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computational complexity theory, the set splitting problem is the following decision problem: given a family F of subsets of a finite set S, decide whether there exists
Set_splitting_problem
Mathematical problem
Necklace splitting is a picturesque name given to several related problems in combinatorics and measure theory. Its name and solutions are due to mathematicians
Necklace_splitting_problem
"minimum cover" problem). This is equivalent, by transposing the incidence matrix, to the hitting set problem. Set packing Set splitting problem Scheduling
List_of_NP-complete_problems
called the set splitting problem. Unsolved problem in mathematics What is the smallest collection of n {\displaystyle n} -uniform sets without Property
Property_B
Monotone NAE3SAT can also be interpreted as an instance of the set splitting problem, or as a generalization of graph bipartiteness testing to 3-uniform
Not-all-equal 3-satisfiability
Not-all-equal_3-satisfiability
mathematical logic, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations. Some problems belong to more than one discipline
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
About direct sums and exact sequences
split or a direct sum (neither 1. nor 3. follows): the problem is that the image of the right splitting need not be normal. What is true in this case is that
Splitting_lemma
Data structure for storing non-overlapping sets
operations of any type, up to n of which are MakeSet operations. The combination of path compression, splitting, or halving, with union by size or by rank,
Disjoint-set_data_structure
Mathematical and computational problem
media, splitting a network prefix into multiple subnets, and technology mapping in FPGA semiconductor chip design. Computationally, the problem is NP-hard
Bin_packing_problem
Study of mathematical algorithms for optimization problems
set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise
Mathematical_optimization
Question in abstract algebra
0} must split if B is also abelian. The Whitehead problem then asks: must A be free? This splitting requirement is equivalent to the condition Ext1(A
Whitehead_problem
Edges that hit all cycles in a graph
vertex set of a given graph G {\displaystyle G} can be obtained from the solution to a minimum feedback arc set problem on a graph obtained by splitting every
Feedback_arc_set
Form of problem solving, often applied to repair failed products or processes
Mike (Nov 15, 2000). "Secrets of a super geek: Use half splitting to solve difficult problems". TechRepublic. Retrieved 22 October 2010.{{cite news}}:
Troubleshooting
Optical mesh network routing concept
This is equivalent to the set-splitting problem, which has been proven NP-complete. Therefore, the SRG diverse routing problem is also NP-complete. (SRLG
Shared_risk_resource_group
Mathematical function used in optimisation
variable splitting is a decomposition method that relaxes a set of constraints. When the variable x {\displaystyle x} appears in two sets of constraints
Variable_splitting
1955. Let A = {ai} and B = {bj} be two complementary subsets, a splitting of the set of natural numbers {1, 2, …, 2n}, such that both have the same cardinality
Minimum_overlap_problem
Episode of Neon Genesis Evangelion
"Splitting of the Breast" is the sixteenth episode of the Japanese anime television series Neon Genesis Evangelion, which was created by Gainax. The episode
Splitting_of_the_Breast
Index of articles associated with the same name
formal interpretation of a logical theory exists. Specifically, we say that a set of clauses of the form Q 1 ∧ ⋯ ∧ Q n ∧ ¬ Q n + 1 ∧ ⋯ ∧ ¬ Q n + m → P {\displaystyle
Stratification_(mathematics)
Algorithms which recursively solve subproblems
constant-bounded size, the work of splitting the problem and combining the partial solutions is proportional to the problem's size n {\displaystyle n} , and
Divide-and-conquer_algorithm
Problem in process of sharing surplus
game is called sequential bargaining. A two-person bargain problem consists of: A feasibility set F {\displaystyle F} , a closed subset of R 2 {\displaystyle
Cooperative_bargaining
Tasks in machine learning
training, test and validation sets is very dependent on the problem and data available. A training data set is a data set of examples used during the learning
Training, validation, and test data sets
Training,_validation,_and_test_data_sets
Axiomatic set theories based on the principles of mathematical constructivism
Axiomatic constructive set theory is an approach to mathematical constructivism following the program of axiomatic set theory. The same first-order language
Constructive_set_theory
Multidimensional search tree for points in k dimensional space
be set by the x value of the point, and its normal would be the unit x-axis. Since there are many possible ways to choose axis-aligned splitting planes
K-d_tree
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
Form of projection
gradient methods can be used instead. Proximal gradient methods starts by a splitting step, in which the functions f 1 , . . . , f n {\displaystyle f_{1},.
Proximal_gradient_method
Election result affecting losing candidate
because of vote splitting from candidates to the right and left. ... Approval voting thus appears to solve the problem of vote splitting simply and elegantly
Spoiler_effect
Use of braces for specifying sets
{Z} ,n=2k\}} — The set of all even integers, expressed in set-builder notation. In mathematics and more specifically in set theory, set-builder notation
Set-builder_notation
Unsolved problem in mathematics
2017-08-29. Retrieved 2016-04-17. Igor R. Shafarevich, The imbedding problem for splitting extensions, Dokl. Akad. Nauk SSSR 120 (1958), 1217-1219. p. 5 of
Inverse_Galois_problem
Statistical model validation technique
analysis will generalize to an independent data set. Cross-validation includes resampling and sample splitting methods that use different portions of the data
Cross-validation_(statistics)
Electricity-induced chemical reaction
production of fertilizers. Because the underlying chemical reaction (water splitting) does not produce greenhouse gases, the emissions footprint of electrolysis
Electrolysis_of_water
satisfiability problem NP-completeness of the Boolean satisfiability problem Cantor's diagonal argument set is smaller than its power set uncountability
List_of_mathematical_proofs
Human writing practice
in computers, which are the subject of natural language processing. The problem is non-trivial, because while some written languages have explicit word
Text_segmentation
Theorem that any three objects in space can be simultaneously bisected by a plane
exist, as if the points are on a moment curve, the problem becomes equivalent to necklace splitting, which is PPA-complete. A linear-time algorithm that
Ham_sandwich_theorem
Describes statistically the splitting of primes in a given Galois extension of Q
theorem, named after Nikolai Chebotarev, statistically describes the splitting of primes in a given Galois extension K {\displaystyle K} of the field
Chebotarev_density_theorem
Internet error message
the proxy server is unable to satisfy a request for a page because of a problem with the remote host (such as hostname resolution failures or refused TCP
HTTP_404
Statistical procedure of testing by group
search in the binary-splitting algorithm to a complex set of sub-algorithms with overlapping test groups. As such, the problem of adaptive combinatorial
Group_testing
Mathematical problem in operations research
practice however additional order splitting constraints may have to be taken into account. There is also a semi-continuous problem, where the produced rolls do
Cutting_stock_problem
Shell command for reporting and running with modified environment variables
found in both versions include -u, for unsetting variables, and -S, for splitting arguments (mainly in shebang). The following command line prints the current
Env
Machine learning algorithm
built by splitting the source set, constituting the root node of the tree, into subsets—which constitute the successor children. The splitting is based
Decision_tree_learning
Concept in machine learning
transform the test set) Duplicate rows between train/validation/test (for example, oversampling a dataset to pad its size before splitting; or, different
Leakage_(machine_learning)
Putative longer version of the Gospel of Mark
Longer Gospel of Mark and the Synoptic Problem", in Foster, Paul; et al. (eds.), New Studies in the Synoptic Problem: Oxford Conference, April 2008: Essays
Secret_Gospel_of_Mark
Irish actor
National Theatre in January 2015 to play Spike in Sir Tom Stoppard's The Hard Problem, which ran until 17 May 2015 and also had a worldwide broadcast via NT
Damien_Molony
Type of fair division
-consensus-splitting, and ε {\displaystyle \varepsilon } -perfect-division. Problem of the Nile – there are infinitely many agents. Necklace splitting – the
Consensus_splitting
This is a list of fictional stories that, when composed, were set in the future, but the future they predicted is now present or past. The list excludes
List of stories set in a future now in the past
List_of_stories_set_in_a_future_now_in_the_past
Study of optimal transportation and allocation of resources
to the study of optimal transportation and allocation of resources. The problem was formalized by the French mathematician Gaspard Monge in 1781. In the
Transportation theory (mathematics)
Transportation_theory_(mathematics)
Problem optimization method
simplifying a complicated problem by breaking it down into simpler sub-problems in a recursive manner. While some decision problems cannot be taken apart
Dynamic_programming
Nuclear reaction splitting an atom into multiple parts
this nucleus into two alpha particles. The feat was popularly known as "splitting the atom", and would win them the 1951 Nobel Prize in Physics for "Transmutation
Nuclear_fission
Numerical integration scheme for Hamiltonian systems
specific problem, a family of high-order explicit non-canonical symplectic integrators can be constructed using the He splitting method. Splitting H {\textstyle
Symplectic_integrator
Type of mathematical proof
the statement, it does not hold. Proof by cases is commonly used when a problem naturally separates into distinct categories, such as: Even and odd integers
Proof_by_exhaustion
fundamental set of rules or defined procedures that are typically designed and used to be a simpler way to solve a specific problem or a broad set of problems. Simply
List_of_algorithms
Biographical film by Antoine Fuqua
gave us countless hits. What's wrong with giving fans what they want?" Splitting Michael into two films was considered during production, but the production
Michael_(2026_film)
Astronomical high energy transient pulse
Stars: A Possible Link Between Fast Radio Bursts and the Missing Pulsar Problem". Monthly Notices of the Royal Astronomical Society: Letters. 450 (1):
Fast_radio_burst
Weakly optimal allocation of resources
It is Pareto efficient, since any other discrete allocation (without splitting items) makes someone worse off. However, it is not fractionally Pareto
Pareto_efficiency
Topics referred to by the same term
solution of the linear least squares problem Normal extensions (or quasi-Galois), field extensions, splitting fields for a set of polynomials over the base field
Normal
Japanese train type
associated discontinuation of service by these sets on the Hokuhoku Line. 108 cars were built in 9-car sets for a total of 12 trainsets. 683-4000 series
683_series
Conceptual framework used in numerical analysis of surfaces and shapes
shapes with sharp corners and shapes that change topology (such as by splitting in two or developing holes). These characteristics make LSM effective
Level-set_method
Declarative logic programming language
The decision problem formulation of Datalog evaluation is as follows: "Given a Datalog program P split into a set of facts (EDB) E and a set of rules R
Datalog
Technique invented by Paul Cohen for proving consistency and independence results
existence of sets that are "too complex for M {\displaystyle M} to describe". Forcing avoids such problems by requiring the newly introduced set X {\displaystyle
Forcing_(mathematics)
Story from the Old Testament
announces an absurd procedure, which is reasonable in some perverse way: splitting the baby, according to the principle of compromise; or a tug of war, in
Judgement_of_Solomon
American system of telecommunications subsidies and fees
with E-rate funds was left unused in a warehouse for years." Lastly, a problem that has plagued the program is the long lag time between the overall application
Universal_Service_Fund
Character encoding
recipient. Some applications alert the user when a message will require splitting, or even send a longer message as a multimedia message (MMS). Since release
GSM_03.38
Data encryption and authentication program
accept them. No satisfactory solution has been found for the underlying problem. In the (more recent) OpenPGP specification, trust signatures can be used
Pretty_Good_Privacy
Measurement method using interference of waves
Jamin developed the first single-beam interferometer (not requiring a splitting aperture as the Arago interferometer did) in 1856. In 1881, the American
Interferometry
Set of philosophical problems
This argument is called the "Dichotomy" because it involves repeatedly splitting a distance into two parts. An example with the original sense can be found
Zeno's_paradoxes
Iterative method in conformal mapping
each of which the Dirichlet problem could be solved, Schwarz described an iterative method for solving the Dirichlet problem in their union, provided their
Schwarz_alternating_method
Home video game console
dirt and dust than an industry-standard card edge connector. The design problems were exacerbated by Nintendo's choice of materials. The console slot nickel
Nintendo_Entertainment_System
the first Catholic priest in Germany who outed himself in public without problems by his bishop, in February 2019. Pierre Valkering became the first Catholic
List of LGBTQ firsts by year (2010s)
List_of_LGBTQ_firsts_by_year_(2010s)
Computer science problem
The firing squad synchronization problem is a problem in computer science and cellular automata in which the goal is to design a cellular automaton that
Firing squad synchronization problem
Firing_squad_synchronization_problem
Graphics structure
buckets of splitting planes, so that only at these splitting points, re-calculation of SAH is required. Bottom-up methods start with the input set as the
Bounding_volume_hierarchy
Political party in the United Kingdom
on the march – and the most popular party on TikTok. There's just one problem". Sky News. Retrieved 20 July 2025. Walker, Peter (27 November 2024). "Constituencies
Reform_UK
1989 historical novel by Ken Follett
convince Ellen, who has remained bitter towards Philip for his role in splitting up her and Tom, to testify on his behalf. At Philip's trial, Ellen's testimony
The_Pillars_of_the_Earth
Basic unit of taxonomic classification, below genus
species concept that emphasise monophyly or diagnosability may lead to splitting of existing species, for example in Bovidae, by recognising old subspecies
Species
Tree-based ensemble machine learning methods
developed further by Ho in 1995. Ho established that forests of trees splitting with oblique hyperplanes can gain accuracy as they grow without suffering
Random_forest
Symbol "#!", used in computing
issue on the kernel end with splitting, it adds the requirement that env supports this particular extension. Another problem is scripts containing a carriage
Shebang_(Unix)
Creation of hip-hop music in a recording studio
Memories A track by Soulker self-described as a "Xavier Wulf Type Beat" Problems playing this file? See media help. Starting in the 2010s, amateur producers
Hip-hop_production
Logic puzzle forming a picture in a grid
joining the two blocks by a box would produce a too large block A box if splitting the two blocks by a space would produce a too small block that does not
Nonogram
2025 American comedy television series
Stacey, Pat (March 26, 2025). "'The Studio' review: Seth Rogan's side-splitting Hollywood satire could be the best comedy of the year". The Irish Independent
The_Studio_(TV_series)
Substrings of length k contained in a biological sequence
are present in the genome. Furthermore, splitting the k-mers into smaller sizes also helps alleviate the problem of different initial read lengths. In this
K-mer
English television personality (born 1988)
dated for a year before splitting up in August 2017 In August 2020, Thomas admitted that he and his twin have a drinking problem; he got sober and celebrated
Scott_Thomas_(TV_personality)
Cooper (May 10, 2022). "What Are Incursions? Marvel's New Multiverse Problem Explained". Screen Rant. Archived from the original on September 13, 2023
Features of the Marvel Cinematic Universe
Features_of_the_Marvel_Cinematic_Universe
Proof that is not easily verified by hand
since been applied to other arguments, mainly those with excessive case splitting and/or with portions dispatched by a difficult-to-verify computer program
Non-surveyable_proof
Large language model and AI chatbot by Anthropic
Ashley (February 27, 2026). "These federal agencies may have a Claude problem now". Axios. Retrieved February 28, 2026. John Ruwitch (March 26, 2026)
Claude_(language_model)
Abandonment of military duty without authorization
capture at Churubusco in August 1847. High desertion rates were a major problem for the Mexican army, depleting forces on the eve of battle. Most of the
Desertion
2019 film by Ric Roman Waugh
the perimeter, killing the would-be attackers as he and Banning escape. Splitting up, Clay goes to Banning's house and saves Leah and Lynne from a kidnapping
Angel_Has_Fallen
Dynamical Stark effect
dipole transition. In this case, the alternating field has the effect of splitting the two bare transition states into doublets or "dressed states" that
Autler–Townes_effect
Optimization by removing non-optimal solutions to subproblems
problem requires some kind of data structure that represents sets of candidate solutions. Such a representation is called an instance of the problem.
Branch_and_bound
Electric guitar pickup
a sound closer to that of two single-coil pickups used together. Coil splitting is often wrongly referred to as a coil tapping. Coil taps are most commonly
Humbucker
Topics referred to by the same term
negative emotional ("affective") responses to one's environment Lane splitting, a practice that cyclists use to pass slow or stopped congested traffic
Filter
discovered during Dionysus' invasion of India and communicate via ear-splitting shrieks. They were part of Tarquin, Caligula, and Commodus' army who attacked
List of characters in mythology novels by Rick Riordan
List_of_characters_in_mythology_novels_by_Rick_Riordan
2.71828…, base of natural logarithms
produces the nth partial sum of the series above. This method uses binary splitting to compute e with fewer single-digit arithmetic operations and thus reduced
E_(mathematical_constant)
Bimini. The commission had proposed creating two new constituencies by splitting Killarney and West Grand Bahama and Bimini, citing the size of those electorates
2026 Bahamian general election
2026_Bahamian_general_election
Path-finding using high-weight graph edges
In graph algorithms, the widest path problem is the problem of finding a path between two designated vertices in a weighted graph, maximizing the weight
Widest_path_problem
Algorithm for solving the quadratic programming problem from training SVMs
α j {\displaystyle \alpha _{j}} . The first approach to splitting large SVM learning problems into a series of smaller optimization tasks was proposed
Sequential minimal optimization
Sequential_minimal_optimization
Optimization algorithm
Combettes and J.-C. Pesquet, "Proximal splitting methods in signal processing," in: Fixed-Point Algorithms for Inverse Problems in Science and Engineering, (H
Dykstra's projection algorithm
Dykstra's_projection_algorithm
Computer program for the Boolean satisfiability problem
w(2;3,17) and w(2;3,18) in 2010 where both the phases (splitting and solving the partial problems) were performed using DPLL. One strategy towards a parallel
SAT_solver
British rock musician and songwriter (1946–1991)
10 position in the UK singles chart. I won't be touring on my own or splitting up with Queen. Without the others I would be nothing. The press always
Freddie_Mercury
Set of gender-neutral pronouns in English
The Spivak pronouns 'e/em/eir' are a set of gender-neutral pronouns in English promoted on the virtual community LambdaMOO based on pronouns used in a
Spivak_pronoun
Spacetime manifold
the "leakage" of information or energy described above. The fundamental splitting theorem by Geroch (1970) establishes the equivalence between global hyperbolicity
Globally_hyperbolic_spacetime
Simplicial complex in Euclidean geometry
straightforward Euler characteristic argument. Triangle Splitting Algorithm : Find the convex hull of the point set P {\displaystyle {\mathcal {P}}} and triangulate
Point-set_triangulation
Matrix in mathematics
splittings A is inverse-positive. That is, A−1 exists and A−1 ≥ 0. A is monotone. That is, Ax ≥ 0 implies x ≥ 0. A has a convergent regular splitting
M-matrix
SET SPLITTING-PROBLEM
SET SPLITTING-PROBLEM
Female
Egyptian
, a sister of Sekherta.
Girl/Female
Indian, Sanskrit
Splitting; Breaking
Surname or Lastname
English
English : variant spelling of See.
Surname or Lastname
English
English : perhaps a variant of Sait, from the Old English personal name Sǣgēat (‘sea Geat’).
Female
Egyptian
, the mother of Fai-hor-ou-oer.
Female
Egyptian
, a wife and daughter of Antef.
Boy/Male
Indian, Sanskrit
Breaking; Splitting
Female
English
Short form of English Elizabeth, BET means "God is my oath."Â
Female
Egyptian
, the wife of Osirtesen.
Surname or Lastname
English and German
English and German : topographic name for someone who lived by the sea-shore or beside a lake, from Middle English see ‘sea’, ‘lake’ (Old English sǣ), Middle High German sē. Alternatively, the English name may denote someone who lived by a watercourse, from an Old English sēoh ‘watercourse’, ‘drain’.
Female
Egyptian
, the wife of the usurper Sipthah.
Male
English
Short form of English Stephen, STE means "crown."
Male
Hebrew
Variant spelling of Hebrew Sheth, SHET means "buttocks."
Female
Egyptian
, second wife of Antef.
Female
Egyptian
, a sister of Sekherta.
Male
English
Anglicized form of Hebrew Sheth, SETH means "buttocks." In the bible, this is the name of the third son of Adam and Eve. Compare with other forms of Seth.
Female
Egyptian
, an uncertain goddess.
Boy/Male
Indian, Sanskrit
Splitting; Opening; Moving Slowly
Male
Hindi/Indian
(सेठ) Hindi name derived from the Sanskrit word setu, SETH means "bridge." Compare with other forms of Seth.
Boy/Male
Egyptian Hebrew Swedish
Son of Seb and Nut.
SET SPLITTING-PROBLEM
SET SPLITTING-PROBLEM
Boy/Male
English American
Forest; cup bearer.
Surname or Lastname
English
English : variant of Maxson.
Boy/Male
English
Noble or famous.
Girl/Female
Indian
The quiet one
Girl/Female
Hebrew American Spanish
Life.
Girl/Female
Anglo, British, English
Noble
Girl/Female
American, Australian, British, English, Latin
Crowned with Laurels; Modern Variant of Lora and Laurie Referring to the Laurel Tree; Sweet Bay Tree Symbolic of Honor and Victory; The Bay; Laurel
Boy/Male
American, Australian, British, Christian, Danish, English, Finnish, German, Greek
Rock; Form of Peter; Stone
Surname or Lastname
English
English : habitational name from a place in Berkshire named Wadley, from Old English wÄd ‘woad’ or the personal name Wada + lÄ“ah ‘woodland clearing’. Wadley in Northumberland, which has the same derivation, appears not to have contributed significantly to the modern surname.
Girl/Female
American, Australian, British, Christian, Danish, English, German, Greek, Norse, Teutonic
Heroine; Hay Meadow; Praise the Lord; From the Hall; Thinking of the Sea; Army Power
SET SPLITTING-PROBLEM
SET SPLITTING-PROBLEM
SET SPLITTING-PROBLEM
SET SPLITTING-PROBLEM
SET SPLITTING-PROBLEM
n.
A sitting up of a woman after her confinement, to receive and entertain her friends.
v. i.
To fit or suit one; to sit; as, the coat sets well.
n.
The act or time of sitting, as to a portrait painter, photographer, etc.
v. t.
To compose; to arrange in words, lines, etc.; as, to set type; to set a page.
n.
Act of cleaving or splitting.
n.
Posture, or way of sitting, on horseback.
n.
The act of cleaving or splitting.
a.
Fixed in position; immovable; rigid; as, a set line; a set countenance.
n.
The actual presence or meeting of any body of men in their seats, clothed with authority to transact business; a session; as, a sitting of the judges of the King's Bench, or of a commission.
p. pr. & vb. n.
of Split
n.
See Set, n., 2 (e) and 3.
n.
A sitting; a right to sit; regular or appropriate place of sitting; as, a seat in a church; a seat for the season in the opera house.
a.
Regular; uniform; formal; as, a set discourse; a set battle.
v. t.
To cause to be seated or in a sitting posture; to furnish a seat to; -- used reflexively.
p. pr. & vb. n.
of Sit
v. t.
To assign a seat to, or the seats of; to give a sitting to; as, to seat a church, or persons in a church.
a.
Deafening; disagreeably loud or shrill; as, ear-splitting strains.
v. t.
To cause to sit; to make to assume a specified position or attitude; to give site or place to; to place; to put; to fix; as, to set a house on a stone foundation; to set a book on a shelf; to set a dish on a table; to set a chest or trunk on its bottom or on end.
imp. & p. p.
of Set