Independent set (graph theory)In graph theory, an independent set, stable set, coclique or anticlique is a set of vertices in a graph, no two of which are adjacent. That is, it is a set S{\displaystyle S} of vertices such that for every two vertices in S{\displaystyle S}, there is no edge connecting the two. Equivalently, each edge in the graph has at most one endpoint in S{\displaystyle S}. A set is independent if and only if it is a clique in the graph's complement.
P versus NP problemUnsolved problem in computer scienceIf the solution to a problem can be verified in polynomial time, must the problem be solvable in polynomial time?More unsolved problems in computer scienceThe P versus NP problem is a major unsolved problem in theoretical computer science. Informally, it asks whether every decision problem for which a proposed positive answer can be quickly verified can also be quickly solved.
Computational complexity theoryIn theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and explores the relationships between these classifications. A computational problem is a task solved by a computer and is solvable by mechanical application of mathematical steps, such as an algorithm.
Graph coloringMethodic assignment of colors to elements of a graphA proper vertex coloring of the Petersen graph with 3 colors, the minimum number possible.In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a graph. The assignment is subject to certain constraints, such as that no two adjacent elements have the same color. Graph coloring is a special case of graph labeling.
Parameterized complexityIn 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. The complexity of a problem is then measured as a function of those parameters.
NP-completenessIn computational complexity theory, NP-complete problems are the hardest of the problems to which solutions can be verified quickly. Somewhat more precisely, a problem is NP-complete when: It is a decision problem, meaning that for any input to the problem, the output is either "yes" or "no".Each input to the problem is associated with a collection of short (polynomial size) solutions, which might or might not validly solve the input.
Function (mathematics)Association of one output to each inputIn mathematics, a function from a setX to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function. Functions were originally the idealization of how a varying quantity depends on another quantity. For example, the position of a planet is a function of time.
Computational problemIn theoretical computer science, a problem is one that asks for a solution in terms of an algorithm. For example, the problem of factoring"Given a positive integer n, find a nontrivial prime factor of n."is a computational problem that has a solution, as there are many known integer factorization algorithms. A computational problem can be viewed as a set of instances or cases together with a, possibly empty, set of solutions for every instance/case.
Time complexityEstimate of time taken for running an algorithmGraphs of functions commonly used in the analysis of algorithms, showing the number of operations N{\displaystyle N} as the result of input size n{\displaystyle n} for each functionIn theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm.
Computer scienceStudy of computationFundamental areas of computer scienceProgramming language theoryComputer architectureArtificial intelligenceComputational complexity theoryComputer science is the study of computation, information, and automation, together with their associated phenomena.
NP-hardnessIn computational complexity theory, a computational problem H is called NP-hard if, for every problem L which can be solved in non-deterministic polynomial-time, there is a polynomial-time reduction from L to H. That is, assuming a solution for H takes 1 unit time, H's solution can be used to solve L in polynomial time.*As an Amazon Associate I earn from qualifying purchases.