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Bipartite Dimension
In the mathematical fields of graph theory and combinatorial optimization, the bipartite dimension or biclique cover number of a graph ''G'' = (''V'', ''E'') is the minimum number of bicliques (that is complete bipartite subgraphs), needed to cover all edges in ''E''. A collection of bicliques covering all edges in ''G'' is called a biclique edge cover, or sometimes biclique cover. The bipartite dimension of ''G'' is often denoted by the symbol ''d''(''G''). Example An example for a biclique edge cover is given in the following diagrams: Image:Bipartite-dimension-bipartite-graph.svg, A bipartite graph... Image:Bipartite-dimension-biclique-cover.svg, ...and a covering with four bicliques Image:Bipartite-dimension-red-biclique.svg, the red biclique from the cover Image:Bipartite-dimension-blue-biclique.svg, the blue biclique from the cover Image:Bipartite-dimension-green-biclique.svg, the green biclique from the cover Image:Bipartite-dimension-black-biclique.svg, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Graph Theory
In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are connected by '' edges'' (also called ''links'' or ''lines''). A distinction is made between undirected graphs, where edges link two vertices symmetrically, and directed graphs, where edges link two vertices asymmetrically. Graphs are one of the principal objects of study in discrete mathematics. Definitions Definitions in graph theory vary. The following are some of the more basic ways of defining graphs and related mathematical structures. Graph In one restricted but very common sense of the term, a graph is an ordered pair G=(V,E) comprising: * V, a set of vertices (also called nodes or points); * E \subseteq \, a set of edges (also called links or lines), which are unordered pairs of vertices (that is, an edge is associated with t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hardness Of Approximation
In computer science, hardness of approximation is a field that studies the algorithmic complexity of finding near-optimal solutions to optimization problems. Scope Hardness of approximation complements the study of approximation algorithms by proving, for certain problems, a limit on the factors with which their solution can be efficiently approximated. Typically such limits show a factor of approximation beyond which a problem becomes NP-hard, implying that finding a polynomial time approximation for the problem is impossible unless NP=P. Some hardness of approximation results, however, are based on other hypotheses, a notable one among which is the unique games conjecture. History Since the early 1970s it was known that many optimization problems could not be solved in polynomial time unless P = NP, but in many of these problems the optimal solution could be efficiently approximated to a certain degree. In the 1970s, Teofilo F. Gonzalez and Sartaj Sahni began the study of ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SIAM Journal On Discrete Mathematics
'' SIAM Journal on Discrete Mathematics'' is a peer-reviewed mathematics journal published quarterly by the Society for Industrial and Applied Mathematics (SIAM). The journal includes articles on pure and applied discrete mathematics. It was established in 1988, along with the ''SIAM Journal on Matrix Analysis and Applications'', to replace the ''SIAM Journal on Algebraic and Discrete Methods''. The journal is indexed by ''Mathematical Reviews'' and Zentralblatt MATH. Its 2009 MCQ was 0.57. According to the ''Journal Citation Reports'', the journal has a 2016 impact factor of 0.755. Although its official ISO abbreviation is ''SIAM J. Discrete Math.'', its publisher and contributors frequently use the shorter abbreviation ''SIDMA''. References External links * Combinatorics journals Publications established in 1988 English-language journals Discrete Mathematics Discrete mathematics is the study of mathematical structures that can be considered "discrete" (in a way ana ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Indagationes Mathematicae
''Indagationes Mathematicae'' (from Latin: ''inquiry, search, investigation of the mathematics'') is a Dutch mathematics journal. The journal originates from the ''Proceedings of the Royal Netherlands Academy of Arts and Sciences'' (or ''Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen''), founded in 1895. From 1939, mathematics articles in this journal were published separately, under the alternative title ''Indagationes Mathematicae''. In 1951 the proceedings officially split into three journals, keeping the same name but distinguished from each other by being in separate series. They were Series A (Mathematical Sciences), Series B (Physical Sciences), and Series C (Biological and Medical Sciences). At that time, Series A became published by the North-Holland Publishing Company; the volumes from this time are now listed by the publisher as ''Indagationes Mathematicae (Proceedings)''. [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Computer Science (journal)
''Theoretical Computer Science'' (TCS) is a computer science journal published by Elsevier, started in 1975 and covering theoretical computer science. The journal publishes 52 issues a year. It is abstracted and indexed by Scopus and the Science Citation Index. According to the Journal Citation Reports, its 2020 impact factor The impact factor (IF) or journal impact factor (JIF) of an academic journal is a scientometric index calculated by Clarivate that reflects the yearly mean number of citations of articles published in the last two years in a given journal, as i ... is 0.827. References Computer science journals Elsevier academic journals Publications established in 1975 {{comp-sci-theory-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Mathematics (journal)
''Discrete Mathematics'' is a biweekly peer-reviewed scientific journal in the broad area of discrete mathematics, combinatorics, graph theory, and their applications. It was established in 1971 and is published by North-Holland Publishing Company. It publishes both short notes, full length contributions, as well as survey articles. In addition, the journal publishes a number of special issues each year dedicated to a particular topic. Although originally it published articles in French and German, it now allows only English language articles. The editor-in-chief is Douglas West ( University of Illinois, Urbana). History The journal was established in 1971. The very first article it published was written by Paul Erdős, who went on to publish a total of 84 papers in the journal. Abstracting and indexing The journal is abstracted and indexed in: According to the ''Journal Citation Reports'', the journal has a 2020 impact factor of 0.87. Notable publications * The 1972 ... [...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 bioinf ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intersection Number (graph Theory)
In the mathematical field of graph theory, the intersection number of a graph G=(V,E) is the smallest number of elements in a representation of G as an intersection graph of finite sets. In such a representation, each vertex is represented as a set, and two vertices are connected by an edge whenever their sets have a common element. Equivalently, the intersection number is the smallest number of cliques needed to cover all of the edges of G. A set of cliques that cover all edges of a graph is called a clique edge cover or edge clique cover, or even just a clique cover, although the last term is ambiguous: a clique cover can also be a set of cliques that cover all vertices of a graph. Sometimes "covering" is used in place of "cover". As well as being called the intersection number, the minimum number of these cliques has been called the ''R''-content, edge clique cover number, or clique cover number. The problem of computing the intersection number has been called the intersection ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of NP-complete Problems
This is a list of some of the more commonly known problems that are NP-complete when expressed as decision problems. As there are hundreds of such problems known, this list is in no way comprehensive. Many problems of this type can be found in . Graphs and hypergraphs Graphs occur frequently in everyday applications. Examples include biological or social networks, which contain hundreds, thousands and even billions of nodes in some cases (e.g. Facebook or LinkedIn). * 1-planarity *3-dimensional matching * Bandwidth problem *Bipartite dimension * Capacitated minimum spanning tree *Route inspection problem (also called Chinese postman problem) for mixed graphs (having both directed and undirected edges). The program is solvable in polynomial time if the graph has all undirected or all directed edges. Variants include the rural postman problem. * Clique cover problem *Clique problem *Complete coloring, a.k.a. achromatic number *Cycle rank a.k.a. Rank coloring * Degree-constrained s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Human Leukocyte Antigen
The human leukocyte antigen (HLA) system or complex is a complex of genes on chromosome 6 in humans which encode cell-surface proteins responsible for the regulation of the immune system. The HLA system is also known as the human version of the major histocompatibility complex (MHC) found in many animals. Mutations in HLA genes may be linked to autoimmune disease such as type I diabetes, and celiac disease. The HLA gene complex resides on a 3 Mbp stretch within chromosome 6, p-arm at 21.3. HLA genes are highly polymorphic, which means that they have many different alleles, allowing them to fine-tune the adaptive immune system. The proteins encoded by certain genes are also known as ''antigens'', as a result of their historic discovery as factors in organ transplants. HLAs corresponding to MHC class I ( A, B, and C), all of which are the HLA Class1 group, present peptides from inside the cell. For example, if the cell is infected by a virus, the HLA system brings fragme ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Broadcast
Broadcasting is the distribution of audio or video content to a dispersed audience via any electronic mass communications medium, but typically one using the electromagnetic spectrum ( radio waves), in a one-to-many model. Broadcasting began with AM radio, which came into popular use around 1920 with the spread of vacuum tube radio transmitters and receivers. Before this, all forms of electronic communication (early radio, telephone, and telegraph) were one-to-one, with the message intended for a single recipient. The term ''broadcasting'' evolved from its use as the agricultural method of sowing seeds in a field by casting them broadly about. It was later adopted for describing the widespread distribution of information by printed materials or by telegraph. Examples applying it to "one-to-many" radio transmissions of an individual station to multiple listeners appeared as early as 1898. Over the air broadcasting is usually associated with radio and television, though more ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Security
Computer security, cybersecurity (cyber security), or information technology security (IT security) is the protection of computer systems and networks from attack by malicious actors that may result in unauthorized information disclosure, theft of, or damage to hardware, software, or data, as well as from the disruption or misdirection of the services they provide. The field has become of significance due to the expanded reliance on computer systems, the Internet, and wireless network standards such as Bluetooth and Wi-Fi, and due to the growth of smart devices, including smartphones, televisions, and the various devices that constitute the Internet of things (IoT). Cybersecurity is one of the most significant challenges of the contemporary world, due to both the complexity of information systems and the societies they support. Security is of especially high importance for systems that govern large-scale systems with far-reaching physical effects, such as power distribution, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
