109 relations: Algorithmica, Approximation algorithm, Arc diagram, Automatic label placement, Backtracking, Binary image, Boolean algebra, Boolean expression, Boolean satisfiability problem, Clause (logic), Cluster analysis, Combinatorica, Complete bipartite graph, Completeness (logic), Complexity class, Computational complexity theory, Computational Geometry (journal), Computational problem, Computer science, Conjunctive normal form, Constraint (mathematics), Constraint satisfaction problem, Counting problem (complexity), Cut (graph theory), Davis–Putnam algorithm, Depth-first search, Diameter, Directed acyclic graph, Directed graph, Discrete Applied Mathematics, Discrete Mathematics (journal), Discrete tomography, Dynamic programming, Equivalence relation, Existential quantification, Exponential time hypothesis, First-order logic, Graph (discrete mathematics), Graph automorphism, Graph drawing, Graph theory, Hamming distance, Heuristic, Horn-satisfiability, Identity matrix, Immerman–Szelepcsényi theorem, Implication graph, Implicit graph, Independent set (graph theory), Information Processing Letters, ..., Interpretation (logic), Journal of Computer and System Sciences, Journal of Graph Algorithms and Applications, Journal of the ACM, Kosaraju's algorithm, Limit of a sequence, Literal (mathematical logic), Logarithm, Logical conjunction, Logical disjunction, Logical equivalence, Logical matrix, Majority function, Many-valued logic, Maximum flow problem, Maximum satisfiability problem, Median graph, Metric space, Necessity and sufficiency, NL (complexity), NL-complete, Nonogram, NP (complexity), NP-completeness, NP-hardness, Orthogonal convex hull, P versus NP problem, Parameterized complexity, Path-based strong component algorithm, Phase transition, Phylogenetic tree, Pixel, Polynomial-time approximation scheme, Polyomino, Resolution (logic), Round-robin tournament, RP (complexity), Second-order logic, Semidefinite programming, Sharp-P-complete, SIAM Journal on Computing, SIAM Journal on Discrete Mathematics, Skew-symmetric graph, Square lattice, Strongly connected component, Symposium on Computational Geometry, Tarjan's strongly connected components algorithm, Theoretical Computer Science (journal), Time complexity, Tomography, Topological sorting, Transitive closure, Transitive relation, True quantified Boolean formula, Unique games conjecture, University of California, Davis, Vertex (graph theory), Vertex cover, Very-large-scale integration. Expand index (59 more) » « Shrink index
Algorithmica is a monthly peer reviewed, scientific journal, published by Springer Science+Business Media focused on research and application of computer science algorithms.
In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to NP-hard optimization problems with provable guarantees on the distance of the returned solution to the optimal one.
In graph drawing, an arc diagram is a style of graph drawing, in which the vertices of a graph are placed along a line in the Euclidean plane, with edges being drawn as semicircles in one of the two halfplanes bounded by the line, or as smooth curves formed by sequences of semicircles.
Automatic label placement, sometimes called text placement or name placement, comprises the computer methods of placing labels automatically on a map or chart.
Backtracking is a general algorithm for finding all (or some) solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, and abandons a candidate ("backtracks") as soon as it determines that the candidate cannot possibly be completed to a valid solution.
A binary image is a digital image that has only two possible values for each pixel.
In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.
In computer science, a Boolean expression is an expression in a programming language that produces a Boolean value when evaluated, i.e. one of true or false.
In computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated as SATISFIABILITY or SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula.
In logic, a clause is an expression formed from a finite collection of literals (atoms or their negations) that is true either whenever at least one of the literals that form it is true (a disjunctive clause, the most common use of the term), or when all of the literals that form it are true (a conjunctive clause, a less common use of the term).
Cluster analysis or clustering is the task of grouping a set of objects in such a way that objects in the same group (called a cluster) are more similar (in some sense) to each other than to those in other groups (clusters).
Combinatorica is an international journal of mathematics, publishing papers in the fields of combinatorics and computer science.
In mathematical logic and metalogic, a formal system is called complete with respect to a particular property if every formula having the property can be derived using that system, i.e. is one of its theorems; otherwise the system is said to be incomplete.
In computational complexity theory, a complexity class is a set of problems of related resource-based complexity.
Computational complexity theory is a branch of the theory of computation in theoretical computer science that focuses on classifying computational problems according to their inherent difficulty, and relating those classes to each other.
Computational Geometry, also known as Computational Geometry: Theory and Applications, is a peer-reviewed mathematics journal for research in theoretical and applied computational geometry, its applications, techniques, and design and analysis of geometric algorithms.
In theoretical computer science, a computational problem is a mathematical object representing a collection of questions that computers might be able to solve.
Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.
In Boolean logic, a formula is in conjunctive normal form (CNF) or clausal normal form if it is a conjunction of one or more clauses, where a clause is a disjunction of literals; otherwise put, it is an AND of ORs.
In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy.
Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations.
In computational complexity theory and computability theory, a counting problem is a type of computational problem.
In graph theory, a cut is a partition of the vertices of a graph into two disjoint subsets.
The Davis–Putnam algorithm was developed by Martin Davis and Hilary Putnam for checking the validity of a first-order logic formula using a resolution-based decision procedure for propositional logic.
Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures.
In geometry, a diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circle.
In mathematics and computer science, a directed acyclic graph (DAG), is a finite directed graph with no directed cycles.
In mathematics, and more specifically in graph theory, a directed graph (or digraph) is a graph that is a set of vertices connected by edges, where the edges have a direction associated with them.
Discrete Applied Mathematics is a peer-reviewed academic journal in mathematics, published by Elsevier.
Discrete Mathematics is a biweekly peer-reviewed scientific journal in the broad area of discrete mathematics, combinatorics, graph theory, and their applications.
Discrete tomography Herman, G. T. and Kuba, A., Discrete Tomography: Foundations, Algorithms, and Applications, Birkhäuser Boston, 1999 Herman, G. T. and Kuba, A., Advances in Discrete Tomography and Its Applications, Birkhäuser Boston, 2007 focuses on the problem of reconstruction of binary images (or finite subsets of the integer lattice) from a small number of their projections.
Dynamic programming is both a mathematical optimization method and a computer programming method.
In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.
In predicate logic, an existential quantification is a type of quantifier, a logical constant which is interpreted as "there exists", "there is at least one", or "for some".
In computational complexity theory, the exponential time hypothesis is an unproven computational hardness assumption that was formulated by.
First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.
In 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".
In the mathematical field of graph theory, an automorphism of a graph is a form of symmetry in which the graph is mapped onto itself while preserving the edge–vertex connectivity.
Graph drawing is an area of mathematics and computer science combining methods from geometric graph theory and information visualization to derive two-dimensional depictions of graphs arising from applications such as social network analysis, cartography, linguistics, and bioinformatics.
In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.
In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different.
A heuristic technique (εὑρίσκω, "find" or "discover"), often called simply a heuristic, is any approach to problem solving, learning, or discovery that employs a practical method, not guaranteed to be optimal, perfect, logical, or rational, but instead sufficient for reaching an immediate goal.
In formal logic, Horn-satisfiability, or HORNSAT, is the problem of deciding whether a given set of propositional Horn clauses is satisfiable or not.
In linear algebra, the identity matrix, or sometimes ambiguously called a unit matrix, of size n is the n × n square matrix with ones on the main diagonal and zeros elsewhere.
In computational complexity theory, the Immerman–Szelepcsényi theorem states that nondeterministic space complexity classes are closed under complementation.
In mathematical logic, an implication graph is a skew-symmetric directed graph G(V, E) composed of vertex set V and directed edge set E. Each vertex in V represents the truth status of a Boolean literal, and each directed edge from vertex u to vertex v represents the material implication "If the literal u is true then the literal v is also true".
In the study of graph algorithms, an implicit graph representation (or more simply implicit graph) is a graph whose vertices or edges are not represented as explicit objects in a computer's memory, but rather are determined algorithmically from some more concise input.
In graph theory, an independent set or stable set is a set of vertices in a graph, no two of which are adjacent.
Information Processing Letters is a peer reviewed scientific journal in the field of computer science, published by Elsevier.
An interpretation is an assignment of meaning to the symbols of a formal language.
The Journal of Computer and System Sciences (JCSS) is a peer-reviewed scientific journal in the field of computer science.
The Journal of Graph Algorithms and Applications is an open access peer-reviewed scientific journal covering the subject of graph algorithms and graph drawing.
The Journal of the ACM is a peer-reviewed scientific journal covering computer science in general, especially theoretical aspects.
In computer science, Kosaraju's algorithm (also known as the Kosaraju–Sharir algorithm) is a linear time algorithm to find the strongly connected components of a directed graph.
As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.
In mathematical logic, a literal is an atomic formula (atom) or its negation.
In mathematics, the logarithm is the inverse function to exponentiation.
In logic, mathematics and linguistics, And (∧) is the truth-functional operator of logical conjunction; the and of a set of operands is true if and only if all of its operands are true.
In logic and mathematics, or is the truth-functional operator of (inclusive) disjunction, also known as alternation; the or of a set of operands is true if and only if one or more of its operands is true.
In logic, statements p and q are logically equivalent if they have the same logical content.
A logical matrix, binary matrix, relation matrix, Boolean matrix, or (0,1) matrix is a matrix with entries from the Boolean domain Such a matrix can be used to represent a binary relation between a pair of finite sets.
In Boolean logic, the majority function (also called the median operator) is a function from n inputs to one output.
In logic, a many-valued logic (also multi- or multiple-valued logic) is a propositional calculus in which there are more than two truth values.
In optimization theory, maximum flow problems involve finding a feasible flow through a single-source, single-sink flow network that is maximum.
In computational complexity theory, the maximum satisfiability problem (MAX-SAT) is the problem of determining the maximum number of clauses, of a given Boolean formula in conjunctive normal form, that can be made true by an assignment of truth values to the variables of the formula.
In graph theory, a division of mathematics, a median graph is an undirected graph in which every three vertices a, b, and c have a unique median: a vertex m(a,b,c) that belongs to shortest paths between each pair of a, b, and c. The concept of median graphs has long been studied, for instance by or (more explicitly) by, but the first paper to call them "median graphs" appears to be.
In mathematics, a metric space is a set for which distances between all members of the set are defined.
In logic, necessity and sufficiency are terms used to describe an implicational relationship between statements.
In computational complexity theory, NL (Nondeterministic Logarithmic-space) is the complexity class containing decision problems which can be solved by a nondeterministic Turing machine using a logarithmic amount of memory space.
In computational complexity theory, NL-complete is a complexity class containing the languages that are complete for NL, the class of decision problems that can be solved by a nondeterministic Turing machine using a logarithmic amount of memory space.
Nonograms, also known as Picross or Griddlers, are picture logic puzzles in which cells in a grid must be colored or left blank according to numbers at the side of the grid to reveal a hidden picture.
In computational complexity theory, NP (for nondeterministic polynomial time) is a complexity class used to describe certain types of decision problems.
In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes.
NP-hardness (''n''on-deterministic ''p''olynomial-time hardness), in computational complexity theory, is the defining property of a class of problems that are, informally, "at least as hard as the hardest problems in NP".
In geometry, a set is defined to be orthogonally convex if, for every line that is parallel to one of standard basis vectors, the intersection of with is empty, a point, or a single segment.
The P versus NP problem is a major unsolved problem in computer science.
In computer science, parameterized complexity is a branch of computational complexity theory that focuses on classifying computational problems according to their inherent difficulty with respect to multiple parameters of the input or output.
In graph theory, the strongly connected components of a directed graph may be found using an algorithm that uses depth-first search in combination with two stacks, one to keep track of the vertices in the current component and the second to keep track of the current search path.
The term phase transition (or phase change) is most commonly used to describe transitions between solid, liquid and gaseous states of matter, and, in rare cases, plasma.
A phylogenetic tree or evolutionary tree is a branching diagram or "tree" showing the evolutionary relationships among various biological species or other entities—their phylogeny—based upon similarities and differences in their physical or genetic characteristics.
In digital imaging, a pixel, pel, dots, or picture element is a physical point in a raster image, or the smallest addressable element in an all points addressable display device; so it is the smallest controllable element of a picture represented on the screen.
In computer science, a polynomial-time approximation scheme (PTAS) is a type of approximation algorithm for optimization problems (most often, NP-hard optimization problems).
A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge.
In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation theorem-proving technique for sentences in propositional logic and first-order logic.
A round-robin tournament (or all-play-all tournament) is a competition in which each contestant meets all other contestants in turn.
In computational complexity theory, randomized polynomial time (RP) is the complexity class of problems for which a probabilistic Turing machine exists with these properties.
In logic and mathematics second-order logic is an extension of first-order logic, which itself is an extension of propositional logic.
Semidefinite programming (SDP) is a subfield of convex optimization concerned with the optimization of a linear objective function (a user-specified function that the user wants to minimize or maximize) over the intersection of the cone of positive semidefinite matrices with an affine space, i.e., a spectrahedron.
#P-complete, pronounced "sharp P complete" or "number P complete" is a complexity class in computational complexity theory.
The SIAM Journal on Computing is a scientific journal focusing on the mathematical and formal aspects of computer science.
SIAM Journal on Discrete Mathematics is a peer-reviewed mathematics journal published quarterly by the Society for Industrial and Applied Mathematics (SIAM).
In graph theory, a branch of mathematics, a skew-symmetric graph is a directed graph that is isomorphic to its own transpose graph, the graph formed by reversing all of its edges, under an isomorphism that is an involution without any fixed points.
In mathematics, the square lattice is a type of lattice in a two-dimensional Euclidean space.
In the mathematical theory of directed graphs, a graph is said to be strongly connected or diconnected if every vertex is reachable from every other vertex.
The Annual Symposium on Computational Geometry (SoCG) is an academic conference in computational geometry.
Tarjan's algorithm is an algorithm in graph theory for finding the strongly connected components of a graph.
Theoretical Computer Science (TCS) is a computer science journal published by Elsevier, started in 1975 and covering theoretical computer science.
In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.
Tomography is imaging by sections or sectioning, through the use of any kind of penetrating wave.
In the field of computer science, a topological sort or topological ordering of a directed graph is a linear ordering of its vertices such that for every directed edge uv from vertex u to vertex v, u comes before v in the ordering.
In mathematics, the transitive closure of a binary relation R on a set X is the smallest relation on X that contains R and is transitive.
In mathematics, a binary relation over a set is transitive if whenever an element is related to an element and is related to an element then is also related to.
In computational complexity theory, the language TQBF is a formal language consisting of the true quantified Boolean formulas.
In computational complexity theory, the unique games conjecture is a conjecture made by Subhash Khot in 2002.
The University of California, Davis (also referred to as UCD, UC Davis, or Davis), is a public research university and land-grant university as well as one of the 10 campuses of the University of California (UC) system.
In 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 the mathematical discipline of graph theory, a vertex cover (sometimes node cover) of a graph is a set of vertices such that each edge of the graph is incident to at least one vertex of the set.
Very-large-scale integration (VLSI) is the process of creating an integrated circuit (IC) by combining hundreds of thousands of transistors or devices into a single chip.