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Combinatorial optimization method for a family of functions of discrete variables
Graph cut optimization is a combinatorial optimization method applicable to a family of functions of discrete variables, named after the concept of cut
Graph_cut_optimization
Optimization technique
As applied in the field of computer vision, graph cut optimization can be employed to efficiently solve a wide variety of low-level computer vision problems
Graph cuts in computer vision and artificial intelligence
Graph_cuts_in_computer_vision_and_artificial_intelligence
Topics referred to by the same term
Graph cut may refer to: Cut (graph theory), in mathematics Graph cut optimization Graph cuts in computer vision This disambiguation page lists articles
Graph_cut
Partition of a graph's nodes into 2 disjoint subsets
In graph theory, a cut is a partition of the vertices of a graph into two disjoint subsets. Any cut determines a cut-set, the set of edges that have one
Cut_(graph_theory)
Problem in graph theory
In a graph, a maximum cut is a cut whose size is at least the size of any other cut. That is, it is a partition of the graph's vertices into two complementary
Maximum_cut
Combinatorial optimization method for pseudo-Boolean functions
submodular then QPBO produces a global optimum equivalently to graph cut optimization, while if f {\displaystyle f} contains non-submodular terms then
Quadratic pseudo-Boolean optimization
Quadratic_pseudo-Boolean_optimization
Optimization algorithm
optimization algorithm (ACO) is a probabilistic technique for solving computational problems that can be reduced to finding good paths through graphs
Ant colony optimization algorithms
Ant_colony_optimization_algorithms
Image segmentation in computer vision
detection builds the object proposal graph with inputs including the spatio-temporal segmentation tubes. Graph cut optimization is a popular tool in computer
Object_co-segmentation
Combinatorial optimization graph problem
the minimum k-cut is a combinatorial optimization problem that requires finding a set of edges whose removal would partition the graph to at least k connected
Minimum_k-cut
Subfield of mathematical optimization
Combinatorial optimization is a subfield of mathematical optimization that consists of finding an optimal object from a finite set of objects, where the
Combinatorial_optimization
Equivalence of optimization problems
In computer science and optimization theory, the max-flow min-cut theorem states that in a flow network, the maximum amount of flow passing from the source
Max-flow_min-cut_theorem
Subdivision of vertices into disjoint sets
al. (2013). Two common examples of graph partitioning are minimum cut and maximum cut problems. Typically, graph partition problems fall under the category
Graph_partition
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
On bipartite matching and vertex cover
Mathematics and Optimization, vol. 33, John Wiley & Sons, pp. 48–49, ISBN 9781118031391. Bondy, J. A.; Murty, U. S. R. (1976), Graph Theory with Applications
Kőnig's theorem (graph theory)
Kőnig's_theorem_(graph_theory)
Computer compiler optimization technique
Combinatorial Optimization, IPCO The Aussois Combinatorial Optimization Workshop Bosscher, Steven; and Novillo, Diego. GCC gets a new Optimizer Framework
Register_allocation
Computer vision algorithm
strong optimality properties can be found in polynomial time using graph cut optimization, however such global methods are generally too expensive for real-time
Semi-global_matching
Optimization algorithms using quantum computing
Quantum optimization algorithms are quantum algorithms that are used to solve optimization problems. Mathematical optimization deals with finding the best
Quantum optimization algorithms
Quantum_optimization_algorithms
Method of image segmentation
prefers connected regions having the same label, and running a graph cut based optimization to infer their values. As this estimate is likely to be more
GrabCut
Graph representing faces of another graph
mathematical discipline of graph theory, the dual graph of a planar graph G is a graph that has a vertex for each face of G. The dual graph has an edge for each
Dual_graph
NP-hard problem in combinatorial optimization
of the most intensively studied problems in optimization. It is used as a benchmark for many optimization methods. Even though the problem is computationally
Travelling_salesman_problem
Combinatorial optimization problem
unconstrained binary optimization (QUBO), also known as unconstrained binary quadratic programming (UBQP), is a combinatorial optimization problem with a wide
Quadratic unconstrained binary optimization
Quadratic_unconstrained_binary_optimization
Sequence of locally optimal choices
Greedy algorithms are often used to solve combinatorial optimization problems. If an optimization problem only depends on the partial solution of solving
Greedy_algorithm
Feature to efficiently execute queries efficiently in DBMS softwares
optimization is a feature of many relational database management systems and other databases such as NoSQL and graph databases. The query optimizer attempts
Query_optimization
Sequential model-based optimization of expensive black-box functions
Bayesian optimization is a sequential model-based strategy for global optimization of black-box objective functions whose evaluations are costly. It is
Bayesian_optimization
Mathematical optimization problem restricted to integers
An integer programming, also known as integer optimization, problem is a mathematical optimization or feasibility program in which some or all of the variables
Integer_programming
American computer scientist and educator
the design and analysis of algorithms, with work in combinatorial optimization, graph partitioning, network flow, metric embeddings, and computational
Satish_B._Rao
Subfield of mathematical optimization
Convex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently
Convex_optimization
Class of computational problems
combinatorial optimization, network flow problems are a class of computational problems in which the input is a flow network (a graph with numerical
Network_flow_problem
graph library written in the C++ language providing implementations of common data structures and algorithms with focus on combinatorial optimization
LEMON_(C++_library)
Graph theory problem
is an optimization problem in graph theory in which the goal is to find a matching of maximum possible total weight in an edge-weighted graph. A matching
Maximum-weight_matching
Study of mathematical algorithms for optimization problems
An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must
Mathematical_optimization
Mathematical combinatorial optimization method
"A Branch-And-Price Approach for Graph Multi-Coloring". Extending the Horizons: Advances in Computing, Optimization, and Decision Technologies. Operations
Branch_and_price
Area of discrete mathematics
computer science, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. A graph in this context
Graph_theory
complex optimization problems on massive graphs into smaller, more manageable ones. The coarsening process involves merging nodes of a graph into clusters
Graph_Coarsening_Algorithm
Optimization algorithm
Gradient descent is a method for unconstrained mathematical optimization. It is a first-order iterative algorithm for minimizing a differentiable multivariate
Gradient_descent
very-high-dimensional spaces Newton's method in optimization Nonlinear optimization BFGS method: a nonlinear optimization algorithm Gauss–Newton algorithm: an algorithm
List_of_algorithms
When every path in a control-flow graph must go through one node to reach another
In computer science, a node d of a control-flow graph dominates a node n if every path from the entry node to n must go through d. Notationally, this
Dominator_(graph_theory)
Least-weight tree connecting graph vertices
For any cut C of the graph, if the weight of an edge e in the cut-set of C is strictly smaller than the weights of all other edges of the cut-set of C
Minimum_spanning_tree
Computational problem in graph theory
In graph theory and combinatorial optimization, a closure of a directed graph is a set of vertices C, such that no edges leave C. The closure problem is
Closure_problem
Optimization by removing non-optimal solutions to subproblems
design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists of a systematic
Branch_and_bound
Solving an optimization problem with a quadratic objective function
of solving certain mathematical optimization problems involving quadratic functions. Specifically, one seeks to optimize (minimize or maximize) a multivariate
Quadratic_programming
Class of algorithms that find approximate solutions to optimization problems
for hard optimization problems. One well-known example of the former is the Goemans–Williamson algorithm for maximum cut, which solves a graph theoretic
Approximation_algorithm
Iterative method for minimizing convex functions
In mathematical optimization, the ellipsoid method is an iterative method for minimizing convex functions over convex sets. The ellipsoid method generates
Ellipsoid_method
Sparse graph with strong connectivity
In graph theory, an expander graph is a sparse graph that has strong connectivity properties, quantified using vertex, edge or spectral expansion. Expander
Expander_graph
Branch of mathematical optimization
Three notable branches of discrete optimization are: combinatorial optimization, which refers to problems on graphs, matroids and other discrete structures
Discrete_optimization
Graph generated by a random process
In mathematics, random graph is the general term to refer to probability distributions over graphs. Random graphs may be described simply by a probability
Random_graph
Degree of connectedness within a graph
In graph theory and network analysis, indicators of centrality assign numbers or rankings to nodes within a graph corresponding to their network position
Centrality
Graph with all vertices of degree 3
of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are
Cubic_graph
Clustering and community detection algorithm
The Louvain method for community detection is a greedy optimization method intended to extract non-overlapping communities from large networks created
Louvain_method
Quantum physics-based metaheuristic for optimization problems
solving QUBO problems, which can encode a wide range of problems like Max-Cut, graph coloring, SAT or the traveling salesman problem. The term "quantum annealing"
Quantum_annealing
Weighted tree representing s-t cuts of a graph
combinatorial optimization, the Gomory–Hu tree of an undirected graph with capacities is a weighted tree that represents the minimum s-t cuts for all s-t
Gomory–Hu_tree
Distributed constraint optimization (DCOP or DisCOP) is the distributed analogue to constraint optimization. A DCOP is a problem in which a group of agents
Distributed constraint optimization
Distributed_constraint_optimization
Two closely related models for generating random graphs
the mathematical field of graph theory, the Erdős–Rényi models are two closely related models for generating random graphs and the evolution of a random
Erdős–Rényi_model
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
Finding shortest walks through all graph edges
In graph theory and combinatorial optimization, Guan's route problem, the Chinese postman problem, postman tour or route inspection problem is to find
Chinese_postman_problem
Optimizing objective functions that have constrained variables
In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function
Constrained_optimization
Czech-Canadian mathematician
Prague. He has published extensively on topics in graph theory, combinatorics, and combinatorial optimization. Chvátal was born in 1946 in Prague and educated
Václav_Chvátal
Approximate nearest neighbor search algorithm
datasets. HNSW stores vectors in a graph. Each vector is a node, and links connect it to some nearby vectors. The graph has several layers: upper layers
Hierarchical navigable small world
Hierarchical_navigable_small_world
Graph drawing with vertices in horizontal layers
Layered graph drawing or hierarchical graph drawing is a type of graph drawing in which the vertices of a directed graph are drawn in horizontal rows or
Layered_graph_drawing
Optimization technique
stochastic optimization, so that the solution found is dependent on the set of random variables generated. In combinatorial optimization, there are many
Metaheuristic
Measure of network community structure
Modularity is a measure of the structure of networks or graphs which measures the strength of division of a network into modules (also called groups, clusters
Modularity_(networks)
Edges that hit all cycles in a graph
In graph theory and graph algorithms, a feedback arc set or feedback edge set in a directed graph is a subset of the edges of the graph that contains at
Feedback_arc_set
Abstraction of ordered linear algebra
matroid is a mathematical structure that abstracts the properties of directed graphs, vector arrangements over ordered fields, and hyperplane arrangements over
Oriented_matroid
Method to solve optimization problems
programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject
Linear_programming
Subfield of convex optimization
field of optimization which is of growing interest for several reasons. Many practical problems in operations research and combinatorial optimization can be
Semidefinite_programming
Subgraph with contracted edges
In graph theory, an undirected graph H is called a minor of the undirected graph G if H can be formed from G by deleting edges and vertices and by contracting
Graph_minor
Theorem in functional analysis
of cut norm is crucial in the study of the space of graphons, and the two definitions of cut norm can be linked via the adjacency matrix of a graph. An
Grothendieck_inequality
Data structure for integer priorities
slower O(nC) time bound that would result without this optimization. A corresponding optimization can be applied in applications where a bucket queue is
Bucket_queue
Set-to-real map with diminishing returns
(2003), Combinatorial Optimization, Springer, ISBN 3-540-44389-4 Lee, Jon (2004), A First Course in Combinatorial Optimization, Cambridge University Press
Submodular_set_function
Optimization algorithm
In numerical analysis, hill climbing is a mathematical optimization technique which belongs to the family of local search. It is an iterative algorithm
Hill_climbing
Clustering and community detection algorithm
well-connected. Consider, for example, the following graph: Three communities are present in this graph (each color represents a community). Additionally
Leiden_algorithm
Process of partitioning a rectilinear polygon
are various optimization problems related to guillotine partition, such as: minimizing the number of rectangles or the total length of cuts. These are
Guillotine_partition
Solving multiple machine learning tasks at the same time
predictive analytics. The key motivation behind multi-task optimization is that if optimization tasks are related to each other in terms of their optimal
Multi-task_learning
Mathematical propositions in network flow theory
In graph theory, approximate max-flow min-cut theorems concern the relationship between the maximum flow rate (max-flow) and the minimum cut (min-cut) in
Approximate max-flow min-cut theorem
Approximate_max-flow_min-cut_theorem
Mathematical tree of cycles
connected graph in which every edge belongs to at most one simple cycle, or (for nontrivial cacti) in which every block (maximal subgraph without a cut-vertex)
Cactus_graph
Algorithm for solving the quadratic programming problem from training SVMs
Sequential minimal optimization (SMO) is an algorithm for solving the quadratic programming (QP) problem that arises during the training of support-vector
Sequential minimal optimization
Sequential_minimal_optimization
Collective behavior of decentralized, self-organized systems
Evolutionary algorithms (EA), particle swarm optimization (PSO), differential evolution (DE), ant colony optimization (ACO) and their variants dominate the field
Swarm_intelligence
Solution process for some optimization problems
nonlinear programming (NLP), also known as nonlinear optimization, is the process of solving an optimization problem where some of the constraints are not linear
Nonlinear_programming
Numerical optimization algorithm
D.; Price, C. J. (2002). "Positive Bases in Numerical Optimization". Computational Optimization and Applications. 21 (2): 169–176. doi:10.1023/A:1013760716801
Nelder–Mead_method
Mixing property of Markov chains and graphs
In theoretical computer science, graph theory, and mathematics, the conductance is a parameter of a Markov chain that is closely tied to its mixing time
Conductance_(graph_theory)
American computer scientist
"A.W. Tucker Prize - Past Winners". Mathematical Optimization Society Prizes. Mathematical Optimization Society. "William O. Baker Award for Initiatives
David_Karger
Class of algorithms for solving constrained optimization problems
solving constrained optimization problems. They have similarities to penalty methods in that they replace a constrained optimization problem by a series
Augmented_Lagrangian_method
Process of producing small rectangular items of fixed dimensions
classes. They then solve the optimization problem using constraint programming on the space of well-sorted normal guillotine graphs. Russo, Boccia, Sforza and
Guillotine_cutting
discussion of the maximum-flow minimum-cut theorem. Cederbaum's theorem applies to a particular type of directed graph: G = (V, E). V {\displaystyle V} is
Cederbaum's maximum flow theorem
Cederbaum's_maximum_flow_theorem
Academic field
foundation of graph theory, a branch of mathematics that studies the properties of pairwise relations in a network structure. The field of graph theory continued
Network_science
Partitioning a digital image into segments
and more. Apart from likelihood estimates, graph-cut using maximum flow and other highly constrained graph based methods exist for solving MRFs. The
Image_segmentation
Algorithm used to solve non-linear least squares problems
converges faster than first-order methods. However, like other iterative optimization algorithms, the LMA finds only a local minimum, which is not necessarily
Levenberg–Marquardt_algorithm
Optimization method
numerical optimization, the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is an iterative method for solving unconstrained nonlinear optimization problems
Broyden–Fletcher–Goldfarb–Shanno algorithm
Broyden–Fletcher–Goldfarb–Shanno_algorithm
Computational problem in graph theory
In optimization theory, maximum flow problems involve finding a feasible flow through a flow network that obtains the maximum possible flow rate. The maximum
Maximum_flow_problem
Study of graphs as a representation of relations between discrete objects
science, and network science, network theory is a part of graph theory. It defines networks as graphs where the vertices or edges possess attributes. Network
Network_theory
Any planar graph can be subdivided by removing a few vertices
fixed-parameter tractable algorithms for solving NP-hard optimization problems on these graphs. Separator hierarchies may also be used in nested dissection
Planar_separator_theorem
On linear-time algorithms for graph logic
a graph have a property or not. However, the same methods also allow the solution to optimization problems in which the vertices or edges of a graph have
Courcelle's_theorem
Optimization algorithm
searching for zeroes. Most quasi-Newton methods used in optimization exploit this symmetry. In optimization, quasi-Newton methods (a special case of variable-metric
Quasi-Newton_method
Algorithms for solving convex optimization problems
linear to convex optimization problems, based on a self-concordant barrier function used to encode the convex set. Any convex optimization problem can be
Interior-point_method
Probabilistic optimization technique and metaheuristic
Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. For large numbers of local optima, SA
Simulated_annealing
Knowledge base that represents semantic relations between concepts in a network
used as a form of knowledge representation. It is a directed or undirected graph consisting of vertices, which represent concepts, and edges, which represent
Semantic_network
Set of objects whose state must satisfy limits
Constraint composite graph Constraint programming Declarative programming Constrained optimization (COP) Distributed constraint optimization Graph homomorphism
Constraint satisfaction problem
Constraint_satisfaction_problem
Transformation defined on a grayscale image
Graph Cuts to optimal spanning forests. More precisely, they show that when the power of the weights of the graph is above a certain number, the cut minimizing
Watershed_(image_processing)
Optimization algorithm
In mathematics, the spiral optimization (SPO) algorithm is a metaheuristic inspired by spiral phenomena in nature. The first SPO algorithm was proposed
Spiral_optimization_algorithm
NP-hard problem in combinatorial optimization
problem (RSP) is a NP-hard problem in combinatorial optimization. In a complete weighted mixed graph, the ring star problem aims to find a minimum cost
Ring_star_problem
GRAPH CUT-OPTIMIZATION
GRAPH CUT-OPTIMIZATION
Boy/Male
Muslim
Grape
Surname or Lastname
English
English : variant of Court.Americanized spelling of German Kurt.Catalan : from curt ‘short’ (Latin curtus ‘cut short’, ‘broken off’), hence a nickname for a short man.
Female
Vietnamese
Vietnamese name KIM CUC means "golden chrysanthemum."
Boy/Male
Hebrew, Hindu, Indian, Marathi
Grape Cluster
Boy/Male
Muslim
A prophets name lot
Male
Scandinavian
Variant spelling of Scandinavian Knut, CNUT means "knot."Â
Girl/Female
Swedish
Beautiful.
Girl/Female
Muslim
Grape like
Boy/Male
Indian
Grape
Girl/Female
Arabic, Assamese, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Telugu
Grape
Girl/Female
Muslim
Grape vine
Boy/Male
African, Arabic
Grape Vines
Girl/Female
Indian
Grape vine
Boy/Male
Hindu, Indian, Punjabi, Sikh
From Kashmir; Grape
Girl/Female
Indian
Grape like
Female
Vietnamese
Vietnamese name CUC means "chrysanthemum."
Male
English
Short form of English Curtis, CURT means "courteous."
Male
Thai/Siamese
Thai name A-WUT means "weapon."
Girl/Female
Biblical
Burning.
Boy/Male
Arabic, Modern
Grape
GRAPH CUT-OPTIMIZATION
GRAPH CUT-OPTIMIZATION
Boy/Male
Tamil
Point or full stop, Rocky
Boy/Male
Hindu, Indian
God of Mind
Surname or Lastname
English
English : unexplained.
Boy/Male
Indian, Tamil
King of Clouds
Boy/Male
Spanish
Small intelligent one.
Boy/Male
Tamil
Ever courageous
Biblical
dry; barren
Girl/Female
Indian, Punjabi, Sikh
Soul of God
Boy/Male
Arabic, Chinese, Muslim
Delightful; Happy
Girl/Female
German, Gujarati, Hindu, Indian, Sanskrit
Dedicated; Awasome; Devotee
GRAPH CUT-OPTIMIZATION
GRAPH CUT-OPTIMIZATION
GRAPH CUT-OPTIMIZATION
GRAPH CUT-OPTIMIZATION
GRAPH CUT-OPTIMIZATION
v. i.
To do the work of an edged tool; to serve in dividing or gashing; as, a knife cuts well.
n.
Manner in which a thing is cut or formed; shape; style; fashion; as, the cut of a garment.
v. t.
To refuse to recognize; to ignore; as, to cut a person in the street; to cut one's acquaintance.
a.
See Clear-cut.
n.
A portion severed or cut off; a division; as, a cut of beef; a cut of timber.
v. t.
To sever and remove by cutting; to cut off; to dock; as, to cut the hair; to cut the nails.
v. t.
To absent one's self from; as, to cut an appointment, a recitation. etc.
n.
The surface left by a cut; as, a smooth or clear cut.
n.
A notch, passage, or channel made by cutting or digging; a furrow; a groove; as, a cut for a railroad.
v. t.
To form or shape by cutting; to make by incision, hewing, etc.; to carve; to hew out.
v. t.
To cut in pieces; to cut out from.
n.
A single cut with a knife.
imp. & p. p.
of Cut
n.
An opening made with an edged instrument; a cleft; a gash; a slash; a wound made by cutting; as, a sword cut.
v. t.
To intersect; to cross; as, one line cuts another at right angles.
n.
The right to divide; as, whose cut is it?
v. t.
To castrate or geld; as, to cut a horse.
n.
An engraved block or plate; the impression from such an engraving; as, a book illustrated with fine cuts.
v. t.
To wound or hurt deeply the sensibilities of; to pierce; to lacerate; as, sarcasm cuts to the quick.