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Independent set (graph theory)

Index 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. [1]

62 relations: Algorithmica, Approximation algorithm, APX, Automatic label placement, Bipartite graph, Brute-force search, BSD licenses, Chordal graph, Claw-free graph, Clique (graph theory), Clique problem, Cograph, Combinatorica, Complement graph, Computational problem, Computer science, Cycle graph, Dense graph, Dominating set, Earliest deadline first scheduling, Edge cover, Glossary of graph theory terms, GNU General Public License, Graph (discrete mathematics), Graph coloring, Graph minor, Graph theory, Greedy algorithm, Information and Computation, Intersection graph, Interval graph, Job scheduler, Journal of Combinatorial Theory, Journal of the ACM, Kőnig's theorem (graph theory), Lecture Notes in Computer Science, Matching (graph theory), Maximal independent set, Modular decomposition, NetworkX, NP-completeness, NP-hardness, Optimization problem, Padovan sequence, Partition of a set, Path graph, Perfect graph, Perrin number, Planar graph, Plastic number, ..., Polynomial-time approximation scheme, Ramsey theory, SIAM Journal on Computing, SNP (complexity), Springer Science+Business Media, SWAT and WADS conferences, Symposium on Discrete Algorithms, Theoretical computer science, Time complexity, Truth value, Vertex (graph theory), Vertex cover. Expand index (12 more) »

Algorithmica

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

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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.

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APX

In complexity theory the class APX (an abbreviation of "approximable") is the set of NP optimization problems that allow polynomial-time approximation algorithms with approximation ratio bounded by a constant (or constant-factor approximation algorithms for short).

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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.

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Bipartite graph

In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets U and V such that every edge connects a vertex in U to one in V. Vertex sets U and V are usually called the parts of the graph.

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Brute-force search

In computer science, brute-force search or exhaustive search, also known as generate and test, is a very general problem-solving technique that consists of systematically enumerating all possible candidates for the solution and checking whether each candidate satisfies the problem's statement.

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BSD licenses

BSD licenses are a family of permissive free software licenses, imposing minimal restrictions on the use and redistribution of covered software.

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Chordal graph

In the mathematical area of graph theory, a chordal graph is one in which all cycles of four or more vertices have a chord, which is an edge that is not part of the cycle but connects two vertices of the cycle.

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Claw-free graph

In graph theory, an area of mathematics, a claw-free graph is a graph that does not have a claw as an induced subgraph.

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Clique (graph theory)

In the mathematical area of graph theory, a clique is a subset of vertices of an undirected graph such that every two distinct vertices in the clique are adjacent; that is, its induced subgraph is complete.

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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.

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Cograph

In graph theory, a cograph, or complement-reducible graph, or P4-free graph, is a graph that can be generated from the single-vertex graph K1 by complementation and disjoint union.

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Combinatorica

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

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Complement graph

In graph theory, the complement or inverse of a graph is a graph on the same vertices such that two distinct vertices of are adjacent if and only if they are not adjacent in.

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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.

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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.

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Cycle graph

In graph theory, a cycle graph or circular graph is a graph that consists of a single cycle, or in other words, some number of vertices connected in a closed chain.

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Dense graph

In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges.

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Dominating set

In graph theory, a dominating set for a graph G.

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Earliest deadline first scheduling

Earliest deadline first (EDF) or least time to go is a dynamic priority scheduling algorithm used in real-time operating systems to place processes in a priority queue.

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Edge cover

In graph theory, an edge cover of a graph is a set of edges such that every vertex of the graph is incident to at least one edge of the set.

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Glossary of graph theory terms

This is a glossary of graph theory terms.

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GNU General Public License

The GNU General Public License (GNU GPL or GPL) is a widely used free software license, which guarantees end users the freedom to run, study, share and modify the software.

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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".

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Graph coloring

In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints.

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Graph minor

In graph theory, an undirected graph H is called a minor of the graph G if H can be formed from G by deleting edges and vertices and by contracting edges.

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Graph theory

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

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Greedy algorithm

A greedy algorithm is an algorithmic paradigm that follows the problem solving heuristic of making the locally optimal choice at each stage with the intent of finding a global optimum.

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Information and Computation

Information and Computation is a computer science journal published by Elsevier (formerly Academic Press).

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Intersection graph

In the mathematical area of graph theory, an intersection graph is a graph that represents the pattern of intersections of a family of sets.

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Interval graph

In graph theory, an interval graph is the intersection graph of a family of intervals on the real line.

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Job scheduler

A job scheduler is a computer application for controlling unattended background program execution of jobs.

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Journal of Combinatorial Theory

The Journal of Combinatorial Theory, Series A and Series B, are mathematical journals specializing in combinatorics and related areas.

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Journal of the ACM

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

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Kőnig's theorem (graph theory)

In the mathematical area of graph theory, Kőnig's theorem, proved by, describes an equivalence between the maximum matching problem and the minimum vertex cover problem in bipartite graphs.

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Lecture Notes in Computer Science

Springer Lecture Notes in Computer Science (LNCS) is a series of computer science books published by Springer Science+Business Media (formerly Springer-Verlag) since 1973.

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Matching (graph theory)

In the mathematical discipline of graph theory, a matching or independent edge set in a graph is a set of edges without common vertices.

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Maximal independent set

In graph theory, a maximal independent set (MIS) or maximal stable set is an independent set that is not a subset of any other independent set.

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Modular decomposition

In graph theory, the modular decomposition is a decomposition of a graph into subsets of vertices called modules. A module is a generalization of a connected component of a graph.

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NetworkX

NetworkX is a Python library for studying graphs and networks.

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NP-completeness

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

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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".

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Optimization problem

In mathematics and computer science, an optimization problem is the problem of finding the best solution from all feasible solutions.

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Padovan sequence

The Padovan sequence is the sequence of integers P(n) defined by the initial values and the recurrence relation The first few values of P(n) are The Padovan sequence is named after Richard Padovan who attributed its discovery to Dutch architect Hans van der Laan in his 1994 essay Dom.

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Partition of a set

In mathematics, a partition of a set is a grouping of the set's elements into non-empty subsets, in such a way that every element is included in one and only one of the subsets.

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Path graph

In the mathematical field of graph theory, a path graph or linear graph is a graph whose vertices can be listed in the order v1, v2, …, vn such that the edges are where i.

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Perfect graph

In graph theory, a perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the largest clique of that subgraph.

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Perrin number

In mathematics, the Perrin numbers are defined by the recurrence relation with initial values The sequence of Perrin numbers starts with The number of different maximal independent sets in an -vertex cycle graph is counted by the th Perrin number for.

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Planar graph

In graph theory, a planar graph is a graph that can be embedded in the plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints.

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Plastic number

In mathematics, the plastic number (also known as the plastic constant, the minimal Pisot number, the platin number, Siegel's number or, in French, le nombre radiant) is a mathematical constant which is the unique real solution of the cubic equation It has the exact value Its decimal expansion begins with.

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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).

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Ramsey theory

Ramsey theory, named after the British mathematician and philosopher Frank P. Ramsey, is a branch of mathematics that studies the conditions under which order must appear.

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SIAM Journal on Computing

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

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SNP (complexity)

In computational complexity theory, SNP (from Strict NP) is a complexity class containing a limited subset of NP based on its logical characterization in terms of graph-theoretical properties.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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SWAT and WADS conferences

WADS, the Algorithms and Data Structures Symposium, is an international academic conference in the field of computer science, focusing on algorithms and data structures.

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Symposium on Discrete Algorithms

The Annual ACM-SIAM Symposium on Discrete Algorithms (SODA) is an academic conference in the fields of algorithm design and discrete mathematics.

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Theoretical computer science

Theoretical computer science, or TCS, is a subset of general computer science and mathematics that focuses on more mathematical topics of computing and includes the theory of computation.

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Time complexity

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

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Truth value

In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth.

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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).

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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.

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Coclique, Independence (graph theory), Independence number, Independent Set problem, Independent set problem, Maximum independent set, Maximum independent set problem, Maximum independent-set, Vertex independent set, Vertex packing.

References

[1] https://en.wikipedia.org/wiki/Independent_set_(graph_theory)

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