find the shortest path
the graph diameter, t d {\displaystyle td} is the tree-depth and t w {\displaystyle tw} is the tree-width. The first analysis of contraction hierarchy
Contraction_hierarchies
Algorithm to search the nodes of a graph
searching a tree data structure for a node that satisfies a given property. It starts at the tree root and explores all nodes at the present depth prior to
Breadth-first_search
Linked node hierarchical data structure
height zero, and a tree with only a single node (hence both a root and leaf) has depth and height zero. Conventionally, an empty tree (tree with no nodes,
Tree_(abstract_data_type)
Decision support tool
some. The accuracy of the decision tree can change based on the depth of the decision tree. In many cases, the tree's leaves are pure nodes. When a node
Decision_tree
Variation of minimax game tree search
negamax(rootNode, depth, −∞, +∞, 1) Alpha (α) and beta (β) represent lower and upper bounds for child node values at a given tree depth. Negamax sets the
Negamax
Homomorphism from an initial algebra into another algebra
Iso $ TconR l r treeDepth :: Algebra (Tcon a) Integer -- again, the treeDepth f-algebra example treeDepth (TconL x) = 1 treeDepth (TconR y z) = 1 + max
Catamorphism
Data compression technique
by replacing a stop () criterion in the induction algorithm (e.g. max. Tree depth or information gain (Attr)> minGain). Pre-pruning methods are considered
Decision_tree_pruning
Binary tree variant
recursion and the extra storage (proportional to the tree's depth) that recursion requires. "A binary tree is threaded by making all right child pointers that
Threaded_binary_tree
Multidimensional search tree for points in k dimensional space
Wikimedia Commons has media related to k-d trees. In computer science, a k-d tree (short for k-dimensional tree) is a space-partitioning data structure for
K-d_tree
Data structure
radix tree (also radix trie or compact prefix tree or compressed trie) is a data structure that represents a space-optimized trie (prefix tree) in which
Radix_tree
Type of tree data structure
strategies for searching the space are possible. These include searching the tree depth-first, breadth-first, or best-first using some measure of desirability
And–or_tree
Tree which includes all vertices of a graph
This tree is known as a depth-first search tree or a breadth-first search tree according to the graph exploration algorithm used to construct it. Depth-first
Spanning_tree
Graph path which is an induced subgraph
graphs, having bounded detour number is equivalent to having bounded tree-depth. The induced path number of a graph G is the smallest number of induced
Induced_path
Limited form of tree data structure
full binary trees. A perfect binary tree is a binary tree in which all interior nodes have two children and all leaves have the same depth or same level
Binary_tree
Connectivity measure in graph theory
rank n. The cycle rank of a directed graph is closely related to the tree-depth of an undirected graph and to the star height of a regular language. It
Cycle_rank
Technique in parallel algorithms
tree has exactly two branches for each vertex except for leaves. This gives a O(log n) bound on the depth of the tree. A linked list is also a tree where
Tree_contraction
Digital image processing technique
taken at different focus distances to give a resulting image with a greater depth of field (DOF) than any of the individual source images. Focus stacking
Focus_stacking
Node labeling problem in graph theory
its tree-depth is at most k log(n/k). In contrast, as noted in the previous section, the star graph Sk, a structurally very simple example of a tree, has
Graph_bandwidth
Data structure for representing a forest
auxiliary tree are keyed by depth, this means that any nodes to the right of v in the auxiliary tree must be disconnected. In a splay tree this is a relatively
Link/cut_tree
Maximal biconnected subgraph
idea is 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
Tree data structure in which each node has at most m children
complete m-ary tree (or, less commonly, a perfect m-ary tree) is a full m-ary tree in which all leaf nodes are at the same depth. For an m-ary tree with height
M-ary_tree
Graph coloring avoiding 2-colored paths
result has been generalized to all low-tree-depth colorings (standard coloring and star coloring being low-tree-depth colorings with respective parameter
Star_coloring
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
Graph coloring related to treedepth
in a centered coloring of a given graph G {\displaystyle G} equals its tree-depth, the minimum height of a rooted forest F {\displaystyle F} on the same
Centered_coloring
Search algorithm
pruning is a tree 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
Cache of previously seen positions, and associated evaluations in a game tree
number of possible positions that may occur in a game tree is an exponential function of depth of search, and can be thousands to millions or even much
Transposition_table
Purely functional data structure
level of the tree contains only values, the leaf nodes of the tree, and is of depth 0. The second level is of depth 1. The third is of depth 2 and so on
Finger_tree
Binary tree selected at random
random trees formed by inserting nodes one at a time according to a random permutation. The resulting trees are very likely to have logarithmic depth and
Random_binary_tree
Technique used in relational databases
to the tree. For more complex systems, hierarchy can be developed through relational models rather than an implicit numeric tree structure. Depth of an
Nested_set_model
Rule in logic programming
the search tree. Prolog searches the tree depth-first, one branch at a time, using backtracking when it encounters a failure node. Depth-first search
SLD_resolution
Scented tea made by infusing tea leaves with jasmine blossoms
Tuyết tea trees (some over 200 years old), known for their distinct mountain character. The resulting cup harmonises earthy old-tree depth with the jasmine
Jasmine_tea
Number denoting a graph's closeness to a tree
least as large as the pathwidth. Other related parameters include the tree-depth, a number that is bounded for a minor-closed graph family if and only
Treewidth
Variation of the minimax algorithm
tree alternate from max to min until the depth limit of the tree has been reached. In an expectiminimax tree, the "chance" nodes are interleaved with
Expectiminimax
Tool for proving a logical formula
visit in a depth-first manner with iterative deepening: one first visits the tree depth first up to a certain depth, then increases the depth and perform
Method_of_analytic_tableaux
Species of banyan tree
elastica, the rubber fig, rubber bush, rubber tree, rubber plant, or Indian rubber bush, Indian rubber tree, or rambung is a species of flowering plant
Ficus_elastica
depth of an output node is the depth of the tree. The leaves of the tree are called output nodes. In a computation tree for a decision problem, each output
Computation_tree
Data type defined by combining other types
the depth of a Tree, given here in Haskell: depth :: Tree -> Int depth Empty = 0 depth (Leaf n) = 1 depth (Node n l r) = 1 + max (depth l) (depth r) Thus
Algebraic_data_type
Computer science data structure
binary balanced tree with at most 4n + 1 leaves, its height is O(log n). Since any interval is stored at most twice at a given depth of the tree, that the total
Segment_tree
Shell command for reporting file system storage use
the storage usage for the specified scope -d #: The maximum directory tree depth of the scope. Deeper directories are ignored; for example, 0 sums the
Du_(Unix)
Model of computational complexity
complexity of an algorithm in the decision tree model corresponds to the depth of the corresponding tree. This notion of computational complexity of
Decision_tree_model
Rendering method
very reflective scene, using this with a maximum depth of 15 resulted in an average ray tree depth of 1.7. Enclosing groups of objects in sets of bounding
Ray_tracing_(graphics)
Hyperparameter optimization framework
learning rate, number of layers or neurons, regularization strength, and tree depth. However, they strongly depend on the specific algorithm (e.g., classification
Optuna
Journaling file system
NSS Maximum open files per server: no practical limit Maximum directory tree depth: limited only by client Maximum volumes per partition: unlimited Maximum
Novell_Storage_Services
Data structure in computer science
tree is that all external nodes are at the same depth. 2–3–4 trees are closely related to red–black trees by interpreting red links (that is, links to red
2–3–4_tree
Visualisation method for hierchical data
{\displaystyle n} - the total number of nodes in the tree, and d {\displaystyle d} - the total depth of the tree. Onak and Sidiropoulos proved an upper bound
Treemapping
Algorithmic search method
exponential tree is a type of search tree where the number of children of its nodes decreases doubly-exponentially with increasing depth. Values are stored
Exponential_tree
Chordal graph with the given graph as a subgraph
proper interval graph with maximum clique size at most k + 1. And it has tree-depth k if and only if it has at least one chordal completion that is a trivially
Chordal_completion
Type of binary search tree
and maximum depth (depth in the reference tree, that is) of nodes in the subtree under that node. To search for an element in the tango tree, we simply
Tango_tree
Data structure for a string
A suffix tree can be built in O ( n ) {\displaystyle {\mathcal {O}}(n)} and can be converted into a suffix array by traversing the tree depth-first also
Suffix_array
English polymath (1642–1727)
analysis indicate that the sole apple tree in a garden at Woolsthorpe Manor was the tree Newton described. The tree blew over in at storm sometime around
Isaac_Newton
File system based on FAT
partition: 8 Maximum open files per server: 100,000 Maximum directory tree depth: 100 levels Characters used: ASCII double-byte Maximum extended attributes:
NetWare_File_System
2017 video game
personal depth." Rebecca Stow of Push Square gave the game's PS4 version an 8/10 rating, praising its voice acting and writing that "The First Tree effortlessly
The_First_Tree
Least-weight tree connecting graph vertices
A minimum spanning tree (MST) or minimum weight spanning tree is a subset of the edges of a connected, edge-weighted undirected graph that connects all
Minimum_spanning_tree
Self-balancing binary search tree data structure
Left-leaning red–black tree AVL tree B-tree (2–3 tree, 2–3–4 tree, B+ tree, B*-tree, UB-tree) Scapegoat tree Splay tree T-tree WAVL tree GNU libavl Cormen
Red–black_tree
Machine learning algorithm
Conditional Inference approach, that does not require pruning). The average depth of the tree that is defined by the number of nodes or tests till classification
Decision_tree_learning
Log that has been floating in Crater Lake since at least 1896
The Old Man of the Lake is a 30-foot (9 m) tall tree trunk, most likely a hemlock, that has been bobbing vertically in Crater Lake in Oregon, United States
Old_Man_of_the_Lake
Programming language
tree: procedure tree(depth: integer, bottom: channel); var left, right: channel; begin if depth > 0 then begin open(left, right); parallel tree(depth
SuperPascal
Tree data structure
depends on the depth of the search tree, and therefore the branching factor, versus the insertion time, which depends on the depth of the tree but more sensitively
Fractal_tree_index
Tree in which each node has at most three children
directed edge. Depth - Length of the path from the root to the node. The set of all nodes at a given depth is sometimes called a level of the tree. The root
Ternary_tree
Mathematical concept for comparing objects
minor" is a well-quasi-order (Robertson–Seymour theorem). Graphs of finite tree-depth ordered by the induced subgraph relation form a well-quasi-order, as do
Well-quasi-ordering
Ordered binary tree of rational numbers
In number theory, the Stern–Brocot tree is an infinite complete binary tree whose vertices correspond one-for-one to the positive rational numbers, whose
Stern–Brocot_tree
Mathematical tree on concentric circles
nodes. A radial tree will spread the larger number of nodes over a larger area as the levels increase. We use the terms level and depth interchangeably
Radial_tree
Soil depression created by a tree
upturned rootwad, but trees are sparse; in deeper soils less rock is upturned, but trees are more common, and in soils deeper than the depth of roots, no bedrock
Tree_throw
Basic unit of a data structure
the furthest leaf node, and the height of the tree is equal to the height of the root node. Node depth is determined by the distance between that particular
Node_(computer_science)
Flowering, deciduous trees, family Ulmaceae
Elms are deciduous and semi-deciduous trees comprising the genus Ulmus in the family Ulmaceae. They are distributed over most of the Northern Hemisphere
Elm
Space partitioning data structure
constructing a tree and the efficiency achieved by this metric. This section briefly describes the simplest of these algorithms. A more in-depth discussion
Ball_tree
Subgraph with contracted edges
pathwidth if and only if its forbidden minors include a forest, F has bounded tree-depth if and only if its forbidden minors include a disjoint union of path graphs
Graph_minor
Series of children's novels by Mary Pope Osborne
Magic Tree House is an American children's series written by American author Mary Pope Osborne. The original American series was illustrated by Salvatore
Magic_Tree_House
tree with n nodes, and let v be an arbitrary node of T. The level ancestor query LA(v,d) requests the ancestor of node v at depth d, where the depth of
Level_ancestor_problem
Educational publishing company
long-term PD, from one-day events or workshops to in-depth, long term arrangements. In 2014, Solution Tree launched Global PD, an online tool designed to help
Solution_Tree
Combinatorial game theory concept to represent all possible game states
for the case of "pathological" game trees (which seem to be quite rare in practice), increasing the search depth (i.e., the number of plies searched)
Game_tree
Component of Tolkien's writings
Tolkien's Middle-earth family trees contribute to the impression of depth and realism in the stories set in his fantasy world by showing that each character
Tolkien's Middle-earth family trees
Tolkien's_Middle-earth_family_trees
Painting by Piet Mondrian
application of paint to create depth. His rhythmic and opaque application indicates a greater sense of substance both in the tree and the space around it. His
Evening;_Red_Tree
costs work O ( n ) {\displaystyle O(n)} and depth O ( log 2 n ) {\displaystyle O(\log ^{2}n)} on a tree of size n {\displaystyle n} , assuming p {\displaystyle
Join-based_tree_algorithms
Graph with at most one crossing per edge
fixed-parameter tractable when parameterized by cyclomatic number or by tree-depth, so it may be solved in polynomial time when those parameters are bounded
1-planar_graph
Notion in combinatorial game theory
linear). The depth-first minimax strategy will use computation time proportional to the game's tree-complexity (since it must explore the whole tree), and an
Game_complexity
Genus of legumes
also known as tipa, rosewood and pride of Bolivia, is a South American tree. It is the only member of the genus Tipuana. It was recently assigned to
Tipuana
Fewest graph edges whose removal breaks all cycles
definition than cyclomatic number (closely related to the definition of tree-depth for undirected graphs) and is more difficult to compute. Another problem
Cyclomatic_number
Israeli mathematician
n-fold integer programming, and the broader theory of sparse and bounded tree-depth integer programming, shown to be fixed-parameter tractable. These theories
Shmuel_Onn
Motif in many mythologies and religions
The world tree, also known as the cosmic tree is a motif present in several religions and mythologies, particularly Indo-European, Siberian, and Native
World_tree
Self-balancing binary search tree
computer science, an AVL tree (named after inventors Adelson-Velsky and Landis) is a self-balancing binary search tree. In an AVL tree, the heights of the
AVL_tree
up to the surface for crops with roots that cannot reach that depth. Fertilizer trees are further useful for preventing fertilizer erosion, soil degradation
Fertilizer_tree
Machine for transplanting trees
ball diameter, root ball depth, and root ball cone angle. The machines can be mounted on a tractor or loader for moving trees a short distance, or on the
Tree_spade
Heuristic pathfinding algorithm
the most promising nodes and thus does not go to the same depth everywhere in the search tree. Unlike A*, IDA* does not utilize dynamic programming and
Iterative_deepening_A*
Species of tree
Boscia albitrunca, commonly known as the shepherd tree or shepherd's tree (Afrikaans: witgat, Sotho: Mohlôpi, Tswana: Motlôpi, Venda: Muvhombwe, Xhosa:
Boscia_albitrunca
Data structures used in spatial indexing
the data set. Similar to the B-tree, the R-tree is also a balanced search tree (so all leaf nodes are at the same depth), organizes the data in pages,
R-tree
TREE DEPTH
TREE DEPTH
Surname or Lastname
English
English : variant of Treece.
Boy/Male
Muslim
Rare, Uncommon, Strange
Surname or Lastname
English
English : variant of Trow, mainly of 1.altered spelling of German Treu.
Surname or Lastname
English
English : variant of Trow, mainly of 1.
Boy/Male
American, Australian, Chinese
Three
Boy/Male
American, Australian, British, Chinese, Christian, English
Three
Female
English
English form of Irish BrÃgh, BREE means "force, strength."
Boy/Male
English American
Three. Also atraigh 'Strand'.
Boy/Male
Scottish American
Derivative of the Scandinavian god of battle 'Tyr.' Tuesday was named for Tyr.
Surname or Lastname
English (chiefly East Anglia)
English (chiefly East Anglia) : nickname or status name from Old English frēo ‘free(-born)’, i.e. not a serf.North German : topographic or habitational name from a place named Frede or Frede(n).North German : nickname from a variant of Middle Low German wrēd ‘crooked’.
Girl/Female
African, Indian, Japanese, Sanskrit
True Record; True Hope; Heaven and Earth Conjoined; Tree
Surname or Lastname
Cornish
Cornish : habitational name from places so named in the parishes of Zennor and St. Levan, both of which appear earlier in the form Trethyn, from Cornish tre ‘homestead’, ‘settlement’ + dyn ‘fort’.English : variant of Treece, from a form with the weak plural ending.
Male
English
English name TREY means "three."
Girl/Female
American, Australian, Christian, Danish, French, Jamaican, Latin
True Image; Womanly; Brave; Yew Tree
Boy/Male
American, Australian, British, English, Jamaican
Three
Female
Spanish
Short form of Spanish Teresa, TERE means "harvester."Â
Surname or Lastname
English (mainly southeastern)
English (mainly southeastern) : topographic name for someone who lived near a conspicuous tree, Middle English tre(w).
Girl/Female
Japanese
Three trees together.
Boy/Male
Japanese
Three trees together.
Male
English
Short form of English Trevor, TREV means "large settlement."
TREE DEPTH
TREE DEPTH
Boy/Male
Latin
Eagle.
Boy/Male
Arabic, Australian, Indian, Lebanese, Parsi
Loving
Boy/Male
Indian, Sanskrit
Religious Mendicant
Boy/Male
British, English, Netherlands, Swedish
Sweet; Playful; Hard Working; Variant of Emily
Female
Egyptian
, an Egyptian goddess.
Girl/Female
Tamil
Arukshita | à®…à®°à¯à®•à¯à®·à¯€à®¤à®¾
Young, Gentle
Surname or Lastname
English, Scottish, and Irish
English, Scottish, and Irish : from Rousel, a common Anglo-Norman French nickname for someone with red hair, a diminutive of Rouse with the hypocoristic suffix -el.Americanized spelling of German Rüssel, from a pet form of any of the various personal names formed with the Old High German element hrÅd ‘renown’.
Girl/Female
African, American, Danish, French, German, Indian, Latin
Stony Place; Song
Boy/Male
Muslim
Beauty of the faith, Beauty of the religion
Girl/Female
American, Australian, Finnish, French, German, Hungarian, Jamaican, Latin, Polish, Portuguese, Romanian, Spanish, Swedish
Golden; Wind; Dawn; Breeze
TREE DEPTH
TREE DEPTH
TREE DEPTH
TREE DEPTH
TREE DEPTH
a.
Alt. of Trewe
a.
True.
n.
A mass of crystals, aggregated in arborescent forms, obtained by precipitation of a metal from solution. See Lead tree, under Lead.
imp. & p. p.
of Tree
n.
Something constructed in the form of, or considered as resembling, a tree, consisting of a stem, or stock, and branches; as, a genealogical tree.
n.
Actual; not counterfeit, adulterated, or pretended; genuine; pure; real; as, true balsam; true love of country; a true Christian.
v. t.
To place upon a tree; to fit with a tree; to stretch upon a tree; as, to tree a boot. See Tree, n., 3.
n.
A cross or gallows; as Tyburn tree.
v. t.
To drive to a tree; to cause to ascend a tree; as, a dog trees a squirrel.