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Set of computational problems stated by Richard Karp (1973)
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
the more commonly known problems that are NP-complete when expressed as decision problems. As there are thousands of such problems known, this list is in
List_of_NP-complete_problems
Complexity class
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:
NP-completeness
Problem of finding a cycle through all vertices of a graph
Intractability: A Guide to the Theory of NP-Completeness and Richard Karp's list of 21 NP-complete problems. The problems of finding a Hamiltonian path and a
Hamiltonian_path_problem
Classical problem in combinatorics
covering is NP-complete. It is one of Karp's 21 NP-complete problems shown to be NP-complete in 1972. The optimization/search version of set cover is NP-hard
Set_cover_problem
Problem in combinatorial optimization
knapsack problem is often used to refer specifically to the subset sum problem. The subset sum problem is one of Karp's 21 NP-complete problems. Knapsack
Knapsack_problem
American mathematician
Problems", in which he proved 21 problems to be NP-complete. In 1973 he and John Hopcroft published the Hopcroft–Karp algorithm, the fastest known method
Richard_M._Karp
Mathematical optimization problem restricted to integers
one of Karp's 21 NP-complete problems. If some decision variables are not discrete, the problem is known as a mixed-integer programming problem. Integer
Integer_programming
Unsolved problem in computer science
attack the P = NP question, the concept of NP-completeness is very useful. NP-complete problems are problems that any other NP problem is reducible to
P_versus_NP_problem
Subset of a graph's vertices, including at least one endpoint of every edge
an NP-hard optimization problem that has an approximation algorithm. Its decision version, the vertex cover problem, was one of Karp's 21 NP-complete problems
Vertex_cover
Task of computing complete subgraphs
problem are hard. The clique decision problem is NP-complete (one of Karp's 21 NP-complete problems). The problem of finding the maximum clique is both
Clique_problem
Problem of determining if a Boolean formula could be made true
the first problem that was proven to be NP-complete—this is the Cook–Levin theorem. This means that all problems in the complexity class NP, which includes
Boolean satisfiability problem
Boolean_satisfiability_problem
Partition into subsets from a given family
problem to determine if an exact cover exists. The exact cover problem is NP-complete and is one of Karp's 21 NP-complete problems. It is NP-complete
Exact_cover
On short connecting nets with added points
number k. The decision problem is one of Karp's 21 NP-complete problems; hence the optimization problem is NP-hard. Steiner tree problems in graphs are applied
Steiner_tree_problem
Problem in graph theory
satisfiability problem). The weighted version of the decision problem was one of Karp's 21 NP-complete problems; Karp showed the NP-completeness by a reduction
Maximum_cut
Partition of a graph's nodes into 2 disjoint subsets
cut is computationally hard. The max-cut problem is one of Karp's 21 NP-complete problems. The max-cut problem is also APX-hard, meaning that there is
Cut_(graph_theory)
Method for solving one problem using another
isomorphism problem itself is GI-complete, as are several other related problems. Karp's 21 NP-complete problems MIT OpenCourseWare: 16. Complexity: P, NP, NP-completeness
Polynomial-time_reduction
NP-hard problem in combinatorial optimization
graph has a tour whose length is at most L) belongs to the class of NP-complete problems. Thus, it is possible that the worst-case running time for any algorithm
Travelling_salesman_problem
Problem of grouping into triples
This decision problem is known to be NP-complete; it is one of Karp's 21 NP-complete problems. It is NP-complete even in the special case that k = |X| = |Y| = |Z|
3-dimensional_matching
Problem in computer science
is a classical NP-complete problem in computational complexity theory and combinatorics, and was one of Karp's 21 NP-complete problems. Suppose one has
Set_packing
Adjacent subset of an undirected graph
maximum clique, or all cliques, in a given graph. It is NP-complete, one of Karp's 21 NP-complete problems. It is also fixed-parameter intractable, and hard
Clique_(graph_theory)
Methodic assignment of colors to elements of a graph
algorithmic problem since the early 1970s: the chromatic number problem (see section § Vertex coloring below) is one of Karp's 21 NP-complete problems from 1972
Graph_coloring
Subfield of mathematical optimization
circulations, spanning trees, matching, and matroid problems. For NP-complete discrete optimization problems, current research literature includes the following
Combinatorial_optimization
Existence of values making formula true
Weispfenning. 2-satisfiability Boolean satisfiability problem Circuit satisfiability Karp's 21 NP-complete problems Validity Constraint satisfaction Boolos, Burgess
Satisfiability
Boolean satisfiability is NP-complete and therefore that NP-complete problems exist
states that the Boolean satisfiability problem is NP-complete. That is, it is in NP, and any problem in NP can be reduced in polynomial time by a deterministic
Cook–Levin_theorem
Edges that hit all cycles in a graph
algorithms. It was one of Richard M. Karp's original set of 21 NP-complete problems; its NP-completeness was proved by Karp and Eugene Lawler by showing that
Feedback_arc_set
Subset of a graph's nodes such that all other nodes link to at least one
was one of Karp's 21 NP-complete problems. There exist a pair of polynomial-time L-reductions between the minimum dominating set problem and the set
Dominating_set
Problem in theoretical computer science
the maximum clique problem and the problem of testing whether a graph contains a Hamiltonian cycle, and is therefore NP-complete. However certain other
Subgraph_isomorphism_problem
Partition of a graph's nodes into cliques
clique cover is NP-hard, and its decision version is NP-complete. It was one of Richard Karp's original 21 problems shown NP-complete in his 1972 paper
Clique_cover
as a version of the classic Steiner tree problem (one of Karp's 21 NP-complete problems), where instead of minimizing the size of the tree, the objective
Wiener_connector
Inherent difficulty of computational problems
what computers can and cannot do. The P versus NP problem, one of the seven Millennium Prize Problems, is part of the field of computational complexity
Computational complexity theory
Computational_complexity_theory
Vertices whose removal breaks all cycles
feedback vertex set of size at most k is an NP-complete problem; it was among the first problems shown to be NP-complete. It has wide applications in operating
Feedback_vertex_set
Mathematical and computational problem
Computationally, the problem is NP-hard, and the corresponding decision problem, deciding if items can fit into a specified number of bins, is NP-complete. Despite
Bin_packing_problem
American computer scientist (1933–1994)
The NP-completeness proofs for two of Karp's 21 NP-complete problems, directed Hamiltonian cycle and 3-dimensional matching, were credited by Karp to Lawler
Eugene_Lawler
computational complexity theory, NP/poly is a complexity class, a non-uniform analogue of the class NP of problems solvable in polynomial time by a non-deterministic
NP/poly
Method to solve optimization problems
arbitrary integers). This problem is also classified as NP-hard, and in fact the decision version was one of Karp's 21 NP-complete problems. If only some of the
Linear_programming
Algorithm for solving the partition problem
algorithm for solving the partition problem and the multiway number partitioning. It is also called the Karmarkar–Karp algorithm after its inventors, Narendra
Largest_differencing_method
Algorithmic problem on pairs of sequences
arbitrary number of input sequences, the problem is NP-hard. When the number of sequences is constant, the problem is solvable in polynomial time by dynamic
Longest_common_subsequence
intractable (#P-complete) in many special cases for which satisfiability is tractable (in P), as well as when satisfiability is intractable (NP-complete). This
♯SAT
clique problem for D = 1 {\displaystyle D=1} , which was one of Karp's 21 NP-complete problems. The order of any graph with maximum degree Δ {\displaystyle
MaxDDBS
Logic problem, AND of pairwise ORs
more general problems, which are NP-complete, 2-satisfiability can be solved in polynomial time. Instances of the 2-satisfiability problem are typically
2-satisfiability
Computational problem in graph theory
{\displaystyle k} , or at most k {\displaystyle k} . Most variants of this problem are NP-complete, except for small values of k {\displaystyle k} . A closure of
Maximum_flow_problem
Set of problems in computational complexity theory
hardest problems in C). Of particular importance is the class of NP-complete problems—the most difficult problems in NP. Because all problems in NP can be
Complexity_class
Type of computational problem
counting problems is the #P class, the counting problems corresponding to the NP class of decision problems. An NP problem a decision problem that asks
Counting_problem_(complexity)
Graph divided into two independent sets
example where bipartite graphs appear naturally is in the (NP-complete) railway optimization problem, in which the input is a schedule of trains and their
Bipartite_graph
They show that 21 of these problems can be solved in linear time; 7 require more complex, but still polynomial-time, algorithms; 3 are NP-hard: maximizing
Balanced_number_partitioning
Computer compiler optimization technique
is passed in R3. NP-Problem Chaitin et al. showed that optimal register allocation is an NP-complete problem. This NP-completeness is entirely dependent
Register_allocation
Quantum physics-based metaheuristic for optimization problems
a fast Grover oracle for the square-root speedup in solving many NP-complete problems. Quantum annealing can be compared to simulated annealing, whose
Quantum_annealing
2nd episode of the 1st season of Numbers
Karp of the University of California, Berkeley proposed a type of problem known as a NP-complete problem. They proposed that if one can solve one NP-type
Uncertainty Principle (Numbers)
Uncertainty_Principle_(Numbers)
All these problems are NP-hard, but there are various algorithms that solve it efficiently in many cases. Some closely-related problems are: The partition
Multiway_number_partitioning
Independent set which is not a subset of any other independent set
solving many NP-complete graph problems. Most obviously, the solutions to the maximum independent set problem, the maximum clique problem, and the minimum
Maximal_independent_set
Award for advancements in discrete mathematics
endowment administered by MOS. 1979: Richard M. Karp for classifying many important NP-complete problems. Kenneth Appel and Wolfgang Haken for the four
Fulkerson_Prize
American mathematician (born 1930)
Grigori Perelman), the P = NP problem, and the Navier–Stokes equations, all of which have been designated Millennium Prize Problems by the Clay Mathematics
Stephen_Smale
American annual computer science prize
2024. Rabin, M. O.; Scott, D. (1959). "Finite automata and their decision problems". IBM Journal of Research and Development. 3 (2): 114. doi:10.1147/rd.32
Turing_Award
Linear programming for Combinatorial optimization
optimization problems. It was introduced in the context of the cutting stock problem. Later, it has been applied to the bin packing and job scheduling problems. In
Configuration_linear_program
Computer system emulating human expert
Usually such problem leads to a satisfiability (SAT) formulation. This is a well-known NP-complete problem Boolean satisfiability problem. If we assume
Expert_system
Mario Tokoro, ed. (2010). "9". e: From Understanding Principles to Solving Problems. IOS Press. pp. 223–224. ISBN 978-1-60750-468-9. Cristopher Moore; Stephan
List of pioneers in computer science
List_of_pioneers_in_computer_science
Indian family of infantry arms
Retrieved 29 August 2018. "Nepali Army | नेपाली सेना". www.nepalarmy.mil.np. Nepalese Army. Retrieved 3 March 2021. Reetika Sharma, Ramvir Goria, Vivek
INSAS_rifle
Field of knowledge
packing were two major problems of discrete mathematics solved in the second half of the 20th century. The P versus NP problem, which remains open to
Mathematics
Criterion of fair item allocation
whether a given allocation is MMS-fair is co-NP complete for agents with additive valuations (it is in co-NP, since it is possible to prove in polynomial
Maximin_share
American mathematician and computer scientist
second-order logic coincides with the complexity class NP in the sense that a decision problem can be expressed in existential second-order logic if and
Ronald_Fagin
Basic notion of sameness in mathematics
uses balance scales as a pictorial approach to help students grasp basic problems of algebra. The mass of some objects on the scale is unknown and represents
Equality_(mathematics)
program for completing the classification of finite simple groups. Richard M. Karp shows that the Hamiltonian cycle problem is NP-complete. January 31
1972_in_science
Model of computational complexity
Hemachandra, L. (1987), "One-way functions, robustness, and non-isomorphism of NP-complete sets", Technical Report DCS TR86-796, Cornell University Tardos, G. (1989)
Decision_tree_model
more by the state of the area in terms of unemployment, alcohol problems and drug problems instead of the laws and regulations. This study analyzed statistics
Gun politics in the United States
Gun_politics_in_the_United_States
Ultrafine particles of silver between 1 nm and 100 nm in size
ultrasonically-assisted synthesis. Under ultrasound treatment, silver nanoparticles (AgNP) are synthesized with κ-carrageenan as a natural stabilizer. The reaction
Silver_nanoparticle
Tropical, edible, staple fruit
April 22, 2016, at the Wayback Machine. Global Invasive Species Database. N.p., July 6, 2005. Thomas, J.E. (ed). 2015. MusaNet Technical Guidelines for
Banana
Type of vaccine for humans
doi:10.1056/NEJMoa2108891. PMC 8314739. PMID 34289274. Evans SJ, Jewell NP (August 2021). "Vaccine Effectiveness Studies in the Field". The New England
Pfizer–BioNTech COVID-19 vaccine
Pfizer–BioNTech_COVID-19_vaccine
contributions to the theory of NP-completeness. Karp introduced the now standard methodology for proving problems to be NP-complete which has led to the identification
List of University of California, Berkeley faculty
List_of_University_of_California,_Berkeley_faculty
Species of bacterium
PMC 6136623. PMID 30274409. Walker, D.H.; Paris, D.H.; Day, N.P.; Shelite, T.R. (2013). "Unresolved problems related to scrub typhus: A seriously neglected life-threatening
Orientia_tsutsugamushi
one-sided t-test based on the asymptotic of the Jensen-Shannon metric. rSeqNP An R package that implements a non-parametric approach to test for differential
List of RNA-Seq bioinformatics tools
List_of_RNA-Seq_bioinformatics_tools
Village in Lithuania
końca czternastego wieku, Warszawa 1895, p. 589 Makarczyk 2022, p. 45 zob. np. Janusz Hrybacz, Miedniki Królewskie, [in:] service Karta dziejów wileńskiej
Medininkai
KARPS 21-NP-COMPLETE-PROBLEMS
KARPS 21-NP-COMPLETE-PROBLEMS
Boy/Male
Tamil
Complete
Girl/Female
Hindu
Complete
Boy/Male
Muslim
Complete
Boy/Male
Indian
Complete
Girl/Female
Tamil
Complete
Male
Greek
(ΚαÏπός) Greek name KARPOS means "fruit." In mythology, this is the name of a son of the nymph Khloris and the god Zephyros. In the bible, it is the name of a Christian at Troas mentioned in the second epistle of Timothy (2 Ti. 4:13).
Girl/Female
Tamil
Complete
Girl/Female
Tamil
Sompurna | ஸோமபà¯à®°à¯à®¨à®¾
Complete
Sompurna | ஸோமபà¯à®°à¯à®¨à®¾
Girl/Female
Tamil
Complete
Girl/Female
Tamil
Complete
Male
Russian
(Карп) Russian form of Greek Karpos, KARP means "fruit, profits."
Boy/Male
Tamil
Complete
Boy/Male
Indian
Complete
Boy/Male
Tamil
Poornan | பூரà¯à®¨à®¾à®¨
Complete
Poornan | பூரà¯à®¨à®¾à®¨
Boy/Male
Tamil
Complete
Girl/Female
Greek
Grace. Phonetic.
Girl/Female
Australian, French, Greek
Victory of the People
Girl/Female
Tamil
Shesha Harani | ஷேஷ ஹரணீÂ
Complete
Shesha Harani | ஷேஷ ஹரணீÂ
Girl/Female
Indian
Complete
Girl/Female
Muslim
Complete
KARPS 21-NP-COMPLETE-PROBLEMS
KARPS 21-NP-COMPLETE-PROBLEMS
Boy/Male
Indian, Telugu
Son of Wind
Girl/Female
Arabic, British, English, Gujarati, Hindu, Indian, Swedish
Light; Pleasure; Desire; Goddess Parvati; Purity
Boy/Male
Hindu, Indian, Sanskrit, Tamil
Victorious
Boy/Male
Hindu, Indian
Monk; Signal
Girl/Female
Tamil
Vernica | வேரà¯à®¨à¯€à®•à®¾
Colorful
Girl/Female
Tamil
Goddess Saraswati, Melodious
Girl/Female
Indian, Sikh
Happy; Happiness
Girl/Female
Muslim
Wisdom
Boy/Male
Indian, Kannada, Sanskrit, Telugu
Straight; Clear
Boy/Male
Bengali, Gujarati, Hindu, Indian, Marathi, Mythological, Tamil, Traditional
Son of King Dasharatha and Sumitra; Lucky; Brother of Lord Ram
KARPS 21-NP-COMPLETE-PROBLEMS
KARPS 21-NP-COMPLETE-PROBLEMS
KARPS 21-NP-COMPLETE-PROBLEMS
KARPS 21-NP-COMPLETE-PROBLEMS
KARPS 21-NP-COMPLETE-PROBLEMS
a.
Making complete.
n.
One who carps; a caviler.
a.
Not complete; not filled up; not finished; not having all its parts, or not having them all adjusted; imperfect; defective.
a.
Incomplete.
a.
Having all the parts or organs which belong to it or to the typical form; having calyx, corolla, stamens, and pistil.
adv.
In a complete manner; fully.
v. t.
To bring to a state in which there is no deficiency; to perfect; to consummate; to accomplish; to fulfill; to finish; as, to complete a task, or a poem; to complete a course of education.
a.
Filled up; with no part or element lacking; free from deficiency; entire; perfect; consummate.
n.
Worn out; far gone; advanced. See Strike, v. t., 21.
imp. & p. p.
of Compete
a.
Complex, complicated.
a.
Finished; ended; concluded; completed; as, the edifice is complete.
n.
Composed of two or more parts; composite; not simple; as, a complex being; a complex idea.
a.
Full; complete.
v. i.
To contend emulously; to seek or strive for the same thing, position, or reward for which another is striving; to contend in rivalry, as for a prize or in business; as, tradesmen compete with one another.
n.
Complete termination.
v. i.
The time of the sun's passing the solstices, or solstitial points, namely, about June 21 and December 21. See Illust. in Appendix.
imp. & p. p.
of Complete
n.
A preparation of fruit in sirup in such a manner as to preserve its form, either whole, halved, or quartered; as, a compote of pears.
adv.
In a whole or complete manner; entirely; completely; perfectly.