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Maximum Common Induced Subgraph
In graph theory and theoretical computer science, a maximum common induced subgraph of two graphs ''G'' and ''H'' is a graph that is an induced subgraph of both ''G'' and ''H'', and that has as many vertices as possible. Finding this graph is NP-hard. In the associated decision problem, the input is two graphs ''G'' and ''H'' and a number ''k''. The problem is to decide whether ''G'' and ''H'' have a common induced subgraph with at least ''k'' vertices. This problem is NP-complete. It is a generalization of the induced subgraph isomorphism problem, which arises when ''k'' equals the number of vertices in the smaller of ''G'' and ''H'', so that this entire graph must appear as an induced subgraph of the other graph. Based on hardness of approximation results for the maximum independent set problem, the maximum common induced subgraph problem is also hard to approximate. This implies that, unless P = NP, there is no approximation algorithm that, in polynomial time on n-vertex graphs, ... [...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] |
Symposium On Theory Of Computing
The Annual ACM Symposium on Theory of Computing (STOC) is an academic conference in the field of theoretical computer science. STOC has been organized annually since 1969, typically in May or June; the conference is sponsored by the Association for Computing Machinery special interest group SIGACT. Acceptance rate of STOC, averaged from 1970 to 2012, is 31%, with the rate of 29% in 2012. As writes, STOC and its annual IEEE counterpart FOCS (the Symposium on Foundations of Computer Science) are considered the two top conferences in theoretical computer science, considered broadly: they “are forums for some of the best work throughout theory of computing that promote breadth among theory of computing researchers and help to keep the community together.” includes regular attendance at STOC and FOCS as one of several defining characteristics of theoretical computer scientists. Awards The Gödel Prize for outstanding papers in theoretical computer science is presented alternately ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NP-complete Problems
In computational complexity theory, a problem is NP-complete when: # it is a problem for which the correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying all possible solutions. # the problem can be used to simulate every other problem for which we can verify quickly that a solution is correct. In this sense, NP-complete problems are the hardest of the problems to which solutions can be verified quickly. If we could find solutions of some NP-complete problem quickly, we could quickly find the solutions of every other problem to which a given solution can be easily verified. The name "NP-complete" is short for "nondeterministic polynomial-time complete". In this name, "nondeterministic" refers to nondeterministic Turing machines, a way of mathematically formalizing the idea of a brute-force search algorithm. Polynomial time refers to an amount of time that is considered "quick" for a det ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Maximum Common Edge Subgraph
Given two graphs G and G', the maximum common edge subgraph problem is the problem of finding a graph H with as many edges as possible which is isomorphic to both a subgraph of G and a subgraph of G'. The maximum common edge subgraph problem on general graphs is NP-complete as it is a generalization of subgraph isomorphism 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 isomorp ...: a graph H is isomorphic to a subgraph of another graph G if and only if the maximum common edge subgraph of G and H has the same number of edges as H. Unless the two inputs G and G' to the maximum common edge subgraph problem are required to have the same number of vertices, the problem is APX-hard.. See also * Maximum common subgraph isomorphism problem * Subgraph isomorphism problem * Induced subgraph iso ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Molecule Mining
This page describes mining for molecules. Since molecules may be represented by molecular graphs this is strongly related to graph mining and structured data mining. The main problem is how to represent molecules while discriminating the data instances. One way to do this is chemical similarity metrics, which has a long tradition in the field of cheminformatics. Typical approaches to calculate chemical similarities use chemical fingerprints, but this loses the underlying information about the molecule topology. Mining the molecular graphs directly avoids this problem. So does the inverse QSAR problem which is preferable for vectorial mappings. Coding(Moleculei,Moleculej\neqi) Kernel methods * Marginalized graph kernelH. Kashima, K. Tsuda, A. Inokuchi, Marginalized Kernels Between Labeled Graphs, The 20th International Conference on Machine Learning (ICML2003), 2003. PDF * Optimal assignment kernelH. Fröhlich, J. K. Wegner, A. Zell, ''Optimal Assignment Kernels For Attrib ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pharmacophore
300px, An example of a pharmacophore model. A pharmacophore is an abstract description of molecular features that are necessary for molecular recognition of a ligand by a biological macromolecule. IUPAC defines a pharmacophore to be "an ensemble of steric and electronic features that is necessary to ensure the optimal supramolecular interactions with a specific biological target and to trigger (or block) its biological response". A pharmacophore model explains how structurally diverse ligands can bind to a common receptor site. Furthermore, pharmacophore models can be used to identify through de novo design or virtual screening novel ligands that will bind to the same receptor. Features Typical pharmacophore features include hydrophobic centroids, aromatic rings, hydrogen bond acceptors or donors, cations, and anions. These pharmacophoric points may be located on the ligand itself or may be projected points presumed to be located in the receptor. The features need to match ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cheminformatics
Cheminformatics (also known as chemoinformatics) refers to 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 research and de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
PageRank
PageRank (PR) is an algorithm used by Google Search to rank web pages in their search engine results. It is named after both the term "web page" and co-founder Larry Page. PageRank is a way of measuring the importance of website pages. According to Google: Currently, PageRank is not the only algorithm used by Google to order search results, but it is the first algorithm that was used by the company, and it is the best known. As of September 24, 2019, PageRank and all associated patents are expired. Description PageRank is a link analysis algorithm and it assigns a numerical weighting to each element of a hyperlinked set of documents, such as the World Wide Web, with the purpose of "measuring" its relative importance within the set. The algorithm may be applied to any collection of entities with reciprocal quotations and references. The numerical weight that it assigns to any given element ''E'' is referred to as the ''PageRank of E'' and denoted by PR(E). A PageRank re ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reinforcement Learning
Reinforcement learning (RL) is an area of machine learning concerned with how intelligent agents ought to take actions in an environment in order to maximize the notion of cumulative reward. Reinforcement learning is one of three basic machine learning paradigms, alongside supervised learning and unsupervised learning. Reinforcement learning differs from supervised learning in not needing labelled input/output pairs to be presented, and in not needing sub-optimal actions to be explicitly corrected. Instead the focus is on finding a balance between exploration (of uncharted territory) and exploitation (of current knowledge). The environment is typically stated in the form of a Markov decision process (MDP), because many reinforcement learning algorithms for this context use dynamic programming techniques. The main difference between the classical dynamic programming methods and reinforcement learning algorithms is that the latter do not assume knowledge of an exact mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Look-ahead (backtracking)
In backtracking algorithms, look ahead is the generic term for a subprocedure that attempts to foresee the effects of choosing a branching variable to evaluate one of its values. The two main aims of look-ahead are to choose a variable to evaluate next and the order of values to assign to it. Constraint satisfaction In a general constraint satisfaction problem, every variable can take a value in a domain. A backtracking algorithm therefore iteratively chooses a variable and tests each of its possible values; for each value the algorithm is recursively run. Look ahead is used to check the effects of choosing a given variable to evaluate or to decide the order of values to give to it. Look ahead techniques The simpler technique for evaluating the effect of a specific assignment to a variable is called forward checking. Given the current partial solution and a candidate assignment to evaluate, it checks whether another variable can take a consistent value. In other words, it f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Clique Problem
In computer science, the clique problem is the computational problem of finding cliques (subsets of vertices, all adjacent to each other, also called complete subgraphs) in a graph. It has several different formulations depending on which cliques, and what information about the cliques, should be found. Common formulations of the clique problem include finding a maximum clique (a clique with the largest possible number of vertices), finding a maximum weight clique in a weighted graph, listing all maximal cliques (cliques that cannot be enlarged), and solving the decision problem of testing whether a graph contains a clique larger than a given size. The clique problem arises in the following real-world setting. Consider a social network, where the graph's vertices represent people, and the graph's edges represent mutual acquaintance. Then a clique represents a subset of people who all know each other, and algorithms for finding cliques can be used to discover these groups of ... [...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] |
