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Problem a computer might be able to solve
factors of n. An example of a computational problem without a solution is the Halting problem. Computational problems are one of the main objects of
Computational_problem
Inherent difficulty of computational problems
theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource usage, and
Computational complexity theory
Computational_complexity_theory
Hypothesis in computational complexity theory
In computational complexity theory, a computational hardness assumption is the hypothesis that a particular problem cannot be solved efficiently (where
Computational hardness assumption
Computational_hardness_assumption
Set of problem-solving methods
Computational thinking (CT) refers to the thought processes involved in formulating problems so their solutions can be represented as computational steps
Computational_thinking
NP-hard problem in combinatorial optimization
In the theory of computational complexity, the travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances
Travelling_salesman_problem
Set of problems in computational complexity theory
In computational complexity theory, a complexity class is a set of computational problems "of related resource-based complexity". The two most commonly
Complexity_class
Set of computational problems stated by Richard Karp (1973)
In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete. In his 1972 paper, "Reducibility
Karp's 21 NP-complete problems
Karp's_21_NP-complete_problems
Unsolved problem in computer science
time. The problem has been called the most important open problem in computer science. Aside from being an important problem in computational theory, a
P_versus_NP_problem
Yes/no problem in computer science
In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question on a
Decision_problem
Any type of calculation
{\displaystyle H} . Computationalism Computational problem Computability theory Hypercomputation Limits of computation Numerical computation The study of non-computable
Computation
Complexity class
In 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
NP-hardness
Unsolved problem in computational complexity theory
The graph isomorphism problem is the computational problem of determining whether two finite graphs are isomorphic. The problem is not known to be solvable
Graph_isomorphism_problem
Task of computing complete subgraphs
In computer science, the clique problem is the computational problem of finding cliques (subsets of vertices, all adjacent to each other, also called complete
Clique_problem
Problem in combinatorial optimization
online knapsack problem. Computer programming portal Bin packing problem – Mathematical and computational problem Change-making problem – Choosing the
Knapsack_problem
Branch of computer science
geometrical problems arise out of the study of computational geometric algorithms, and such problems are also considered to be part of computational geometry
Computational_geometry
Problem used to illustrate synchronization issues and techniques for resolving them
In computer science, the dining philosophers problem is an example problem often used in concurrent algorithm design to illustrate synchronization issues
Dining_philosophers_problem
Academic subfield of computer science
mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation using an algorithm, how efficiently
Theory_of_computation
Problem of finding the best feasible solution
decision problems, the problem is more naturally characterized as an optimization problem. Counting problem (complexity) – Type of computational problem Design
Optimization_problem
Computational problem
problem (or circuit evaluation problem) is the computational problem of computing the output of a given Boolean circuit on a given input. The problem
Circuit_value_problem
Unrelated vertices in graphs
Therefore, many computational results may be applied equally well to either problem. For example, the results related to the clique problem have the following
Independent set (graph theory)
Independent_set_(graph_theory)
In computational complexity theory, a fine-grained reduction is a transformation from one computational problem to another, used to relate the difficulty
Fine-grained_reduction
Computational problem of graph theory
Directed graph where edges have a capacity K shortest path routing – Computational problem of graph theory Min-plus matrix multiplication – Mathematical operation
Shortest_path_problem
Aspect of computational complexity theory
computational complexity theory, a computational resource is a resource used by some computational models in the solution of computational problems.
Computational_resource
Numerical simulations of physical problems via computers
biological problems. Computational thermodynamics Computational aeroacoustics Computational optics Due to the broad class of problems computational physics
Computational_physics
Type of computational problem
In computational complexity theory and computability theory, a counting problem is a type of computational problem that is obtained by strengthening a
Counting_problem_(complexity)
Class of computational problems
In computational complexity theory, a transcomputational problem is a problem that requires processing of more than 1093 bits of information. Any number
Transcomputational_problem
Subunit of a computational problem
In computational complexity theory, a gadget is a subunit of a problem instance that simulates the behavior of one of the fundamental units of a different
Gadget_(computer_science)
On short connecting nets with added points
the Steiner tree problem, or minimum Steiner tree problem, named after Jakob Steiner, is an umbrella term for a class of problems in combinatorial optimization
Steiner_tree_problem
System with multiple networked computers
theoretical computer science, such tasks are called computational problems. Formally, a computational problem consists of instances together with a solution
Distributed_computing
Computational problem
path planning (also known as the navigation problem or the piano mover's problem) is a computational problem to find a sequence of valid configurations
Motion_planning
Decision problem pertaining to equivalence of expressions
In computational mathematics, a word problem is the problem of deciding whether two given expressions are equivalent with respect to a set of rewriting
Word_problem_(mathematics)
Computer system simulating intelligence
Recognized journals include Computational Intelligence, International Journal of Computational Intelligence Systems, Applied Computational Intelligence and Soft
Computational_intelligence
Class of computational problems
In computational complexity theory and computability theory, a search problem is a computational problem of finding an admissible answer for a given input
Search_problem
Specialist field of computer science
known for computational solutions.[citation needed] Problem domains for computational science/scientific computing include: Predictive computational science
Computational_science
Path in a graph that visits each vertex exactly once
path. The computational problems of determining whether such paths and cycles exist in graphs are NP-complete; see Hamiltonian path problem for details
Hamiltonian_path
Type of computational problem
In combinatorics and computer science, covering problems are computational problems that ask whether a certain combinatorial structure 'covers' another
Covering_problems
Type of computational problem
In computational complexity theory, a function problem is a computational problem where a single output is expected for every input, but the output is
Function_problem
Measurement of computational complexity
complexity of algorithms and computational problems, commonly associated with the use of the big O notation. With respect to computational resources, asymptotic
Asymptotic computational complexity
Asymptotic_computational_complexity
Topics referred to by the same term
types include: Chess problem Computational problem Mathematical problem Problem(s) or The Problem may also refer to: Problems (Aristotle), an Aristotelian
Problem_(disambiguation)
majority of positive results about computational problems are constructive proofs, i.e., a computational problem is proved to be solvable by showing
Non-constructive algorithm existence proofs
Non-constructive_algorithm_existence_proofs
Subset of a graph's vertices, including at least one endpoint of every edge
NP-complete problem in computational complexity theory. Furthermore, the vertex cover problem is fixed-parameter tractable and a central problem in parameterized
Vertex_cover
Finding shortest walks through all graph edges
O(n3) computational steps. For the route inspection problem, T should be chosen as the set of all odd-degree vertices. By the assumptions of the problem, the
Chinese_postman_problem
Problem in computer science
computability theory and computational complexity theory, a reduction is an algorithm for transforming one computational problem into another problem. A sufficiently
Halting_problem
Mathematical problem in cryptography
introducing noise to it. In more technical terms, it refers to the computational problem of inferring a linear n-ary function f over a finite ring from given
Learning_with_errors
Strategies to make sure approximate calculations stay close to accurate
measured in petaflops, floating-point error is a major concern for computational problem solvers. The following sections describe the strengths and weaknesses
Floating-point error mitigation
Floating-point_error_mitigation
Problem of finding a cycle through all vertices of a graph
easy computational task. Papadimitriou defined the complexity class PPA to encapsulate problems such as this one. The Hamiltonian path problem is NP
Hamiltonian_path_problem
Type of computational problem
In computational complexity theory, a promise problem is a generalization of a decision problem where the input is promised to belong to a particular subset
Promise_problem
AI field of problem generation and solving
with the generation, representation, verification, and solution of computational problems. It was introduced by Phillip C.-Y. Sheu and his students in a 2025
Generative_Problem_Solving
Computational problem about sorting
The Dutch national flag problem is a computational problem proposed by Edsger Dijkstra. The flag of the Netherlands consists of three colors: red, white
Dutch_national_flag_problem
Mathematical counting-out question
computer science and mathematics, the Josephus problem (or Josephus permutation) is a theoretical problem related to a certain counting-out game. Such games
Josephus_problem
monotone dualization is a computational problem of constructing the dual of a monotone Boolean function. Equivalent problems can also be formulated as
Monotone_dualization
Term in computer science
Collision detection is the computational problem of detecting an intersection of two or more objects in virtual space. More precisely, it deals with the
Collision_detection
Branch of chemistry
Computational chemistry is a branch of chemistry that uses computer simulations to assist in solving chemical problems. It uses methods of theoretical
Computational_chemistry
Graph made from disjoint union of complete graphs
cluster graphs are exactly the graphs of subchromatic number 1. The computational problem of finding a small set of edges to add or remove from a graph to
Cluster_graph
Theoretical model of computation
theoretical computer science and computational theory, a nondeterministic Turing machine (NTM) is a theoretical model of computation whose governing rules specify
Nondeterministic Turing machine
Nondeterministic_Turing_machine
Subfield of computer science and mathematics
game theory, machine learning, computational biology, computational economics, computational geometry, and computational number theory and algebra. Work
Theoretical_computer_science
Amount of resources to perform an algorithm
computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus is given to computation
Computational_complexity
NP-complete graph problem
can witness differences from a computational complexity point of view. For example, the subgraph isomorphism problem is NP-complete on connected proper
Induced subgraph isomorphism problem
Induced_subgraph_isomorphism_problem
Analysis and solving of problems that involve fluid flows
Computational fluid dynamics (CFD) is a branch of both fluid mechanics and computational physics that uses numerical analysis and data structures to analyze
Computational_fluid_dynamics
Computational problem used in cryptography
Short integer solution (SIS) and ring-SIS problems are two average-case problems that are used in lattice-based cryptography constructions. Lattice-based
Short integer solution problem
Short_integer_solution_problem
Computational problem in graph theory
maximum flow problems involve finding a feasible flow through a flow network that obtains the maximum possible flow rate. The maximum flow problem can be seen
Maximum_flow_problem
Partition of a graph's nodes into cliques
cover problem in computational complexity theory is the algorithmic problem of finding a minimum clique cover, or (rephrased as a decision problem) finding
Clique_cover
theoretical computer science, the closest string is an NP-hard computational problem, which tries to find the geometrical center of a set of input strings
Closest_string
Class of problems solvable in polynomial time
polynomial amount of computation time, or polynomial time. Cobham's thesis holds that P is the class of computational problems that are "efficiently
P_(complexity)
Term describing difficult problems in AI
any real world problem, whether navigation, planning, or the kind of reasoning done by expert systems.[citation needed] Computational complexity theory
AI-complete
Complexity class
In computational complexity theory, NP-complete problems are the hardest of the problems to which solutions can be verified quickly. NP is short for "nondeterministic
NP-completeness
Computational problem in algebraic topology
simplicial complex recognition problem is a computational problem in algebraic topology. Given a simplicial complex, the problem is to decide whether it is
Simplicial complex recognition problem
Simplicial_complex_recognition_problem
Concept in computational complexity theory
Cobham and Jack Edmonds), asserts that computational problems can be feasibly computed on some computational device only if they can be computed in polynomial
Cobham's_thesis
order. Computational origami is a recent branch of computer science that is concerned with studying algorithms that solve paper-folding problems. The field
Mathematics_of_paper_folding
Problem in computer science
sum problem (SRS) is a computational decision problem from the field of numerical analysis, with applications to computational geometry. The problem was
Square-root_sum_problem
Yes-or-no question that cannot ever be solved by a computer
In computability theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct
Undecidable_problem
List of unsolved computational problems
design, and computational theory. What is the relationship between BQP and NP? NC = P problem NP = co-NP problem P = BPP problem P = PSPACE problem L = NL
List of unsolved problems in computer science
List_of_unsolved_problems_in_computer_science
Tree which includes all vertices of a graph
of computation. In certain fields of graph theory it is often useful to find a minimum spanning tree of a weighted graph. Other optimization problems on
Spanning_tree
Shape bounded by non-intersecting line segments
are commonly seen as the input to computational geometry problems, including point in polygon testing, area computation, the convex hull of a simple polygon
Simple_polygon
quantum memory. Computational algorithms can then be designed that require arbitrarily small amounts of energy/time per one elementary computation step. Landauer's
Limits_of_computation
Problem in physics and celestial mechanics
that have applicability to the gravitational n-body problem as well. A technique in Computational fluid dynamics called Vortex Methods sees the vorticity
N-body_problem
database or an operating system. hard problem Computational complexity theory focuses on classifying computational problems according to their inherent difficulty
Glossary_of_computer_science
Use of functions that call themselves
a computational problem where the solution depends on solutions to smaller instances of the same problem. Recursion solves such recursive problems by
Recursion_(computer_science)
Problem in computer science
In computational complexity theory and quantum computing, Simon's problem is a computational problem that is proven to be solved exponentially faster
Simon's_problem
Classic NP-complete problem in computer science
science, the circuit satisfiability problem (also known as CIRCUIT-SAT, CircuitSAT, CSAT, etc.) is the decision problem of determining whether a given Boolean
Circuit satisfiability problem
Circuit_satisfiability_problem
Computer memory needed by an algorithm
algorithm Computational complexity theory – Inherent difficulty of computational problems Computational resource – Aspect of computational complexity
Space_complexity
Path-finding using high-weight graph edges
analysis, and the computation of maximum flows. A closely related problem, the minimax path problem or bottleneck shortest path problem asks for the path
Widest_path_problem
System that regulates the formation of blocks on a blockchain
puzzle, computational puzzle, or CPU pricing function. Another common feature is built-in incentive-structures that reward allocating computational capacity
Proof_of_work
Notion of the "hardest" or "most general" problem in a complexity class
In computational complexity theory, a computational problem is complete for a complexity class if it is, in a technical sense, among the "hardest" (or
Complete_(complexity)
Abstract machine used to study decision problems
performed in a single computational step: the contents of the oracle tape are viewed as an instance of the oracle's computational problem; the oracle is consulted
Oracle_machine
Problem of finding the longest simple path for a given graph
graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph. A path
Longest_path_problem
Computer hardware technology that uses quantum mechanics
(2021). "The prospects of quantum computing in computational molecular biology". WIREs Computational Molecular Science. 11 e1481. arXiv:2005.12792. doi:10
Quantum_computing
Complete subgraph added to a random graph
In computational complexity theory, a planted clique or hidden clique in an undirected graph is a clique formed from another graph by selecting a subset
Planted_clique
List of concepts in artificial intelligence
nervous system. computational number theory The study of algorithms for performing number theoretic computations. computational problem In theoretical
Glossary of artificial intelligence
Glossary_of_artificial_intelligence
respectively. Roughly speaking, the computational security parameter is a measure for the input size of the computational problem on which the cryptographic scheme
Security_parameter
Overview of and topical guide to algorithms
efficiency, computational complexity, and implementation in computer programs. Algorithm — finite sequence of instructions for solving a problem or performing
Outline_of_algorithms
Index of articles associated with the same name
Query complexity in computational complexity describes the number of queries needed to solve a computational problem for an input that can be accessed
Query_complexity
Set of edges without common vertices
one; it is used in computational chemistry and mathematical chemistry investigations for organic compounds. The Chinese postman problem involves finding
Matching_(graph_theory)
Topics referred to by the same term
lemma, a technique used to reduce the number of solutions to a computational problem. Isolated point, a topological notion of having no points near a
Isolation
Subfield of computational complexity theory
complexity is a subfield of computational complexity theory that studies the time required to solve computational problems, especially those within the
Fine_grained_complexity
Computational geometry problem
The closest pair of points problem or closest pair problem is a problem of computational geometry: given n {\displaystyle n} points in metric space, find
Closest pair of points problem
Closest_pair_of_points_problem
Subset of a graph's nodes such that all other nodes link to at least one
dominating set problem concerns testing whether γ(G) ≤ K for a given graph G and input K; it is a classical NP-complete decision problem in computational complexity
Dominating_set
Computational search problem
In computational complexity theory, the linear search problem is an optimal search problem introduced by Richard E. Bellman and independently considered
Linear_search_problem
Type of computing function
In computer science, a computational problem is memory-bound when the time it takes for it to complete is decided primarily by the amount of free memory
Memory-bound_function
Determining whether a knot is the unknot
class P. First steps toward determining the computational complexity were undertaken in proving that the problem is in larger complexity classes, which contain
Unknotting_problem
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COMPUTATIONAL PROBLEM
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COMPUTATIONAL PROBLEM
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