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Scaling Similarity Joins over Tree-Structured Data

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Join (SQL)

A join clause in the Structured Query Language (SQL) combines columns from one or more tables into a new table. The operation corresponds to a join operation in relational algebra. Informally, a join stitches two tables and puts on the same row records with matching fields : INNER, LEFT OUTER, RIGHT OUTER, FULL OUTER and CROSS. To explain join types, the rest of this article uses the following tables: Department.DepartmentID is the primary key of the Department table, whereas Employee.DepartmentID is a foreign key.

Hash join

The hash join is an example of a join algorithm and is used in the implementation of a relational database management system. All variants of hash join algorithms involve building hash tables from the tuples of one or both of the joined relations, and subsequently probing those tables so that only tuples with the same hash code need to be compared for equality in equijoins. Hash joins are typically more efficient than nested loops joins, except when the probe side of the join is very small.

Purely functional data structure

In computer science, a purely functional data structure is a data structure that can be directly implemented in a purely functional language. The main difference between an arbitrary data structure and a purely functional one is that the latter is (strongly) immutable. This restriction ensures the data structure possesses the advantages of immutable objects: (full) persistency, quick copy of objects, and thread safety. Efficient purely functional data structures may require the use of lazy evaluation and memoization.

Cograph

In graph theory, a cograph, or complement-reducible graph, or P4-free graph, is a graph that can be generated from the single-vertex graph K1 by complementation and disjoint union. That is, the family of cographs is the smallest class of graphs that includes K1 and is closed under complementation and disjoint union. Cographs have been discovered independently by several authors since the 1970s; early references include , , , and . They have also been called D*-graphs, hereditary Dacey graphs (after the related work of James C.

XML

Extensible Markup Language (XML) is a markup language and for storing, transmitting, and reconstructing arbitrary data. It defines a set of rules for encoding documents in a format that is both human-readable and machine-readable. The World Wide Web Consortium's XML 1.0 Specification of 1998 and several other related specifications—all of them free open standards—define XML. The design goals of XML emphasize simplicity, generality, and usability across the Internet.

Tree-depth

In graph theory, the tree-depth of a connected undirected graph is a numerical invariant of , the minimum height of a Trémaux tree for a supergraph of . This invariant and its close relatives have gone under many different names in the literature, including vertex ranking number, ordered chromatic number, and minimum elimination tree height; it is also closely related to the cycle rank of directed graphs and the star height of regular languages.

XML schema

An XML schema is a description of a type of XML document, typically expressed in terms of constraints on the structure and content of documents of that type, above and beyond the basic syntactical constraints imposed by XML itself. These constraints are generally expressed using some combination of grammatical rules governing the order of elements, Boolean predicates that the content must satisfy, data types governing the content of elements and attributes, and more specialized rules such as uniqueness and referential integrity constraints.

Jaccard index

The Jaccard index, also known as the Jaccard similarity coefficient, is a statistic used for gauging the similarity and diversity of sample sets. It was developed by Grove Karl Gilbert in 1884 as his ratio of verification (v) and now is frequently referred to as the Critical Success Index in meteorology. It was later developed independently by Paul Jaccard, originally giving the French name coefficient de communauté, and independently formulated again by T. Tanimoto. Thus, the Tanimoto index or Tanimoto coefficient are also used in some fields.

Similarity measure

In statistics and related fields, a similarity measure or similarity function or similarity metric is a real-valued function that quantifies the similarity between two objects. Although no single definition of a similarity exists, usually such measures are in some sense the inverse of distance metrics: they take on large values for similar objects and either zero or a negative value for very dissimilar objects. Though, in more broad terms, a similarity function may also satisfy metric axioms.

Sort-merge join

The sort-merge join (also known as merge join) is a join algorithm and is used in the implementation of a relational database management system. The basic problem of a join algorithm is to find, for each distinct value of the join attribute, the set of tuples in each relation which display that value. The key idea of the sort-merge algorithm is to first sort the relations by the join attribute, so that interleaved linear scans will encounter these sets at the same time.