Concepts inFinding top-k similar graphs in graph databases
Graph database
A graph database uses graph structures with nodes, edges, and properties to represent and store data. By definition, a graph database is any storage system that provides index-free adjacency. This means that every element contains a direct pointer to its adjacent element and no index lookups are necessary. General graph databases that can store any graph are distinct from specialized graph databases such as triplestores and network databases.
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Maximum common subgraph isomorphism problem
In complexity theory, maximum common subgraph-isomorphism (MCS) is an optimization problem that is known to be NP-hard. The formal description of the problem is as follows: Maximum common subgraph-isomorphism(G1, G2) Input: Two graphs G1 and G2. Question: What is the largest induced subgraph of G1 isomorphic to an induced subgraph of G2? The associated decision problem, i.e.
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Nearest neighbor search
Nearest neighbor search (NNS), also known as proximity search, similarity search or closest point search, is an optimization problem for finding closest points in metric spaces. The problem is: given a set S of points in a metric space M and a query point q ¿ M, find the closest point in S to q. In many cases, M is taken to be d-dimensional Euclidean space and distance is measured by Euclidean distance or Manhattan distance. Donald Knuth in vol.
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Glossary of graph theory
Graph theory is a growing area in mathematical research, and has a large specialized vocabulary. Some authors use the same word with different meanings. Some authors use different words to mean the same thing. This page attempts to describe current usage.
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NP-hard
NP-hard, in computational complexity theory, is a class of problems that are, informally, "at least as hard as the hardest problems in NP". A problem H is NP-hard if and only if there is an NP-complete problem L that is polynomial time Turing-reducible to H (i.e. , L¿¿¿TH). In other words, L can be solved in polynomial time by an oracle machine with an oracle for H.
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Graph (mathematics)
In mathematics, a graph is an abstract representation of a set of objects where some pairs of the objects are connected by links. The interconnected objects are represented by mathematical abstractions called vertices, and the links that connect some pairs of vertices are called edges. Typically, a graph is depicted in diagrammatic form as a set of dots for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics.
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Upper and lower bounds
In mathematics, especially in order theory, an upper bound of a subset S of some partially ordered set (P, ¿) is an element of P which is greater than or equal to every element of S. The term lower bound is defined dually as an element of P which is less than or equal to every element of S. A set with an upper bound is said to be bounded from above by that bound, a set with a lower bound is said to be bounded from below by that bound.
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