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of algorithms, partition refinement is a technique for representing a partition of a set as a data structure that allows the partition to be refined by
Partition_refinement
Mathematical ways to group elements of a set
representative element from every equivalence class. A partition α of a set X is a refinement of a partition ρ of X—and we say that α is finer than ρ and that
Partition_of_a_set
Mathematical ranking of a set
ordered Bell numbers. They are used in computer science as part of partition refinement algorithms, and in the C++ Standard Library. In horse racing, the
Weak_ordering
Sets with no element in common
the partition. Disjoint-set data structures and partition refinement are two techniques in computer science for efficiently maintaining partitions of a
Disjoint_sets
Subsets whose union equals the whole set
a refinement of a given structure is another that in some sense contains it. Examples are to be found when partitioning an interval (one refinement of
Cover_(topology)
the partition function Partition of an interval Partition of a set Ordered partition Partition refinement Disjoint-set data structure Partition problem
List_of_partition_topics
Increasing sequence of numbers that span an interval
a subinterval of the partition x. Another partition Q of the given interval [a, b] is defined as a refinement of the partition P, if Q contains all the
Partition_of_an_interval
Task of transforming a deterministic finite automaton
nondistinguishable states of a DFA, due to Hopcroft (1971), is based on partition refinement, partitioning the DFA states into groups by their behavior. These groups
DFA_minimization
Clustering and community detection algorithm
steps: local moving of nodes, refinement of the partition, and aggregation of the network based on the refined partition. All of the functions in the following
Leiden_algorithm
The Iteration Number of Colour Refinement, arXiv:2005.10182 Cardon, A.; Crochemore, M. (1982-07-01). "Partitioning a graph in O(¦A¦log2¦V¦)". Theoretical
Colour_refinement_algorithm
Partition-based graph traversal method
lexicographic breadth-first search algorithm is based on the idea of partition refinement and was first developed by Donald J. Rose, Robert E. Tarjan, and
Lexicographic breadth-first search
Lexicographic_breadth-first_search
Subdivision of vertices into disjoint sets
graph, then maps back and refines this partition of the original graph. A wide variety of partitioning and refinement methods can be applied within the overall
Graph_partition
Data structure for storing non-overlapping sets
used to implement reasonably performant Type inference algorithms. Partition refinement, a different data structure for maintaining disjoint sets, with updates
Disjoint-set_data_structure
Graph where all long cycles have a chord
McConnell, Ross; Paul, Christophe; Viennot, Laurent (2000), "Lex-BFS and partition refinement, with applications to transitive orientation, interval graph recognition
Chordal_graph
Method for partitioning partial orders into levels
Coffman–Graham algorithm can be implemented in linear time using the partition refinement data structure as a subroutine. If the transitive reduction is not
Coffman–Graham_algorithm
Basic integral in elementary calculus
all tagged partitions into a directed set by saying that one tagged partition is greater than or equal to another if the former is a refinement of the latter
Riemann_integral
Topological space which is a generalization of certain compact spaces
paracompact space is a topological space in which every open cover has an open refinement that is locally finite. These spaces were introduced by Dieudonné (1944)
Paracompact_space
Integral constructed using Darboux sums
Darboux integrals are unequal. A refinement of the partition x 0 , … , x n {\displaystyle x_{0},\ldots ,x_{n}} is a partition y 0 , … , y m {\displaystyle
Darboux_integral
Graph partition into regular subgraphs
just one, and shows that there exists a partition with an extremely regular refinement, where the refinement doesn't have too large of an energy increment
Szemerédi_regularity_lemma
Relation between transition systems in computer science
fastest algorithms are quasilinear time using partition refinement through a reduction to the coarsest partition problem. Simulation preorder Congruence relation
Bisimulation
Intersection graph for intervals on the real number line
McConnell, Ross; Paul, Christophe; Viennot, Laurent (2000), "Lex-BFS and partition refinement, with applications to transitive orientation, interval graph recognition
Interval_graph
1016/0304-3975(87)90067-3. Paige, R.; Tarjan, R. E. (1987), "Three partition refinement algorithms", SIAM Journal on Computing, 16 (6): 973–989, doi:10.1137/0216062
Chordal_bipartite_graph
Concept in combinatorial mathematics
In combinatorics, the topic of noncrossing partitions has assumed some importance because of (among other things) its application to the theory of free
Noncrossing_partition
Graph formed by complementation and disjoint union
cotree representation constructed, using modular decomposition, partition refinement, LexBFS , or split decomposition. Once a cotree representation has
Cograph
Chordal graph where all cycles of even length have odd chords
doi:10.1006/jagm.2001.1195. Paige, R.; Tarjan, R. E. (1987), "Three partition refinement algorithms", SIAM Journal on Computing, 16 (6): 973–989, doi:10.1137/0216062
Strongly_chordal_graph
Data structure that maintains info about the connected components of a graph
link-cut tree in log(n) per operation. Dynamic problem (algorithms) Partition refinement Tarjan, Robert Endre (1975). "Efficiency of a Good But Not Linear
Dynamic_connectivity
Heuristic test for graph isomorphism
isomorphism between two graphs G and H. It is a generalization of the color refinement algorithm and has been first described by Weisfeiler and Leman in 1968
Weisfeiler Leman graph isomorphism test
Weisfeiler_Leman_graph_isomorphism_test
Uncoarsening and Refinement: The partition is progressively projected back to the larger, original graphs. At each stage of uncoarsening, the partition boundaries
Graph_Coarsening_Algorithm
Vector quantization algorithm minimizing the sum of squared deviations
vector quantization, originally from signal processing, that aims to partition n observations into k clusters in which each observation belongs to the
K-means_clustering
1980 novel by Anita Desai
Set primarily in Old Delhi, the story describes the tensions in a post-partition Indian family, starting with the characters as adults and moving back
Clear_Light_of_Day
difficult to detect. Fibration symmetries can be identified using partition-refinement algorithms closely related to those employed in graph isomorphism
Fibration_symmetry
Family of problems in computational geometry
aided design (CAD). In one of its general forms, the problem is, given a partition of the space into disjoint regions, to determine the region where a query
Point_location
Mathematical concept for comparing objects
than ≈ {\displaystyle \approx } if the partition created by ∼ {\displaystyle \sim } is a refinement of the partition created by ≈ {\displaystyle \approx
Equivalence_relation
Subject of study in ergodic theory
,T^{-1}Q_{k}\}.} Further, given two partitions Q = {Q1, ..., Qk} and R = {R1, ..., Rm}, define their refinement as Q ∨ R = { Q i ∩ R j ∣ i = 1 , … ,
Measure-preserving dynamical system
Measure-preserving_dynamical_system
Biotechnological procedure
reaction (digital PCR, DigitalPCR, dPCR, or dePCR) is a biotechnological refinement of conventional polymerase chain reaction methods that can be used to
Digital polymerase chain reaction
Digital_polymerase_chain_reaction
Clustering and community detection algorithm
stops improving. function moveNodes(Graph G, Partition P): do old_modularity <- current_modularity_of_partition for v in V(G), do # find the community that
Louvain_method
Programming paradigm restricted to provably terminating programs
those inputs; or excluding them by use of type system features such as refinement types. These restrictions mean that total functional programming is not
Total_functional_programming
technique based on the generalized finite element method (GFEM) and the partition of unity method (PUM). It extends the classical finite element method
Extended finite element method
Extended_finite_element_method
Equilibrium partitioning Sediment Benchmarks (ESBs) are a type of Sediment Quality Guideline (SQG) derived by the US Environmental Protection Agency (EPA)
Equilibrium partitioning sediment benchmark
Equilibrium_partitioning_sediment_benchmark
American manufacturing company
hunting rifles. The original Partition design bullet still is the company's flagship product. It has undergone many refinements over the years, but the basic
Nosler
points and Steiner points may be used as triangle vertices. Delaunay refinement Hwang, F. K.; Richards, D. S.; Winter, P. (1992), The Steiner Tree Problem
Steiner point (computational geometry)
Steiner_point_(computational_geometry)
Real-time operating system
has a separation kernel-based hypervisor that supports multiple logical partition types for various operating systems (OS) and applications, each referred
PikeOS
Type of distributed computing architecture
on a single node is a shard. A SN system typically partitions its data among many nodes. A refinement is to replicate commonly used but infrequently modified
Shared-nothing_architecture
Technique in analytical chemistry
can be described as a mass transfer process involving adsorption and/or partition. As mentioned, HPLC relies on pumps to pass a pressurized liquid and a
High-performance liquid chromatography
High-performance_liquid_chromatography
Gelatinous candy
developed by Chandu Halwai which later relocated to Bombay (Mumbai) after the partition in 1947. Some of the confectioners termed it Bombay Halwa to avoid its
Turkish_delight
Tree data structure that partitions a 2D area
return pointsInRange; } } Adaptive mesh refinement Binary space partitioning Binary tiling k-d tree Octree R-tree UB-tree Spatial database
Quadtree
Country in South Asia
large-scale loss of life and an unprecedented migration accompanied the partition. India has been a federal republic since 1950, governed through a democratic
India
A subdivision (also called refinement) of a simplicial complex is another simplicial complex in which, intuitively, one or more simplices of the original
Subdivision (simplicial complex)
Subdivision_(simplicial_complex)
Concept in geometry
proves the existence of such a partition (in fact, of many such partitions) but does not exhibit any particular partition. Circles can be defined in non-Euclidean
Area_of_a_circle
Indian writer and poet (1907–1987)
her compositions are noted for their expressive language and stylistic refinement. Scholars and literary historians consider her to be one of the most influential
Mahadevi_Varma
Monster and modular connection
remaining odd primes, using a combination of Hodge theory and an integral refinement of the no-ghost theorem. The case of order 2 requires the existence of
Monstrous_moonshine
Multidimensional search tree for points in k dimensional space
computer science, a k-d tree (short for k-dimensional tree) is a space-partitioning data structure for organizing points in a k-dimensional space. K-dimensional
K-d_tree
Grouping a set of objects by similarity
Cluster analysis, or clustering, is a data analysis technique aimed at partitioning a set of objects into groups such that objects within the same group
Cluster_analysis
Indo-Aryan language
seats of refinement, grace and style. Mirza Ghalib of Delhi could not resist the charm of Lucknow's language and in spite of his refinements in language
Urdu
choice of starting values produces a bias in the calculated values. The refinement process continues by setting the new calculated structure factor to the
Le_Bail_method
Procedure in computing
performance are: Partition tables (and indices): try to keep partitions similar in size (watch for null values that can skew the partitioning) Do all validation
Extract,_transform,_load
Parallel processing technique
sets are intended for faster video coding. Wesley A. Clark introduced partitioned subword data operations in the 1950s[citation needed]. This can be seen
SWAR
Measure of the accuracy of probabilistic predictions
calibration), and is equal to reliability. The second term is known as refinement, and it is an aggregation of resolution and uncertainty, and is related
Brier_score
Computer-aided design approach
MIGFEM is another IGA code which is implemented in Matlab and supports Partition of Unity enrichment IGA for 2D and 3D fracture. Furthermore, G+Smo is
Isogeometric_analysis
Integral using products instead of sums
of approximation does not depend on the partition, as long as the partition is a refinement of the partition defining the step function, whereas the value
Product_integral
Set that intersects every one of a family of sets
theory, the axiom of choice is equivalent to the statement that every partition has a transversal. A fundamental question in the study of SDR is whether
Transversal_(combinatorics)
British mathematician
is possible to find in O(n) time an equitable partition P ′ {\displaystyle P'} (which is a refinement of P {\displaystyle P} ) into 1 + k 4 k {\displaystyle
Alan_M._Frieze
Subdivision of space into cells
cells. Often these cells form a simplicial complex. Usually the cells partition the geometric input domain. Mesh cells are used as discrete local approximations
Mesh_generation
Partitioning a digital image into segments
processing and computer vision, image segmentation is the process of partitioning a digital image into multiple image segments, also known as image regions
Image_segmentation
left or right covering, left or right-resolving map, equitable partition, color refinement, and Weisfeiler–Leman canonical form. A directed graph G {\displaystyle
Fibrations_of_graphs
Formalism for Thom class representation in differential geometry
detail, using the superconnection formalism of Quillen, they obtained a refinement of the Riemann–Roch formula, which links together the Thom classes in
Mathai–Quillen_formalism
Ultra-luxury flagship automobile in its eighth generation
technology was first used on the Phantom Celestial. The interior features a partition between the front cockpit and the rear passenger compartment, and the
Rolls-Royce_Phantom_VIII
equilibrium, in game theory, a refinement of Nash Equilibrium for extensive form games Sequential equilibrium, in game theory, a refinement of Nash Equilibrium for
List_of_types_of_equilibrium
Motor vehicle
Europe. The fuel injected petrol engines gave better performance and refinement than the previously used carbureted units. They were mounted transversely
Volkswagen_Passat_(B3)
Profession in software engineering
identifying and right-sizing components. This method emphasizes continuous refinement as teams develop a more nuanced understanding of system behavior and requirements
Software_architect
Hand tool used for turning screws
increase in popularity gradually led to refinement and eventually diversification of the screwdriver. Refinement of the precision of screws also significantly
Screwdriver
2016 Android mobile operating system
be released quarterly as maintenance releases focusing on "continued refinements and polish". On September 6, 2016, LG announced the V20, the first smartphone
Android_Nougat
2009 operating system version
Leopard as having "zero new features". Its name signified its goal to be a refinement of the previous OS X version, Leopard. Much of the software in Mac OS
Mac_OS_X_Snow_Leopard
Symmetric function invariant of graphs
H}=X_{G}\cdot X_{H}} A stable partition π {\displaystyle \pi } of G {\displaystyle G} is defined to be a set partition of vertices V {\displaystyle V}
Chromatic_symmetric_function
Open-source C++ library
conforming, discontinuous (L2), and NURBS finite element spaces. Local mesh refinement, both conforming (simplex meshes) and non-conforming (quadrilateral/hexahedral
MFEM
Approximate quantum chemistry model
thermodynamic equilibrium properties such as activity coefficients, solubility, partition coefficients, vapor pressure and free energy of solvation. The method
COSMO-RS
Algebraic structure of set algebra
A_{3},\ldots \},} is a countable partition of X {\displaystyle X} then the collection of all unions of sets in the partition (including the empty set) is
Σ-algebra
Types of solidification within castings
rupture life of single crystals grown by directional solidification due to refinement of the y’ precipitates. In directional solidification growths of single
Directional_solidification
Matroid with graph forests as independent sets
the partition corresponding to flat x {\displaystyle x} is a refinement of the partition corresponding to flat y {\displaystyle y} . In this aspect of
Graphic_matroid
Literature written in the Bengali language
This continued roughly until the partition of India. Fifth phase: The post-partition phase (1947–1970). After the partition, Bangla literature started developing
Bengali_literature
All numbers between two given numbers
relevant to several areas of numerical analysis, including adaptive mesh refinement, multigrid methods and wavelet analysis. Another way to represent such
Interval_(mathematics)
Lossy image compression algorithm
the significant coefficient is included in a list for further refinement in the refinement pass. And if any coefficient already known to be zero, it will
Embedded zerotrees of wavelet transforms
Embedded_zerotrees_of_wavelet_transforms
Object in graph theory
mathematical subfield of graph theory a level structure of a rooted graph is a partition of the vertices into subsets that have the same distance from a given
Level_structure
Process of planning software solutions
Abstraction and Refinement are complementary concepts. Software procedure Focuses on the processing of each module individually. Structural partitioning The program
Software_design
Description of particle density in statistical mechanics
using the Ornstein–Zernike equation or structure-optimized potential refinement. Consider a system of N {\displaystyle N} particles in a volume V {\displaystyle
Radial_distribution_function
Office skyscraper in Manhattan, New York
elements that were innovative when the structure was constructed. The partitions between the offices are soundproofed and divided into interchangeable
Chrysler_Building
Sculpture of the Hellenistic culture of antiquity
Greek tradition of sculpture were the development of new techniques, the refinement of the representation of human anatomy and emotional expression, and a
Hellenistic_sculpture
Japanese sliding paper door
more elaborate, later adding screw adjustments and other machined-metal refinements). Before hiki-chigai (sliding panels that overlap when closed) became
Shoji
Type of fair division
equilibrium exists. I.e, there is a price vector P {\displaystyle P} and a partition X {\displaystyle X} such that: (CE) All agents maximize their utilities
Efficient_envy-free_division
Property of a mathematical space
smallest integer n for which the following holds: any open cover has an open refinement (a second open cover in which each element is a subset of an element in
Dimension
Branch of computer science
segments. Delaunay triangulation Voronoi diagram: Given a set of points, partition the space according to which points are closest to the given points. Linear
Computational_geometry
Motor vehicle
by statesmen and business leaders, it offered options such as a glass partition, VHF mobile telephone, and dictation machine. All but hand-built, the
Mercedes-Benz_W189
Subdivision of a planar object into triangles
nonobtuse meshes. Many meshing techniques are known, including Delaunay refinement algorithms such as Chew's second algorithm and Ruppert's algorithm. In
Triangulation_(geometry)
Statistical function that defines the quantiles of a probability distribution
F-distribution", ACM Trans. Math. Softw., 9 (4), 478–480 doi:10.1145/168173.168387 Refinement of the Normal Quantile New Methods for Managing "Student's" T Distribution
Quantile_function
Number of forests a graph's edges may be partitioned into
undirected graph is the minimum number of forests into which its edges can be partitioned. Equivalently it is the minimum number of spanning forests needed to
Arboricity
Partition of Earth's surface into subdivided cells
surface. Mathematically it is a space partitioning: it consists of a set of non-empty regions that form a partition of the Earth's surface. In a usual grid-modeling
Discrete_global_grid
Concepts in theoretical computer science
decomposition of properties into safety and liveness (as opposed to some other partitioning) was a useful one—knowing the type of property to be proved dictated
Safety and liveness properties
Safety_and_liveness_properties
GUI and CLI interfaces mesh adaptive-refinement: Yes, full adaptive mesh refinement (h-refinement); no p-refinement but several higher-order elements are
List of finite element software packages
List_of_finite_element_software_packages
Any collection of sets, or subsets of a set
member of C {\displaystyle {\mathcal {C}}} . A star refinement is a particular type of refinement. A Sperner family is a set family in which none of the
Family_of_sets
Number representing system complexity
C and D, let C ∨ D {\displaystyle C\vee D} be their (minimal) common refinement, which consists of all the non-empty intersections of a set from C with
Topological_entropy
PARTITION REFINEMENT
PARTITION REFINEMENT
Boy/Male
Arabic
Partition; Curtain
Biblical
perdition, destruction
Girl/Female
Arabic, Muslim
Purity; Refinement; Clarity
Girl/Female
Arabic, Gujarati, Hindu, Indian, Kannada, Muslim, Punjabi, Sikh
Wish; Petition to God; Special Prayer
Boy/Male
Arabic, Muslim, Sindhi
Refinement
Girl/Female
Muslim
Purity, Refinement, Clarity
Boy/Male
Indian, Sikh
A Partition in the World
Girl/Female
Arabic, Muslim
Purity; Refinement
Boy/Male
Biblical
That hears, or obeys, perdition.
Biblical
Shimeath, that hears, or obeys; perdition
Boy/Male
Biblical
That hears, or obeys, perdition.
Male
English
Hebrew name SHELAH means "a petition, prayer." In the bible, this is the name of a son of Judah. Compare with another form of Shelah.
Girl/Female
Biblical Greek Latin
Perdition, destruction.
Boy/Male
Hindu, Indian, Traditional
Noble Partition
Boy/Male
Muslim/Islamic
Refinement
PARTITION REFINEMENT
PARTITION REFINEMENT
Girl/Female
Hindu, Indian, Tamil
A Precious Stones
Boy/Male
Hindu, Indian
Name of God
Girl/Female
Latin
Eveningstar.
Surname or Lastname
English
English : nickname from Middle English hobi ‘hobby’, a small falcon, or from the same word denoting a small horse.English : habitational name from Hoby in Leicestershire, named with Old English hÅh ‘spur of a hill’ + Old Norse býr ‘farmstead’, ‘settlement’.
Girl/Female
Arabic, Muslim
Noble
Girl/Female
Hebrew
Incense.
Boy/Male
Tamil
Vishwdeep | விஷà¯à®µà®¤à¯€à®ªÂ
Big lighting
Boy/Male
Indian
An heir, A master, A Lord, Supreme inheritor
Surname or Lastname
English
English : variant spelling of Hamlett.
Boy/Male
Tamil
Famous battle
PARTITION REFINEMENT
PARTITION REFINEMENT
PARTITION REFINEMENT
PARTITION REFINEMENT
PARTITION REFINEMENT
n.
Destruction; perdition.
v. t.
To divide into parts or shares; to divide and distribute; as, to partition an estate among various heirs.
n.
A screen or partition wall behind an altar.
n.
A word expressing partition, or denoting a part.
a.
Divided by partition or partitions; having septa; as, a septate pod or shell.
n.
Parturition.
v. i.
To make a petition or solicitation.
v. t.
To make a prayer or request to; to ask from; to solicit; to entreat; especially, to make a formal written supplication, or application to, as to any branch of the government; as, to petition the court; to petition the governor.
v.
A score.
v.
The act of parting or dividing; the state of being parted; separation; division; distribution; as, the partition of a kingdom.
imp. & p. p.
of Partition
p. pr. & vb. n.
of Partition
a.
Denoting a part; as, a partitive genitive.
n.
A separating tissue; a partition; a septum.
v.
A part divided off by walls; an apartment; a compartment.
a.
With two partitions or septa.
v. t.
To divide into distinct parts by lines, walls, etc.; as, to partition a house.
v.
That which divides or separates; that by which different things, or distinct parts of the same thing, are separated; separating boundary; dividing line or space; specifically, an interior wall dividing one part or apartment of a house, an inclosure, or the like, from another; as, a brick partition; lath and plaster partitions.
v.
The servance of common or undivided interests, particularly in real estate. It may be effected by consent of parties, or by compulsion of law.
n.
A partition between flues in a chimney.