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Partition of a graph by removing fewest possible edges
In graph theory, a minimum cut or min-cut of a graph is a cut (a partition of the vertices of a graph into two disjoint subsets) that is minimal in some
Minimum_cut
Combinatorial optimization graph problem
In mathematics, the minimum k-cut is a combinatorial optimization problem that requires finding a set of edges whose removal would partition the graph
Minimum_k-cut
Equivalence of optimization problems
the source to the sink is equal to the total weight of the edges in a minimum cut, i.e., the smallest total weight of the edges which if removed would
Max-flow_min-cut_theorem
Recursive algorithm in graph theory
theory, the Stoer–Wagner algorithm is a recursive algorithm to solve the minimum cut problem in undirected weighted graphs with non-negative weights. It was
Stoer–Wagner_algorithm
Randomized algorithm for minimum cuts
graph theory, Karger's algorithm is a randomized algorithm to compute a minimum cut of a connected graph. It was invented by David Karger and first published
Karger's_algorithm
Partition of a graph's nodes into 2 disjoint subsets
have any other cut-set as a proper subset. A cut is minimum if the size or weight of the cut is not larger than the size of any other cut. The illustration
Cut_(graph_theory)
Mathematical propositions in network flow theory
approximate max-flow min-cut theorems concern the relationship between the maximum flow rate (max-flow) and the minimum cut (min-cut) in multi-commodity flow
Approximate max-flow min-cut theorem
Approximate_max-flow_min-cut_theorem
On bipartite matching and vertex cover
in turn, is the size of a minimum cut in the network G ∞ ′ {\displaystyle G'_{\infty }} , as follows from the max-flow min-cut theorem. Let ( S , T ) {\displaystyle
Kőnig's theorem (graph theory)
Kőnig's_theorem_(graph_theory)
solution to the minimum s–t cut problem. Alternatively, simulation of such a network will also produce a solution to the minimum s–t cut problem. This article
Cederbaum's maximum flow theorem
Cederbaum's_maximum_flow_theorem
Least-weight tree connecting graph vertices
than one edge is of minimum weight across a cut, then each such edge is contained in some minimum spanning tree. If the minimum cost edge e of a graph
Minimum_spanning_tree
1992 murder in Manchester, England
after having his 18 year minimum cut by two years in 2002. McNeilly was paroled in 2015, after having her 25 year minimum cut by one year, and being described
Murder_of_Suzanne_Capper
Problem in graph theory
The weighted max-cut problem allowing both positive and negative weights can be trivially transformed into a weighted minimum cut problem by flipping
Maximum_cut
Combinatorial optimization method for a family of functions of discrete variables
the theory of flow networks. Thanks to the max-flow min-cut theorem, determining the minimum cut over a graph representing a flow network is equivalent
Graph_cut_optimization
Concept in graph theory
for dividing networks into parts is the minimum cut method (and variants such as ratio cut and normalized cut). This method sees use, for example, in
Community_structure
the United States, the minimum wage is set by federal U.S. labor law and a range of state and local laws. The first federal minimum wage was instituted in
Minimum wage in the United States
Minimum_wage_in_the_United_States
Class of computational problems
of nonzero values The max-flow min-cut theorem equates the value of a maximum flow to the value of a minimum cut, a partition of the vertices of the
Network_flow_problem
Property in graph theory
problem of computing this ordering and the cutwidth, have been called minimum cut linear arrangement. Cutwidth is related to several other width parameters
Cutwidth
Theorem in graph theory
theory, Menger's theorem says that in a finite graph, the size of a minimum cut set is equal to the maximum number of disjoint paths that can be found
Menger's_theorem
Splitting a deck of cards by someone other than the dealer
in making a cut. Multiple cuts may also be allowed. According to Parlett, a sensible minimum cut size is about one-fifth of the deck. A cut should be completed
Cut_(cards)
Algorithm that employs a degree of randomness as part of its logic or procedure
only 2 nodes remain obtain the corresponding cut result Ci i = i + 1 until i = m output the minimum cut among C1, C2, ..., Cm. end In each execution of
Randomized_algorithm
Lowest remuneration which can be paid legally in a state for working
introduced minimum wage legislation by the end of the 20th century. Because minimum wages increase the cost of labor, companies often try to avoid minimum wage
Minimum_wage
Computational problem in graph theory
t) is equal to the minimum capacity of an s-t cut (i.e., cut severing s from t) in the network, as stated in the max-flow min-cut theorem. The maximum
Maximum_flow_problem
becomes disconnected, the more similar the vertices in this graph. Minimum cut is a minimum set of edges without which the graph will become disconnected.
HCS_clustering_algorithm
Controller for the valves on a steam engine
notches and a shorter minimum cut-off (allowing efficiency at high speeds at the expense of tractive effort). If the minimum cut-off provided for by the
Reversing_gear
approaches to image segmentation applying graph partitioning via minimum cut or maximum cut. Segmentation-based object categorization can be viewed as a specific
Segmentation-based object categorization
Segmentation-based_object_categorization
Subdivision of vertices into disjoint sets
et al. (2013). Two common examples of graph partitioning are minimum cut and maximum cut problems. Typically, graph partition problems fall under the
Graph_partition
Combinatorial optimization method for pseudo-Boolean functions
The minimum cut of the graph can be computed with a max-flow algorithm. In the general case, the minimum cut is not unique, and each minimum cut correspond
Quadratic pseudo-Boolean optimization
Quadratic_pseudo-Boolean_optimization
US military and civilian decoration
excellence category of competition. Also in 2015, the CMP established minimum cut scores that must be achieved for a given weapon in the authorized excellence
Marksmanship badges (United States)
Marksmanship_badges_(United_States)
College in Assam, India
Pragjyotish College has announced the cut-off marks for its undergraduate courses for the academic year 2023. These minimum cut-off marks provide prospective
Pragjyotish_College
Optimization technique
max-flow min-cut theorem, define a minimal cut of the graph). Under most formulations of such problems in computer vision, the minimum energy solution
Graph cuts in computer vision and artificial intelligence
Graph_cuts_in_computer_vision_and_artificial_intelligence
2021 film by Zack Snyder
Zack Snyder's Justice League is the 2021 director's cut and the original version of the 2017 American superhero film Justice League, the fifth film set
Zack_Snyder's_Justice_League
German operations researcher
her work on the minimum cut problem and in network design. She is one of the namesakes of the Stoer–Wagner algorithm for minimum cuts, which she published
Mechthild_Stoer
Social network
the maximum flow – minimum cut Ford–Fulkerson algorithm from “source” Mr. Hi to “sink” John A: the cut closest to Mr. Hi that cuts saturated edges divides
Zachary's_karate_club
Graph which remains connected when fewer than k edges are removed
k-edge-connected. The smallest set X whose removal disconnects G is a minimum cut in G. The edge connectivity version of Menger's theorem provides an alternative
Edge_connectivity
Computational problem in graph theory
capacity in H. A minimum cut separating s from t in this graph cannot have any edges of G passing in the forward direction across the cut: a cut with such an
Closure_problem
Nigerian examination board
(2024-07-18). "JAMB adopts 140 as minimum cut-off mark for 2024 varsity admissions". TheCable. Retrieved 2024-09-02. "JAMB Cut Off Mark 2024/2025 for All School
Joint Admissions and Matriculation Board
Joint_Admissions_and_Matriculation_Board
Framework in mathematics
problem can be reformulated into a minimum cut problem on a special graph termed GTW graph, where the minimum cut and the warping paths are equivalent
Graphical_time_warping
Algorithm to compute the maximum flow in a flow network
equal to the capacity across the minimum cut in the graph separating the source and the sink. There is only one minimal cut in this graph, partitioning the
Edmonds–Karp_algorithm
Graph nodes linked to, but not part of, a subgraph
particularly relevant for isoperimetric problems in graphs, separator theorems, minimum cuts, expander graphs, and percolation theory. Benjamini, Itai (2013), Coarse
Boundary_(graph_theory)
American computer scientist
algorithm, a Monte Carlo method to compute the minimum cut of a connected graph. Karger developed the fastest minimum spanning tree algorithm to date, with Philip
David_Karger
flow algorithms Minimum cost flow algorithms Minimum cut algorithms Connectivity and other graph properties Maximum cardinality and minimum cost perfect
LEMON_(C++_library)
Function type in graph theory
should compute the minimum cut norm over all possible "relabellings" of the vertices. This motivates the following definition of the cut distance. Definition
Graphon
Photo editing algorithm
segmentation of videos. Graph-based segmentation methods search for a minimum cut and therefore tend to not perform optimally with complex structures.
Simple interactive object extraction
Simple_interactive_object_extraction
Prominent transgender Indian historical figure
With legal recourse in a competent court, she was able to lower the minimum cut-off marks for written test for such a recruitment from 28.5 to 25.00
K._Prithika_Yashini
Legislation to protect workers
Minimum wage law is the body of law which prohibits employers from hiring employees or workers for less than a given hourly, daily or monthly minimum
Minimum_wage_law
Type of randomized algorithm
Karger, David R.; Stein, Clifford (July 1996). "A New Approach to the Minimum Cut Problem". J. ACM. 43 (4): 601–640. doi:10.1145/234533.234534. ISSN 0004-5411
Monte_Carlo_algorithm
2005 live album by Kraftwerk
Minimum-Maximum is the first official live album release by Kraftwerk, released in June 2005, almost 35 years after the group gave its first live performance
Minimum-Maximum
Weighted tree representing s-t cuts of a graph
undirected graph with capacities is a weighted tree that represents the minimum s-t cuts for all s-t pairs in the graph. The Gomory–Hu tree can be constructed
Gomory–Hu_tree
Social-welfare system
Guaranteed minimum income (GMI), also called minimum income (or mincome for short), is a social-welfare system that guarantees all citizens or families
Guaranteed_minimum_income
Abstraction of graph shortest cycles
the number of edges in a minimum cut of the graph. The girth of a transversal matroid gives the cardinality of a minimum Hall set in a bipartite graph:
Matroid_girth
Image edge detection algorithm
maps to 0°. Minimum cut-off suppression of gradient magnitudes, or lower bound thresholding, is an edge thinning technique. Lower bound cut-off suppression
Canny_edge_detector
Type of cut used when shaping a diamond
A diamond cut is a style or design guide used when shaping a diamond for polishing such as the brilliant cut. Cut refers to shape (pear, oval), and also
Diamond_cut
Set-to-real map with diminishing returns
polynomial time, and even in strongly-polynomial time. Computing the minimum cut in a graph is a special case of this minimization problem. The problem
Submodular_set_function
Basic concept of graph theory
if every minimum vertex cut isolates a vertex. A graph is said to be hyper-connected or hyper-κ if the deletion of each minimum vertex cut creates exactly
Connectivity_(graph_theory)
Algorithm to search the nodes of a graph
S2CID 29440871. Karger, David R.; Motwani, Rajeev (1997), "An NC algorithm for minimum cuts", SIAM Journal on Computing, 26 (1): 255–272, CiteSeerX 10.1.1.33.1701
Depth-first_search
American computer scientist and educator
Jason; Rao, Satish; Wang, Di (2024). "Deterministic near-linear time minimum cut in weighted graphs". Proceedings of the 2024 Annual ACM-SIAM Symposium
Satish_B._Rao
analogues of the max-flow min-cut theorem for undirected multi-commodity flow problems. The ratio of the maximum flow to the minimum cut, in such problems, is
GNRS_conjecture
Ramp from elevated sidewalk to road
curb cuts transition from the low side of a curb to the high side (usually 15 cm or 5.9 in change in level). Accessible curb ramps are a minimum of 1
Curb_cut
the subgraphs with the property. minimum cut A cut whose cut-set has minimum total weight, possibly restricted to cuts that separate a designated pair
Glossary_of_graph_theory
Technique used to increase the number of structures a microchip may contain
features over lines at the minimum pitch, without edge placement errors. Cut-friendly layouts are processed with the same minimum number of masks (3), regardless
Multiple_patterning
Sparse graph with strong connectivity
{|\partial S|}=\min |E({S},{\overline {S}})|} is the minimum number of edges that need to be cut in order to split the graph in two. The edge expansion
Expander_graph
Mathematical optimization problem
variations): Cycle canceling: a general primal method. Cut canceling: a general dual method. Minimum mean cycle canceling: a simple strongly polynomial algorithm
Minimum-cost_flow_problem
Combinatorial optimization method
Branch and cut is a method of combinatorial optimization for solving integer linear programs (ILPs), that is, linear programming (LP) problems where some
Branch_and_cut
flow in a graph Karger's algorithm: a Monte Carlo method to compute the minimum cut of a connected graph Push–relabel algorithm: computes a maximum flow
List_of_algorithms
Agrawal and Ramakrishnan Srikant 1993 – Karger's algorithm to compute the minimum cut of a connected graph by David Karger 1994 – Shor's algorithm developed
Timeline_of_algorithms
Black-box description of a convex set
a separation oracle can be implemented using n-1 applications of the minimum cut procedure. The maximum independent set problem. It can be approximated
Separation_oracle
Graph representing faces of another graph
minimum-weight cycle basis of the graph is dual to the Gomory–Hu tree of the dual graph, a collection of nested cuts that together include a minimum cut
Dual_graph
Simple design of valve gear
over-compression at the end of the stroke when very short cut-offs are used, and therefore the minimum cut-off cannot be as low as on a locomotive with Walschaerts
Stephenson_valve_gear
All even-degree subgraphs of a graph
spaces and cut spaces, this basis for a planar graph corresponds to a Gomory–Hu tree of the dual graph, a minimum weight basis for its cut space. In planar
Cycle_space
universities in Nigeria include: a minimum of SSCE/GCE Ordinary Level Credits, with a maximum of two sittings; and a minimum cut-off mark score in the Joint
Education_in_Nigeria
Lowest possible mass of the celestial object
astronomy, minimum mass is the lower-bound calculated mass of observed objects such as planets, stars, binary systems, nebulae, and black holes. Minimum mass
Minimum_mass
Any planar graph can be subdivided by removing a few vertices
but undirected planar graphs, the shortest cycle is equivalent to the minimum cut in the dual graph and can be found in O ( n log log n ) {\displaystyle
Planar_separator_theorem
U.S. federal tax legislation
The Tax Cuts and Jobs Act (Pub. L. 115–97 (text) (PDF)), is a United States federal law that amended the Internal Revenue Code of 1986, and also known
Tax_Cuts_and_Jobs_Act
Legislation of Hong Kong
The Minimum Wage Ordinance Cap. 608 is an ordinance enacted by the Legislative Council of Hong Kong to introduce a minimum wage in Hong Kong in July 2010
Minimum_Wage_Ordinance
Partitioning a digital image into segments
algorithms of this category are normalized cuts, random walker, minimum cut, isoperimetric partitioning, minimum spanning tree-based segmentation, and segmentation-based
Image_segmentation
Method of construction of the real numbers
both A and B are nonempty. If neither A has a maximum, nor B has a minimum, the cut is called a gap. A linearly ordered set endowed with the order topology
Dedekind_cut
Suicide in India
The minimum eligibility cut-off for making it into the merit list was 40 percentage for students in the reserved category. The minimum eligibility cut-off
Suicide_of_S._Anitha
Cycles in a graph that generate all cycles
given planar graph, to a set of cuts that form a Gomory–Hu tree of the dual graph, the minimum weight basis of its cut space. Based on this duality, an
Cycle_basis
United States wage law
The Fair Minimum Wage Act of 2007 is an act of Congress that amended the Fair Labor Standards Act of 1938 to gradually raise the federal minimum wage from
Fair_Minimum_Wage_Act_of_2007
Waterway in Oxfordshire, England
Duke's Cut is a short waterway in Oxfordshire, England, which connects the Oxford Canal with the River Thames via the Wolvercote Mill Stream. It is named
Duke's_Cut
employee relations have seen the introduction of statutory agreements for minimum employee leave from work—that is the amount of entitlement to paid vacation
List of minimum annual leave by country
List_of_minimum_annual_leave_by_country
considered to be legally competent to consent to sexual acts and is thus the minimum age of a person who is with whom another person is legally permitted to
Age_of_consent_by_country
United States tax law provision
The alternative minimum tax (AMT) is a tax imposed by the United States federal government in addition to the regular income tax for certain individuals
Alternative_minimum_tax
In evolutionary computation, Minimum Population Search (MPS) is a computational method that optimizes a problem by iteratively trying to improve a set
Minimum_Population_Search
American chef and politician (born 1988)
first term in the legislature, Hong sponsored efforts to raise the tipped minimum wage and introduced a bill to establish an Economic Bill of Rights in Wisconsin
Francesca_Hong
Financial services company
Price announced that his employees at the Seattle office would receive a minimum salary of $70,000. In September 2019, Price issued an additional increase
Gravity_Payments
Process through which students enter tertiary education
limiting minimum for acceptance, and consequently take students with averages below 60 percent. Unlike universities, colleges do not have admission cut-offs
University and college admission
University_and_college_admission
English filmmaker (born 1937)
intricate shots as swiftly as possible: "I like working, always, with a minimum of three cameras. [...] So those 50 set-ups [a day] might only be 25 set-ups
Ridley_Scott
Creative and technical part of the post-production process of filmmaking
for anyone until the minimum period of ten weeks is complete. While collaborating on what is referred to as the "director's cut", the director and the
Film_editing
American political party
"Top GOP Presidential Contenders Support Mandatory Minimum Reform". Families Against Mandatory Minimums. Archived from the original on November 29, 2014
Republican Party (United States)
Republican_Party_(United_States)
Maximal biconnected subgraph
(with minimum degree 2) is a cut vertex if and only if v is incident to a bridge or v is the first vertex of a cycle in C – C1. The list of cut vertices
Biconnected_component
Algorithm used to solve non-linear least squares problems
optimization algorithms, the LMA finds only a local minimum, which is not necessarily the global minimum. The primary application of the Levenberg–Marquardt
Levenberg–Marquardt_algorithm
Packet switching method
In computer networking, cut-through switching, also called cut-through forwarding is a method for packet switching systems, wherein the switch starts forwarding
Cut-through_switching
American politician (born 1963)
no-knock warrants. Paul says policies such as the war on drugs and mandatory minimum sentencing have particularly harmed minorities. In 2020, Paul held up bipartisan
Rand_Paul
Proposed international tax scheme
The global minimum corporate tax rate, or simply the global minimum tax (abbreviated GMCT or GMCTR), is a minimum rate of tax on corporate income internationally
Global minimum corporate tax rate
Global_minimum_corporate_tax_rate
1973 film by Robin Hardy
shorter than the director's cut but longer than the theatrical cut, and is known as The Wicker Man: The Final Cut. The Final Cut (UK) Blu-ray (2013) features
The_Wicker_Man
2025 legislation in the United States
rise by 2.7% by 2034 mainly due to tax cuts, while the lowest 10% would see incomes fall by 3.1% mainly due to cuts to programs such as Medicaid and food
One_Big_Beautiful_Bill_Act
American lawyer and politician (born 1979)
raise in the Missouri minimum wage from $7.85/hour to $8.60 in 2019 and $12 by 2023. In 2021, Hawley expressed support for a $15 minimum wage for businesses
Josh_Hawley
The alcohol laws of the United States regarding minimum age for purchase have changed over time. In colonial America, generally speaking, there were no
History of alcohol minimum purchase age by U.S. jurisdiction
History_of_alcohol_minimum_purchase_age_by_U.S._jurisdiction
American multinational technology conglomerate
into a 10-year agreement with Amazon, valued at $50 million per year plus a cut of sales, under which Toys "R" Us would be the exclusive supplier of toys
Amazon_(company)
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