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GYO Algorithm
The GYO algorithm is an algorithm that applies to hypergraphs. The algorithm takes as input a hypergraph and determines if the hypergraph is α-acyclic. If so, it computes a decomposition of the hypergraph. The algorithm was proposed in 1979 by Graham and independently by Yu and Özsoyoğlu, hence its name. Definition A hypergraph is a generalization of a graph. Formally, a hypergraph H = (V, E) consists of a set of vertices ''V'', and of a set ''E'' of hyperedges, each of which is a subset of the vertices ''V''. Given a hypergraph, we can define its ''primal graph'' as the undirected graph defined on the same set of vertices, in which we put an edge between any two vertices which occur together in some hyperedge. A hypergraph ''H'' is α-acyclic if it satisfies two conditions: being chordal and being conformal. More precisely, we say that ''H'' is chordal if its primal graph is a chordal graph In the mathematical area of graph theory, a chordal graph is one in which al ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hypergraph
In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two vertices. Formally, an undirected hypergraph H is a pair H = (X,E) where X is a set of elements called ''nodes'' or ''vertices'', and E is a set of non-empty subsets of X called '' hyperedges'' or ''edges''. Therefore, E is a subset of \mathcal(X) \setminus\, where \mathcal(X) is the power set of X. The size of the vertex set is called the ''order of the hypergraph'', and the size of edges set is the ''size of the hypergraph''. A directed hypergraph differs in that its hyperedges are not sets, but ordered pairs of subsets of X, with each pair's first and second entries constituting the tail and head of the hyperedge respectively. While graph edges connect only 2 nodes, hyperedges connect an arbitrary number of nodes. However, it is often desirable to study hypergraphs where all hyperedges have the same c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acyclic Hypergraph
In mathematics, a hypergraph is a generalization of a graph in which an edge can join any number of vertices. In contrast, in an ordinary graph, an edge connects exactly two vertices. Formally, an undirected hypergraph H is a pair H = (X,E) where X is a set of elements called ''nodes'' or ''vertices'', and E is a set of non-empty subsets of X called ''hyperedges'' or ''edges''. Therefore, E is a subset of \mathcal(X) \setminus\, where \mathcal(X) is the power set of X. The size of the vertex set is called the ''order of the hypergraph'', and the size of edges set is the ''size of the hypergraph''. A directed hypergraph differs in that its hyperedges are not sets, but ordered pairs of subsets of X, with each pair's first and second entries constituting the tail and head of the hyperedge respectively. While graph edges connect only 2 nodes, hyperedges connect an arbitrary number of nodes. However, it is often desirable to study hypergraphs where all hyperedges have the same c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Martin H
Martin may refer to: Places * Martin City (other) * Martin County (other) * Martin Township (other) Antarctica * Martin Peninsula, Marie Byrd Land * Port Martin, Adelie Land * Point Martin, South Orkney Islands Australia * Martin, Western Australia * Martin Place, Sydney Caribbean * Martin, Saint-Jean-du-Sud, Haiti, a village in the Sud Department of Haiti Europe * Martin, Croatia, a village in Slavonia, Croatia * Martin, Slovakia, a city * Martín del Río, Aragón, Spain * Martin (Val Poschiavo), Switzerland England * Martin, Hampshire * Martin, Kent * Martin, East Lindsey, Lincolnshire, hamlet and former parish in East Lindsey district * Martin, North Kesteven, village and parish in Lincolnshire in North Kesteven district * Martin Hussingtree, Worcestershire * Martin Mere, a lake in Lancashire ** WWT Martin Mere, a wetland nature reserve that includes the lake and surrounding areas * Martin Mill, Kent North America Canada * Rural Municipality of M ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Meral Özsoyoglu
Zehra Meral Özsoyoglu is a Turkish-American computer scientist specializing in databases, including research on query languages, database model, and indexes, and applications of databases in science, bioinformatics, and medical informatics. She is the Andrew R. Jennings Professor Emeritus of Computer Science at Case Western Reserve University. Education and career Özsoyoglu earned bachelor's and master's degrees from Middle East Technical University in Ankara before moving to the University of Alberta in Edmonton, Canada for her doctoral studies. Her 1980 dissertation, ''Distributed Database Query Optimization Using Semi-Joins'', was supervised by Clement T. Yu. She joined the faculty at Case Western Reserve University in 1980, becoming the first female faculty member in her department and the second in the engineering school. She also became the first female chair of her department. She was editor-in-chief for '' ACM Transactions on Database Systems'' from 2007 to 2014, the fir ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph (discrete Mathematics)
In discrete mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related". The objects correspond to mathematical abstractions called '' vertices'' (also called ''nodes'' or ''points'') and each of the related pairs of vertices is called an ''edge'' (also called ''link'' or ''line''). Typically, a graph is depicted in diagrammatic form as a set of dots or circles for the vertices, joined by lines or curves for the edges. Graphs are one of the objects of study in discrete mathematics. The edges may be directed or undirected. For example, if the vertices represent people at a party, and there is an edge between two people if they shake hands, then this graph is undirected because any person ''A'' can shake hands with a person ''B'' only if ''B'' also shakes hands with ''A''. In contrast, if an edge from a person ''A'' to a person ''B'' means that ''A'' owes money to ''B'', th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vertex (graph Theory)
In discrete mathematics, and more specifically in graph theory, a vertex (plural vertices) or node is the fundamental unit of which graphs are formed: an undirected graph consists of a set of vertices and a set of edges (unordered pairs of vertices), while a directed graph consists of a set of vertices and a set of arcs (ordered pairs of vertices). In a diagram of a graph, a vertex is usually represented by a circle with a label, and an edge is represented by a line or arrow extending from one vertex to another. From the point of view of graph theory, vertices are treated as featureless and indivisible objects, although they may have additional structure depending on the application from which the graph arises; for instance, a semantic network is a graph in which the vertices represent concepts or classes of objects. The two vertices forming an edge are said to be the endpoints of this edge, and the edge is said to be incident to the vertices. A vertex ''w'' is said to be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperedge
This is a glossary of graph theory. Graph theory is the study of graphs, systems of nodes or vertices connected in pairs by lines or edges. Symbols A B C D E F G H I K L M N O ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chordal Graph
In the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a ''chord'', which is an edge that is not part of the cycle but connects two vertices of the cycle. Equivalently, every induced cycle in the graph should have exactly three vertices. The chordal graphs may also be characterized as the graphs that have perfect elimination orderings, as the graphs in which each minimal separator is a clique, and as the intersection graphs of subtrees of a tree. They are sometimes also called rigid circuit graphs. or triangulated graphs.. Chordal graphs are a subset of the perfect graphs. They may be recognized in linear time, and several problems that are hard on other classes of graphs such as graph coloring may be solved in polynomial time when the input is chordal. The treewidth of an arbitrary graph may be characterized by the size of the cliques in the chordal graphs that contain it. Perfect elimination and efficient recogn ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clique (graph Theory)
In the mathematical area of graph theory, a clique ( or ) is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent. That is, a clique of a graph G is an induced subgraph of G that is complete. Cliques are one of the basic concepts of graph theory and are used in many other mathematical problems and constructions on graphs. Cliques have also been studied in computer science: the task of finding whether there is a clique of a given size in a graph (the clique problem) is NP-complete, but despite this hardness result, many algorithms for finding cliques have been studied. Although the study of complete subgraphs goes back at least to the graph-theoretic reformulation of Ramsey theory by , the term ''clique'' comes from , who used complete subgraphs in social networks to model cliques of people; that is, groups of people all of whom know each other. Cliques have many other applications in the sciences and particularly in b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Database Algorithms
In computing, a database is an organized collection of data stored and accessed electronically. Small databases can be stored on a file system, while large databases are hosted on computer clusters or cloud storage. The design of databases spans formal techniques and practical considerations, including data modeling, efficient data representation and storage, query languages, security and privacy of sensitive data, and distributed computing issues, including supporting concurrent access and fault tolerance. A database management system (DBMS) is the software that interacts with end users, applications, and the database itself to capture and analyze the data. The DBMS software additionally encompasses the core facilities provided to administer the database. The sum total of the database, the DBMS and the associated applications can be referred to as a database system. Often the term "database" is also used loosely to refer to any of the DBMS, the database system or an application ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
