Communication
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# 2-satisfiability

In computer science, 2-satisfiability, 2-SAT or just 2SAT is a computational problem of assigning values to variables, each of which has two possible values, in order to satisfy a system of constraints on pairs of variables. [1]

## Algorithmica

Algorithmica is a monthly peer reviewed, scientific journal, published by Springer Science+Business Media focused on research and application of computer science algorithms.

## Approximation algorithm

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.

## Arc diagram

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

Automatic label placement, sometimes called text placement or name placement, comprises the computer methods of placing labels automatically on a map or chart.

## Backtracking

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.

## Binary image

A binary image is a digital image that has only two possible values for each pixel.

## Boolean algebra

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.

## Boolean expression

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.

## Boolean satisfiability problem

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.

## Clause (logic)

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

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

Combinatorica is an international journal of mathematics, publishing papers in the fields of combinatorics and computer science.

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## Completeness (logic)

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.

## Complexity class

In computational complexity theory, a complexity class is a set of problems of related resource-based complexity.

## Computational complexity theory

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 (journal)

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.

## Computational problem

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

Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.

## Conjunctive normal form

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.

## Constraint (mathematics)

In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy.

## Constraint satisfaction problem

Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations.

## Counting problem (complexity)

In computational complexity theory and computability theory, a counting problem is a type of computational problem.

## Cut (graph theory)

In graph theory, a cut is a partition of the vertices of a graph into two disjoint subsets.

## Davis–Putnam algorithm

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

Depth-first search (DFS) is an algorithm for traversing or searching tree or graph data structures.

## Diameter

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.

## Directed acyclic graph

In mathematics and computer science, a directed acyclic graph (DAG), is a finite directed graph with no directed cycles.

## Directed graph

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

Discrete Applied Mathematics is a peer-reviewed academic journal in mathematics, published by Elsevier.

## 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.

## Discrete tomography

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

Dynamic programming is both a mathematical optimization method and a computer programming method.

## Equivalence relation

In mathematics, an equivalence relation is a binary relation that is reflexive, symmetric and transitive.

## Existential quantification

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".

## Exponential time hypothesis

In computational complexity theory, the exponential time hypothesis is an unproven computational hardness assumption that was formulated by.

## First-order logic

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.

## Graph (discrete mathematics)

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".

## Graph automorphism

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

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.

## Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

## Hamming distance

In information theory, the Hamming distance between two strings of equal length is the number of positions at which the corresponding symbols are different.

## Heuristic

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.

## Horn-satisfiability

In formal logic, Horn-satisfiability, or HORNSAT, is the problem of deciding whether a given set of propositional Horn clauses is satisfiable or not.

## Identity matrix

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.

## Immerman–Szelepcsényi theorem

In computational complexity theory, the Immerman–Szelepcsényi theorem states that nondeterministic space complexity classes are closed under complementation.

## Implication graph

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".

## Implicit graph

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.

## Independent set (graph theory)

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

Information Processing Letters is a peer reviewed scientific journal in the field of computer science, published by Elsevier.

## Interpretation (logic)

An interpretation is an assignment of meaning to the symbols of a formal language.

## Journal of Computer and System Sciences

The Journal of Computer and System Sciences (JCSS) is a peer-reviewed scientific journal in the field of computer science.

## Journal of Graph Algorithms and Applications

The Journal of Graph Algorithms and Applications is an open access peer-reviewed scientific journal covering the subject of graph algorithms and graph drawing.

## Journal of the ACM

The Journal of the ACM is a peer-reviewed scientific journal covering computer science in general, especially theoretical aspects.

## Kosaraju's algorithm

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.

## Limit of a sequence

As the positive integer n becomes larger and larger, the value n\cdot \sin\bigg(\frac1\bigg) becomes arbitrarily close to 1.

## Literal (mathematical logic)

In mathematical logic, a literal is an atomic formula (atom) or its negation.

## Logarithm

In mathematics, the logarithm is the inverse function to exponentiation.

## Logical conjunction

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.

## Logical disjunction

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.

## Logical equivalence

In logic, statements p and q are logically equivalent if they have the same logical content.

## Logical matrix

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.

## Majority function

In Boolean logic, the majority function (also called the median operator) is a function from n inputs to one output.

## Many-valued logic

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.

## Maximum flow problem

In optimization theory, maximum flow problems involve finding a feasible flow through a single-source, single-sink flow network that is maximum.

## Maximum satisfiability problem

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.

## Median graph

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.

## Metric space

In mathematics, a metric space is a set for which distances between all members of the set are defined.

## Necessity and sufficiency

In logic, necessity and sufficiency are terms used to describe an implicational relationship between statements.

## NL (complexity)

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.

## NL-complete

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.

## Nonogram

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.

## NP (complexity)

In computational complexity theory, NP (for nondeterministic polynomial time) is a complexity class used to describe certain types of decision problems.

## NP-completeness

In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes.

## NP-hardness

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".

## Orthogonal convex hull

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.

## P versus NP problem

The P versus NP problem is a major unsolved problem in computer science.

## Parameterized complexity

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.

## Path-based strong component algorithm

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.

## Phase transition

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.

## Phylogenetic tree

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.

## Pixel

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.

## Polynomial-time approximation scheme

In computer science, a polynomial-time approximation scheme (PTAS) is a type of approximation algorithm for optimization problems (most often, NP-hard optimization problems).

## Polyomino

A polyomino is a plane geometric figure formed by joining one or more equal squares edge to edge.

## Resolution (logic)

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.

## Round-robin tournament

A round-robin tournament (or all-play-all tournament) is a competition in which each contestant meets all other contestants in turn.

## RP (complexity)

In computational complexity theory, randomized polynomial time (RP) is the complexity class of problems for which a probabilistic Turing machine exists with these properties.

## Second-order logic

In logic and mathematics second-order logic is an extension of first-order logic, which itself is an extension of propositional logic.

## Semidefinite programming

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.

## Sharp-P-complete

#P-complete, pronounced "sharp P complete" or "number P complete" is a complexity class in computational complexity theory.

## SIAM Journal on Computing

The SIAM Journal on Computing is a scientific journal focusing on the mathematical and formal aspects of computer science.

## 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).

## Skew-symmetric graph

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.

## Square lattice

In mathematics, the square lattice is a type of lattice in a two-dimensional Euclidean space.

## Strongly connected component

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.

## Symposium on Computational Geometry

The Annual Symposium on Computational Geometry (SoCG) is an academic conference in computational geometry.

## Tarjan's strongly connected components algorithm

Tarjan's algorithm is an algorithm in graph theory for finding the strongly connected components of a graph.

## Theoretical Computer Science (journal)

Theoretical Computer Science (TCS) is a computer science journal published by Elsevier, started in 1975 and covering theoretical computer science.

## Time complexity

In computer science, the time complexity is the computational complexity that describes the amount of time it takes to run an algorithm.

## Tomography

Tomography is imaging by sections or sectioning, through the use of any kind of penetrating wave.

## Topological sorting

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.

## Transitive closure

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.

## Transitive relation

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.

## True quantified Boolean formula

In computational complexity theory, the language TQBF is a formal language consisting of the true quantified Boolean formulas.

## Unique games conjecture

In computational complexity theory, the unique games conjecture is a conjecture made by Subhash Khot in 2002.

## University of California, Davis

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.

## Vertex (graph theory)

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).

## Vertex cover

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

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.

## References

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