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Unsolved problem in computational complexity theory
Unsolved problem in computer science Can the graph isomorphism problem be solved in polynomial time? More unsolved problems in computer science The graph
Graph_isomorphism_problem
Topics referred to by the same term
Isomorphism problem may refer to: graph isomorphism problem group isomorphism problem isomorphism problem of Coxeter groups This disambiguation page lists
Isomorphism_problem
Problem in theoretical computer science
In theoretical computer science, the subgraph isomorphism problem is a computational task in which two graphs G {\displaystyle G} and H {\displaystyle
Subgraph_isomorphism_problem
Decision problem
isomorphism problem is the decision problem of determining whether two given finite group presentations refer to isomorphic groups. The isomorphism problem
Group_isomorphism_problem
Bijection between the vertex set of two graphs
called an isomorphism class of graphs. The question of whether graph isomorphism can be determined in polynomial time is a major unsolved problem in computer
Graph_isomorphism
Very general problem in computer science
problems including factoring, discrete logarithm, graph isomorphism, and the shortest vector problem. This makes it especially important in the theory of
Hidden_subgroup_problem
Unsolved problem in computer science
"Graph isomorphism is in SPP". Information and Computation. 204 (5): 835–852. doi:10.1016/j.ic.2006.02.002. Schöning, Uwe (1988). "Graph isomorphism is in
P_versus_NP_problem
Complexity class
interesting example is the graph isomorphism problem, the graph theory problem of determining whether a graph isomorphism exists between two graphs. Two
NP-completeness
Mathematical theory on random variables
around 1986 in order to attack the free group factors isomorphism problem, an important unsolved problem in the theory of operator algebras. Given a free group
Free_probability
List of unsolved computational problems
computer? Can the graph isomorphism problem be solved in polynomial time on a classical computer? The graph isomorphism problem involves determining whether
List of unsolved problems in computer science
List_of_unsolved_problems_in_computer_science
questions motivated by it. Mühlherr, Bernhard (2005-06-28). "The isomorphism problem for Coxeter groups". arXiv:math.GR/0506572. Santos Rego, Yuri; Schwer
Isomorphism problem of Coxeter groups
Isomorphism_problem_of_Coxeter_groups
Area of discrete mathematics
NP-complete problem. For example: Finding the largest complete subgraph is called the clique problem (NP-complete). One special case of subgraph isomorphism is
Graph_theory
Mapping a graph onto itself without changing edge-vertex connectivity
a list of generators, is polynomial-time equivalent to the graph isomorphism problem, and therefore solvable in quasi-polynomial time, that is with running
Graph_automorphism
The inverse Galois problem: is every finite group the Galois group of a Galois extension of the rationals? Isomorphism problem of Coxeter groups Are
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
NP-complete graph problem
subgraph isomorphism is an NP-complete decision problem that involves finding a given graph as an induced subgraph of a larger graph. Formally, the problem takes
Induced subgraph isomorphism problem
Induced_subgraph_isomorphism_problem
Inherent difficulty of computational problems
"Graph isomorphism is in SPP", Information and Computation, 204 (5): 835–852, doi:10.1016/j.ic.2006.02.002. Schöning, Uwe (1988), "Graph Isomorphism is in
Computational complexity theory
Computational_complexity_theory
Hamiltonian path problem, directed and undirected. Induced subgraph isomorphism problem Graph intersection number Longest path problem Maximum bipartite
List_of_NP-complete_problems
Set of mathematical functions concerning algebraic group isomorphism
generators. A particularly simple case of the word problem for groups and the isomorphism problem for groups asks if a finitely presented group is the
Nielsen_transformation
Method for solving one problem using another
-complete problem is NP-hard. Similarly, the complexity class GI consists of the problems that can be reduced to the graph isomorphism problem. Since graph
Polynomial-time_reduction
Complexity class used to classify decision problems
version repeatedly (a polynomial number of times). The subgraph isomorphism problem of determining whether graph G contains a subgraph that is isomorphic
NP_(complexity)
In mathematics, invertible homomorphism
an isomorphism from a structure to itself. An isomorphism between two structures is a canonical isomorphism (a canonical map that is an isomorphism) if
Isomorphism
Hungarian-American mathematician and computer scientist
methods in graph isomorphism testing. In November 2015, he announced a quasipolynomial time algorithm for the graph isomorphism problem. He is editor-in-chief
László_Babai
Complexity class of problems
satisfiability problems cannot be in NPI. Some problems that are considered good candidates for being NP-intermediate are the graph isomorphism problem, and decision
NP-intermediate
Logical formulation of graph properties
{\displaystyle v} that is adjacent to u {\displaystyle u} . The subgraph isomorphism problem for a fixed subgraph H {\displaystyle H} asks whether H {\displaystyle
Logic_of_graphs
Index of articles associated with the same name
In graph theory and theoretical computer science, a maximum common subgraph may mean either: Maximum common induced subgraph, a graph that is an induced
Maximum_common_subgraph
Convex hull of a finite set of points in a Euclidean space
graph isomorphism problem. However, it is also possible to translate these problems in the opposite direction, showing that polytope isomorphism testing
Convex_polytope
Problem in finite group theory
the conjugacy problem and the group isomorphism problem. In 1912 he gave an algorithm that solves both the word and conjugacy problem for the fundamental
Word_problem_for_groups
Estimate of time taken for running an algorithm
Subgroup Problem with Polynomial Space". arXiv:quant-ph/0406151v1. Grohe, Martin; Neuen, Daniel (2021). "Recent advances on the graph isomorphism problem". In
Time_complexity
Task in computational graph theory
from a solution to the graph canonization problem, one could also solve the problem of graph isomorphism: to test whether two graphs G and H are isomorphic
Graph_canonization
Bijective group homomorphism
bijective correspondence. Thus, the definition of an isomorphism is quite natural. An isomorphism of groups may equivalently be defined as an invertible
Group_isomorphism
American mathematician and computer scientist
University of Oregon. He is known for his research on the graph isomorphism problem and on algorithms for computational group theory. Luks did his undergraduate
Eugene_M._Luks
graph isomorphism. Fractional isomorphism is the coarsest of several different relaxations of graph isomorphism. Whereas the graph isomorphism problem is
Fractional_graph_isomorphism
Computational problems no algorithm can solve
undecidable. The word problem for groups. The conjugacy problem. The group isomorphism problem. Determining whether two finite simplicial complexes are
List_of_undecidable_problems
Manifold upon which it is possible to perform calculus
open set in Rn. f#: O|f(U) → f∗ (OM|U) is an isomorphism of sheaves. The localization of f# is an isomorphism of local rings f#f(p) : Of(p) → OM,p. There
Differentiable_manifold
Graph made from a subset of another graph's nodes and their edges
vertices adjacent to it. The induced subgraph isomorphism problem is a form of the subgraph isomorphism problem in which the goal is to test whether one graph
Induced_subgraph
Problem on words in group theory
theory; the other two being the word problem and the isomorphism problem. The conjugacy problem contains the word problem as a special case: if x and y are
Conjugacy_problem
Graph in graph theory
showed, the problem of recognizing whether a graph is a lexicographic product is equivalent in complexity to the graph isomorphism problem. The lexicographic
Lexicographic product of graphs
Lexicographic_product_of_graphs
Proving validity without revealing other data
ask Peggy. He can either ask her to show the isomorphism between H and G (see graph isomorphism problem), or he can ask her to show a Hamiltonian cycle
Zero-knowledge_proof
Family of graphs whose shallow minors are sparse graphs
with these properties have efficient algorithms for problems including the subgraph isomorphism problem and model checking for the first order theory of
Bounded_expansion
Creating a new graph from an existing graph
of the pattern graph (pattern matching, thus solving the subgraph isomorphism problem) and by replacing the found occurrence by an instance of the replacement
Graph_rewriting
Israeli mathematician
Hebrew University of Jerusalem. Sela is known for the solution of the isomorphism problem for torsion-free word-hyperbolic groups and for the solution of the
Zlil_Sela
Property of graphs that depends only on abstract structure
invariants are instrumental for fast recognition of graph isomorphism, or rather non-isomorphism, since for any invariant at all, two graphs with different
Graph_property
Type of computational problem
asks: "Given a problem instance, is the number of solutions divisible by k?". For all k≥2, ModkP contains the graph isomorphism problem. Further, the graph
Counting_problem_(complexity)
Undirected graph acted on by a vertex-transitive cyclic group of symmetries
polynomial-time recognition algorithm for circulant graphs, and the isomorphism problem for circulant graphs can be solved in polynomial time. Small Ramsey
Circulant_graph
Problem of finding similarity between graphs
the graph isomorphism problem. The problem of exact matching of a graph to a part of another graph is called subgraph isomorphism problem. Inexact graph
Graph_matching
Decision problem pertaining to equivalence of expressions
different in non-abelian groups. Conjugacy problem Group isomorphism problem Evans, Trevor (1978). "Word problems". Bulletin of the American Mathematical
Word_problem_(mathematics)
Set of edges without common vertices
Hitchcock transport problem involves bipartite matching as sub-problem. Subtree isomorphism problem involves bipartite matching as sub-problem. Matching in hypergraphs
Matching_(graph_theory)
Venezuelan computer scientist
Vazirani, Luis von Ahn, and Ryan Williams. List of Venezuelans Graph isomorphism problem Non-interactive zero-knowledge proof Quantum coin flipping Pancake
Manuel_Blum
Mathematical concept
decidable marked isomorphism problem. It is notable that this means that the isomorphism problem, orbit problems (in particular the conjugacy problem) and Whitehead's
Hyperbolic_group
with at least k vertices. This problem is NP-complete. It is a generalization of the induced subgraph isomorphism problem, which arises when k equals the
Maximum common induced subgraph
Maximum_common_induced_subgraph
Topics referred to by the same term
Sport in Ireland § Gymnastics GI, a complexity class in the graph isomorphism problem Galvanized iron Gi alpha subunit, a protein Gastrointestinal tract
GI
Relationship between programs and proofs
first formulation of the isomorphism was referred to (a variant of) Gentzen's sequent calculus. The observation that the isomorphism is best understood with
Curry–Howard_correspondence
Branch of mathematics that studies the properties of groups
Another, generally harder, algorithmically insoluble problem is the group isomorphism problem, which asks whether two groups given by different presentations
Group_theory
Abstract machine that models computation
demonstrate the power of these classes, consider the graph isomorphism problem, the problem of determining whether it is possible to permute the vertices
Interactive_proof_system
Topological space associated to a vector bundle
B} be a real vector bundle of rank n. Then there is an isomorphism called a Thom isomorphism Φ : H k ( B ; Z 2 ) → H ~ k + n ( T ( E ) ; Z 2 ) , {\displaystyle
Thom_space
Graph which is isomorphic to its complement
self-complementary are polynomial-time equivalent to the general graph isomorphism problem. Sachs, Horst (1962), "Über selbstkomplementäre Graphen", Publicationes
Self-complementary_graph
Computational problem in graph theory
induced subgraph isomorphism problem. There is a similar problem of finding long induced cycles in hypercubes, called the coil-in-the-box problem. The snake-in-the-box
Snake-in-the-box
Problem in computer science
In computability theory, the halting problem is the decision problem of determining, from a description of an arbitrary computer program and an input
Halting_problem
Graph that can be embedded in the plane
in time O(v) whether they are isomorphic or not (see also graph isomorphism problem). Any planar graph on n nodes has at most 8(n-2) maximal cliques
Planar_graph
Similarity between organizations
institutional isomorphism and collective rationality in organizational fields. The term is borrowed from the mathematical concept of isomorphism. Isomorphism in
Isomorphism_(sociology)
Computer algebra system
for most index contractions with an approach based on the graph isomorphism problem rather than canonicalisation. Free and open-source software portal
Cadabra_(computer_program)
Austrian mathematician
transformations for group presentations, and was the first to pose the group isomorphism problem. Tietze's graph is also named after him; it describes the boundaries
Heinrich_Tietze
German mathematician (1940–2021)
of units of integral group rings, dealing with problems connected with the "integral isomorphism problem", which was proposed by Graham Higman in his 1940
Klaus_Wilhelm_Roggenkamp
Area in mathematics devoted to the study of finitely generated groups
the work of Zlil Sela in 1990s resulting in the solution of the isomorphism problem for word-hyperbolic groups. The notion of a relatively hyperbolic
Geometric_group_theory
Yes/no problem in computer science
decision problem is a computational problem that can be posed as a yes–no question on a set of input values. An example of a decision problem is deciding
Decision_problem
German computer scientist (born 1955)
hierarchies play an important role in the complexity of the graph isomorphism problem, which Schöning further developed in a 1993 monograph with Köbler
Uwe_Schöning
Group that admits a formal description in terms of reflections
Chevalley–Shephard–Todd theorem Complex reflection group Coxeter element Isomorphism problem of Coxeter groups Iwahori–Hecke algebra, a quantum deformation of
Coxeter_group
Peruvian mathematician (born 1977)
in the proof of the quasipolynomial time algorithm for the graph isomorphism problem that was announced by László Babai in 2015. Babai subsequently fixed
Harald_Helfgott
Australian mathematician
2022, ISBN 978-0691234366 Stillwell, John (1982). "The word problem and the isomorphism problem for groups". Bulletin of the American Mathematical Society
John_Stillwell
Graph coloring related to treedepth
{\displaystyle q} , and can be used in algorithms for subgraph isomorphism and related problems. The number of colors needed for a q {\displaystyle q} -centered
Centered_coloring
Yes-or-no question that cannot ever be solved by a computer
theory and computational complexity theory, an undecidable problem is a decision problem for which it is proved to be impossible to construct an algorithm
Undecidable_problem
Theorem classifying finite simple groups
breakthrough in the best known theoretical algorithm for the graph isomorphism problem in 1982 The Schreier conjecture The Signalizer functor theorem The
Classification of finite simple groups
Classification_of_finite_simple_groups
American mathematician and educator (1921–2008)
deeper mathematics related to permutation groups and the graph isomorphism problem.) OP-20-G then turned to the Japanese navy's "Coral" cipher. A key
Andrew_M._Gleason
maximum common edge subgraph problem on general graphs is NP-complete as it is a generalization of subgraph isomorphism: a graph H {\displaystyle H} is
Maximum_common_edge_subgraph
Computational complexity class
n)}} . Problems for which a quasi-polynomial time algorithm has been announced but not fully published include: The graph isomorphism problem, determining
Quasi-polynomial_time
algorithm Tarjan's strongly connected components algorithm Subgraph isomorphism problem Bitap algorithm: fuzzy algorithm that determines if strings are approximately
List_of_algorithms
Type of randomized algorithm
introduced by László Babai in 1979, in the context of the graph isomorphism problem, as a dual to Monte Carlo algorithms. Babai introduced the term "Las
Las_Vegas_algorithm
Maximum number of colors obtainable by a greedy graph coloring algorithm
results on subgraph isomorphism in sparse graphs to search for atoms) for graphs of bounded expansion. However, on general graphs the problem is W[1]-hard when
Grundy_number
Erdős discrepancy problem. 2015 – László Babai finds that a quasipolynomial complexity algorithm would solve the Graph isomorphism problem. 2016 – Maryna
Timeline_of_mathematics
Consistency of the axioms of arithmetic
In mathematics, Hilbert's second problem was posed by David Hilbert in 1900 as one of his 23 problems. It asks for a proof that arithmetic is consistent
Hilbert's_second_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
October–December 1977 Klin, M.H. and R. Poschel: The Konig problem, the isomorphism problem for cyclic graphs and the method of Schur rings, Algebraic
Toida's_conjecture
B. Neumann, The isomorphism problem for algebraically closed groups, in: Word Problems, Decision Problems, and the Burnside Problem in Group Theory,
Absolute presentation of a group
Absolute_presentation_of_a_group
German-American mathematician (1878–1952)
equations Other topics of interest Chiral knot Conjugacy problem Freiheitssatz Group isomorphism problem Lotschnittaxiom Mapping class group of a surface Non-Archimedean
Max_Dehn
Type of group in mathematics
unknown if one-relator groups have solvable conjugacy problem. It is unknown if the isomorphism problem is decidable for the class of one-relator groups.
One-relator_group
Graph layout on multiple half-planes
number is zero. As a consequence of bounded expansion, the subgraph isomorphism problem, of finding whether a pattern graph of bounded size exists as a subgraph
Book_embedding
If G is a finitely generated group with exponent n, is G necessarily finite?
finite groups with m generators of exponent n, up to isomorphism? This variant of the Burnside problem can also be stated in terms of category theory: an
Burnside_problem
Binary operation in graph theory
to isomorphisms of induced subgraphs of G and H. Therefore, the modular product graph can be used to reduce problems of induced subgraph isomorphism to
Modular_product_of_graphs
On lattices and sphere packing in Euclidean space
{\displaystyle n} , there are only a finite number of possibilities for the isomorphism class of the underlying group of a space group, and the action of the
Hilbert's_eighteenth_problem
Biclique-free graph Erdős–Hajnal conjecture Turán number Subgraph isomorphism problem Forbidden graph characterization Combinatorics: Set Systems, Hypergraphs
Forbidden_subgraph_problem
Permutation of the elements of a set in which no element appears in its original position
27 December 2011. Lubiw, Anna (1981). "Some NP-complete problems similar to graph isomorphism". SIAM Journal on Computing. 10 (1): 11–21. doi:10.1137/0210002
Derangement
Branch of mathematics
as small cancellation theory and algorithmic problems (e.g. the word, conjugacy, and isomorphism problems). Other group-theoretic topics like mapping class
Geometry
Problem of inverting exponentiation in groups
_{b}a} is also unique, and the discrete logarithm amounts to a group isomorphism log b : H → Z . {\displaystyle \log _{b}\colon H\to \mathbf {Z} .} On
Discrete_logarithm
Proposition in mathematical logic
problems in set theory, and establishing its truth or falsehood was the first of Hilbert's 23 problems presented in 1900. The answer to this problem is
Continuum_hypothesis
Combinatorics problem proposed by Thomas Penyngton Kirkman
Kirkman's schoolgirl problem is a problem in combinatorics proposed by Thomas Penyngton Kirkman in 1850 as Query VI in The Lady's and Gentleman's Diary
Kirkman's_schoolgirl_problem
Mathematical problem
In mathematical logic, Tarski's high school algebra problem was a question posed by Alfred Tarski. It asks whether there are identities involving addition
Tarski's high school algebra problem
Tarski's_high_school_algebra_problem
Impossible task in computing
mathematics and computer science, the Entscheidungsproblem (German for 'decision problem'; pronounced [ɛntˈʃaɪ̯dʊŋspʁoˌbleːm]) is a challenge posed by David Hilbert
Entscheidungsproblem
Method for finding patterns in networks
length, and more generally it applies to the subgraph isomorphism problem (an NP-complete problem), where it yields polynomial time algorithms when the
Color-coding
Topics referred to by the same term
glucose-dependent insulinotropic polypeptide Genome India Project Graph isomorphism problem GSM Interworking Profile, a telecommunications standard Francisco
GIP
Probability problem
extension of T proves the claim. A function model is given by the natural isomorphism from F0(Z+) to the family of polynomials, in one single real variable
Hamburger_moment_problem
ISOMORPHISM PROBLEM
ISOMORPHISM PROBLEM
Girl/Female
Muslim/Islamic
Away from all Problems
Boy/Male
Hindu, Indian
Problem
Boy/Male
Arabic, Indian, Muslim
Problem Solver
Girl/Female
Bengali, Indian
Eternity; Problem Solver
Boy/Male
Muslim
Problem solver
Girl/Female
Indian, Telugu
Destroyer of Problems
Boy/Male
Indian, Tamil
People with this Name are Preferably Intelligent and Very Generous; Highly Knowledgeable in Problem Solving Skills
ISOMORPHISM PROBLEM
ISOMORPHISM PROBLEM
Boy/Male
Muslim
Faith, Belief, Faith in Allah
Boy/Male
Hindu, Indian
Cool Like Autumn
Girl/Female
Hindu
The most beautiful
Male
Greek
(Ανατόλιος) Greek name derived from the word anatole, ANATOLIOS means "east" and "sunrise."
Girl/Female
Hindu, Indian, Malayalam
Lighten
Girl/Female
Tamil
Abhijna | அபீஜà¯à®¨à®¾
Remembrance, Recollection
Surname or Lastname
German
German : occupational name for a roofer (thatcher, tiler, slater, or shingler) or a carpenter or builder, from an agent derivative of Middle High German decke ‘covering’, a word which was normally used to refer to roofs, but sometimes also to other sorts of covering; modern German Decke still has the twin senses ‘ceiling’ and ‘blanket’.Dutch : variant of Dekker, cognate with 1.English : variant of Dicker.
Boy/Male
Indian
Lover of Pranavi
Girl/Female
Tamil
Decorated, Adorned
Boy/Male
Latin
Song.
ISOMORPHISM PROBLEM
ISOMORPHISM PROBLEM
ISOMORPHISM PROBLEM
ISOMORPHISM PROBLEM
ISOMORPHISM PROBLEM
n.
A problem of more than usual difficulty added to another on an examination paper.
n.
Isomorphism between the two forms severally of two dimorphous substances.
n.
The quality of representing or using animal forms; as, zoomorphism in ornament.
a.
Of or pertaining to zoomorphism.
v. t.
To have just and adequate ideas of; to apprehended the meaning or intention of; to have knowledge of; to comprehend; to know; as, to understand a problem in Euclid; to understand a proposition or a declaration; the court understands the advocate or his argument; to understand the sacred oracles; to understand a nod or a wink.
n.
Isomorphism between the three forms, severally, of two trimorphous substances.
n.
A near similarity of crystalline forms between unlike chemical compounds. See Isomorphism.
a.
Having the quality of isomorphism.
n.
One who proposes problems.
v. t.
To propose problems.
a.
Alt. of Problematical
a.
Having the quality of isodimorphism.
a.
Questionable; equivocal; indefinite; problematical.
n.
Isomorphism between substances that are isomeric.
n.
The transformation of men into beasts.
a.
Isomorphous.
a.
Having the nature of a problem; not shown in fact; questionable; uncertain; unsettled; doubtful.
n.
The representation of God, or of gods, in the form, or with the attributes, of the lower animals.
n.
A certain function relating to a system of forces and their points of application, -- first used by Clausius in the investigation of problems in molecular physics.
n.
A similarity of crystalline form between substances of similar composition, as between the sulphates of barium (BaSO4) and strontium (SrSO4). It is sometimes extended to include similarity of form between substances of unlike composition, which is more properly called homoeomorphism.