B+ tree

A B+ tree is an n-ary tree with a variable but often large number of children per node. A B+ tree consists of a root, internal nodes and leaves. The root may be either a leaf or a node with two or more children.

A B+ tree can be viewed as a B-tree in which each node contains only keys (not key-value pairs), and to which an additional level is added at the bottom with linked leaves.

The primary value of a B+ tree is in storing data for efficient retrieval in a block-oriented storage context — in particular, filesystems. This is primarily because unlike binary search trees, B+ trees have very high fanout (number of pointers to child nodes in a node, typically on the order of 100 or more), which reduces the number of I/O operations required to find an element in the tree.

The ReiserFS, NSS, XFS, JFS, ReFS, and BFS filesystems all use this type of tree for metadata indexing; BFS also uses B+ trees for storing directories. NTFS uses B+ trees for directory indexing. EXT4 uses extent trees (a modified B+ tree data structure) for file extent indexing. Relational database management systems such as IBM DB2,Informix,Microsoft SQL Server,Oracle 8,Sybase ASE, and SQLite support this type of tree for table indices. Key-value database management systems such as CouchDB and Tokyo Cabinet support this type of tree for data access.

B-tree

In computer science, a B-tree is a self-balancing tree data structure that keeps data sorted and allows searches, sequential access, insertions, and deletions in logarithmic time. The B-tree is a generalization of a binary search tree in that a node can have more than two children (Comer 1979, p. 123). Unlike self-balancing binary search trees, the B-tree is optimized for systems that read and write large blocks of data. B-trees are a good example of a data structure for external memory. It is commonly used in databases and filesystems.

Overview

In B-trees, internal (non-leaf) nodes can have a variable number of child nodes within some pre-defined range. When data is inserted or removed from a node, its number of child nodes changes. In order to maintain the pre-defined range, internal nodes may be joined or split. Because a range of child nodes is permitted, B-trees do not need re-balancing as frequently as other self-balancing search trees, but may waste some space, since nodes are not entirely full. The lower and upper bounds on the number of child nodes are typically fixed for a particular implementation. For example, in a 2-3 B-tree (often simply referred to as a 2-3 tree), each internal node may have only 2 or 3 child nodes.

Ṭūbā

Ṭūbā (Arabic: طُوبَىٰ‎ ṭūbā, lit. "blessedness") is a tree that Muslims believe grows in Jannah, or Islamic heaven.

The tree is only mentioned once in the Koran but its attributes can be ascertained from various hadiths and other writings. Ṣaḥīḥ al-Bukhārī 4:474 notes that the tree spreads over a distance that can be covered in a hundred years and that the gowns of righteous dwellers of heaven are made from the fiber of its blossoms. A sage in Sohrevardi's The Red Intellect says that "any fruit you see in the world will be on that tree". The tree is sometimes described as being inverted and having its roots in the air. Mehmed Yazıcıoğlu (Yazıcızade, Yaziji-Oglu) wrote of the tree in "The Creation of Paradise" in his 1449 Book of Muhammad (Muhammediye):

That a tree which hangeth downward, high aloft its roots are there: Thus its radiance all the Heavens lighteth up from end to end, Flooding every tent and palace, every lane and every square. Such a tree the Tuba, that the Gracious One hath in its sap Hidden whatsoe'er there be of gifts and presents good and fair; Forth therefrom crowns, thrones, and jewels, yea, and steeds and coursers come, Golden leaves and clearest crystals, wines most pure beyond compare. For his sake there into being hath he called the Tuba-Tree, That from Ebu-Qasim's hand might every one receive his share.

Tree

In botany, a tree is a perennial plant with an elongated stem, or trunk, supporting branches and leaves in most species. In some usages, the definition of a tree may be narrower, including only woody plants with secondary growth, plants that are usable as lumber or plants above a specified height. Trees are not a taxonomic group but include a variety of plant species that have independently evolved a woody trunk and branches as a way to tower above other plants to compete for sunlight. In looser senses, the taller palms, the tree ferns, bananas and bamboos are also trees. Trees tend to be long-lived, some reaching several thousand years old. The tallest known tree, a coast redwood named Hyperion, stands 115.6 m (379 ft) high. Trees have been in existence for 370 million years. It is estimated that there are just over 3 trillion mature trees in the world.

A tree typically has many secondary branches supported clear of the ground by the trunk. This trunk typically contains woody tissue for strength, and vascular tissue to carry materials from one part of the tree to another. For most trees it is surrounded by a layer of bark which serves as a protective barrier. Below the ground, the roots branch and spread out widely; they serve to anchor the tree and extract moisture and nutrients from the soil. Above ground, the branches divide into smaller branches and shoots. The shoots typically bear leaves, which capture light energy and convert it into sugars by photosynthesis, providing the food for the tree's growth and development. Flowers and fruit may also be present, but some trees, such as conifers, instead have pollen cones and seed cones; others, such as tree ferns, produce spores instead.

Trees in mythology

Trees are significant in many of the world's mythologies and religions, and have been given deep and sacred meanings throughout the ages. Human beings, observing the growth and death of trees, and the annual death and revival of their foliage, have often seen them as powerful symbols of growth, death and rebirth. Evergreen trees, which largely stay green throughout these cycles, are sometimes considered symbols of the eternal, immortality or fertility. The image of the Tree of life or world tree occurs in many mythologies.

Sacred or symbolic trees include the Banyan and the Peepal (Ficus religiosa) trees in Hinduism, the Yule Tree in Germanic mythology, the Tree of Knowledge of Judaism and Christianity, the Bodhi tree in Buddhism and Saglagar tree in Mongolian Tengriism. In folk religion and folklore, trees are often said to be the homes of tree spirits. Germanic paganism as well as Celtic polytheism both appear to have involved cultic practice in sacred groves, especially grove of oak. The term druid itself possibly derives from the Celtic word for oak. The Egyptian Book of the Dead mentions sycamores as part of the scenery where the soul of the deceased finds blissful repose.

Wood (Wu Xing)

Wood (Chinese: 木; pinyin: mù), sometimes translated as Tree, is the growing of the matter, or the matter's growing stage. Wood is the first phase of Wu Xing. Wood is yang in character. It stands for springtime, the east, the planet Jupiter, the color green, wind, and the Azure Dragon (Qing Long) in Four Symbols.

The Wu Xing are chiefly an ancient mnemonic device for systems with 5 stages; hence the preferred translation of "tree" over "wood".

Attributes

In Chinese Taoist thought, Wood attributes are considered to be strength and flexibility, as with bamboo. It is also associated with qualities of warmth, generosity, co-operation and idealism. The Wood person will be expansive, outgoing and socially conscious. The wood element is one that seeks ways to grow and expand. Wood heralds the beginning of life, springtime and buds, sensuality and fecundity. Wood needs moisture to thrive.

In Chinese medicine, wood is associated with negative feelings of anger, positive feelings of patience, and altruism.