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Subgraph Matching
In theoretical computer science, the subgraph isomorphism problem is a computational task in which two graphs G and H are given as input, and one must determine whether G contains a subgraph that is isomorphic to H. Subgraph isomorphism is a generalization of both the maximum clique problem and the problem of testing whether a graph contains a Hamiltonian cycle, and is therefore NP-complete. However certain other cases of subgraph isomorphism may be solved in polynomial time. Sometimes the name subgraph matching is also used for the same problem. This name puts emphasis on finding such a subgraph as opposed to the bare decision problem. Decision problem and computational complexity To prove subgraph isomorphism is NP-complete, it must be formulated as a decision problem. The input to the decision problem is a pair of graphs G and ''H''. The answer to the problem is positive if ''H'' is isomorphic to a subgraph of ''G'', and negative otherwise. Formal question: Let G=(V,E), H= ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subgraph Isomorphism
The term subgraph can refer to: *The security-focused Linux-based Subgraph operating system, see Subgraph (operating system) *Subgraph of a function, see Hypograph (mathematics) *In graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ..., see Glossary of graph theory#subgraph {{Disambig ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aanderaa–Karp–Rosenberg Conjecture
In theoretical computer science, the Aanderaa–Karp–Rosenberg conjecture (also known as the Aanderaa–Rosenberg conjecture or the evasiveness conjecture) is a group of related conjectures about the number of questions of the form "Is there an edge between vertex u and vertex v?" that have to be answered to determine whether or not an undirected graph has a particular property such as planarity or bipartiteness. They are named after Stål Aanderaa, Richard M. Karp, and Arnold L. Rosenberg. According to the conjecture, for a wide class of properties, no algorithm can guarantee that it will be able to skip any questions: any algorithm for determining whether the graph has the property, no matter how clever, might need to examine every pair of vertices before it can give its answer. A property satisfying this conjecture is called evasive. More precisely, the Aanderaa–Rosenberg conjecture states that any deterministic algorithm must test at least a constant fraction of all p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
SMILES
A smile is a facial expression formed primarily by flexing the muscles at the sides of the mouth. Some smiles include a contraction of the muscles at the corner of the eyes, an action known as a Duchenne smile. Among humans, a smile expresses delight, sociability, happiness, joy, or amusement. It is distinct from a similar but usually involuntary expression of anxiety known as a grimace. Although cross-cultural studies have shown that smiling is a means of communication throughout the world, there are large differences among different cultures, religions, and societies, with some using smiles to convey confusion, embarrassment, or awkwardness. Evolutionary background Primatologist Signe Preuschoft traces the smile back over 30 million years of evolution to a "fear grin" stemming from monkeys and apes, who often used barely clenched teeth to portray to predators that they were harmless or to signal submission to more dominant group members. The smile may have evolved differen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structure Editor
A structure editor, also structured editor or projectional editor, is any document editor that is cognizant of the document's underlying structure. Structure editors can be used to edit hierarchical or marked up text, computer programs, diagrams, chemical formulas, and any other type of content with clear and well-defined structure. In contrast, a text editor is any document editor used for editing plain text files. Typically, the benefits of text and structure editing are combined in the user interface of a single hybrid tool. For example, Emacs is fundamentally a text editor, but supports the manipulation of words, sentences, and paragraphs as structures that are inferred from the text. Conversely, Dreamweaver is fundamentally a structure editor for marked up web documents, but supports the display and manipulation of raw HTML Hypertext Markup Language (HTML) is the standard markup language for documents designed to be displayed in a web browser. It defines the content an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Substructure Search
Substructure search (SSS) is a method to retrieve from a Chemical database, database only those Chemical compound, chemicals matching a pattern of atoms and bonds which a user specifies. It is an application of graph theory, specifically subgraph matching in which the query is a hydrogen-depleted molecular graph. The mathematical foundations for the method were laid in the 1870s, when it was suggested that Molecule editor, chemical structure drawings were equivalent to graphs with atoms as vertices and bonds as edges. SSS is now a standard part of cheminformatics and is widely used by pharmaceutical chemists in drug discovery. There are many commercial systems that provide SSS, typically having a graphical user interface and chemical drawing software. Large publicly-available databases like PubChem and ChemSpider can be searched this way, as can Wikipedia's articles describing individual chemicals. Definitions Substructure search is used to retrieve from a chemical database, data ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Structural Formula
The structural formula of a chemical compound is a graphic representation of the molecular structure (determined by structural chemistry methods), showing how the atoms are connected to one another. The chemical bonding within the molecule is also shown, either explicitly or implicitly. Unlike other chemical formula types, which have a limited number of symbols and are capable of only limited descriptive power, structural formulas provide a more complete geometric representation of the molecular structure. For example, many chemical compounds exist in different isomeric forms, which have different enantiomeric structures but the same molecular formula. There are multiple types of ways to draw these structural formulas such as: Lewis structures, condensed formulas, skeletal formulas, Newman projections, Cyclohexane conformations, Haworth projections, and Fischer projections. Several systematic chemical naming formats, as in chemical databases, are used that are equivalent to, an ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cheminformatics
Cheminformatics (also known as chemoinformatics) refers to the use of physical chemistry theory with computer and information science techniques—so called "'' in silico''" techniques—in application to a range of descriptive and prescriptive problems in the field of chemistry, including in its applications to biology and related molecular fields. Such '' in silico'' techniques are used, for example, by pharmaceutical companies and in academic settings to aid and inform the process of drug discovery, for instance in the design of well-defined combinatorial libraries of synthetic compounds, or to assist in structure-based drug design. The methods can also be used in chemical and allied industries, and such fields as environmental science and pharmacology, where chemical processes are involved or studied. History Cheminformatics has been an active field in various guises since the 1970s and earlier, with activity in academic departments and commercial pharmaceutical rese ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constraint Programming
Constraint programming (CP) is a paradigm for solving combinatorial problems that draws on a wide range of techniques from artificial intelligence, computer science, and operations research. In constraint programming, users declaratively state the constraints on the feasible solutions for a set of decision variables. Constraints differ from the common primitives of imperative programming languages in that they do not specify a step or sequence of steps to execute, but rather the properties of a solution to be found. In addition to constraints, users also need to specify a method to solve these constraints. This typically draws upon standard methods like chronological backtracking and constraint propagation, but may use customized code like a problem-specific branching heuristic. Constraint programming takes its root from and can be expressed in the form of constraint logic programming, which embeds constraints into a logic program. This variant of logic programming is due ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Time
In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a fixed amount of time to perform. Thus, the amount of time taken and the number of elementary operations performed by the algorithm are taken to be related by a constant factor. Since an algorithm's running time may vary among different inputs of the same size, one commonly considers the worst-case time complexity, which is the maximum amount of time required for inputs of a given size. Less common, and usually specified explicitly, is the average-case complexity, which is the average of the time taken on inputs of a given size (this makes sense because there are only a finite number of possible inputs of a given size). In both cases, the time complexity is gene ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bounded Expansion
In graph theory, a family of graphs is said to have bounded expansion if all of its shallow minors are sparse graphs. Many natural families of sparse graphs have bounded expansion. A closely related but stronger property, polynomial expansion, is equivalent to the existence of separator theorems for these families. Families with these properties have efficient algorithms for problems including the subgraph isomorphism problem and model checking for the first order theory of graphs. Definition and equivalent characterizations A ''t''-shallow minor of a graph ''G'' is defined to be a graph formed from ''G'' by contracting a collection of vertex-disjoint subgraphs of radius ''t'', and deleting the remaining vertices of ''G''. A family of graphs has bounded expansion if there exists a function ''f'' such that, in every ''t''-shallow minor of a graph in the family, the ratio of edges to vertices is at most ''f''(''t'').. Equivalent definitions of classes of bounded expansions are th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Planar Graph
In graph theory, a planar graph is a graph (discrete mathematics), graph that can be graph embedding, embedded in the plane (geometry), plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. In other words, it can be drawn in such a way that no edges cross each other. Such a drawing is called a plane graph, or a planar embedding of the graph. A plane graph can be defined as a planar graph with a mapping from every node to a point on a plane, and from every edge to a plane curve on that plane, such that the extreme points of each curve are the points mapped from its end nodes, and all curves are disjoint except on their extreme points. Every graph that can be drawn on a plane can be drawn on the sphere as well, and vice versa, by means of stereographic projection. Plane graphs can be encoded by combinatorial maps or rotation systems. An equivalence class of topologically equivalent drawings on the sphere, usually with addit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
