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Node ordering for directed acyclic graphs
Any DAG has at least one topological ordering, and there are linear time algorithms for constructing it. Topological sorting has many applications, especially
Topological_sorting
Directed graph with no directed cycles
find a topological ordering and then testing for each edge whether the resulting ordering is valid or alternatively, for some topological sorting algorithms
Directed_acyclic_graph
Directed graph representing dependencies
acyclic graph, and an evaluation order may be found by topological sorting. Most topological sorting algorithms are also capable of detecting cycles in their
Dependency_graph
Graph algorithm
always magically at your fingertips. And his algorithm also does topological sorting as a byproduct. Tarjan, R. E. (1972), "Depth-first search and linear
Tarjan's strongly connected components algorithm
Tarjan's_strongly_connected_components_algorithm
Algorithm to search the nodes of a graph
postorderings are A C B D and A B C D. Reverse postordering produces a topological sorting of any directed acyclic graph. This ordering is also useful in control-flow
Depth-first_search
Origins and events of data
reconstruction is the topological sorting of the association graph. The directed graph created in the previous step is topologically sorted to obtain the order
Data_lineage
Graph with oriented edges
undirected graph Preorder – Reflexive and transitive binary relation Topological sorting – Node ordering for directed acyclic graphs Transpose graph – Directed
Directed_graph
Standard UNIX utility
tsort: c a b c Free and open-source software portal Sort (Unix) Make (software) Topological sorting List of Unix commands Call graph From 1997 until 2024
Tsort
Trail in which only the first and last vertices are equal
edges can be tree edges. Many topological sorting algorithms will detect cycles too, since those are obstacles for topological order to exist. Also, if a
Cycle_(graph_theory)
Mathematical ordering of a partial order
extension principle is constructively provable for finite sets using topological sorting algorithms, where the partial order is represented by a directed
Linear_extension
Programming paradigm based on asynchronous data streams
[citation needed] This is usually achieved by topologically sorting expressions and updating values in topological order. This can, however, have performance
Reactive_programming
Mathematical set with an ordering
topological space, then it is customary to assume that { ( a , b ) : a ≤ b } {\displaystyle \{(a,b):a\leq b\}} is a closed subset of the topological product
Partially_ordered_set
Free software package management system
policy. A major feature of APT is the way it calls dpkg –it performs topological sorting of the list of packages to be installed or removed and calls dpkg
APT_(software)
Complexity class
number of satisfying assignments. Topologically sorting is easy in contrast to counting the number of topological sortings. A single perfect matching can
♯P-complete
Computational problem of graph theory
found in Cherkassky, Goldberg & Radzik (1996). An algorithm using topological sorting can solve the single-source shortest path problem in time Θ(E + V)
Shortest_path_problem
Logic problem, AND of pairwise ORs
Kosaraju's algorithm in topological order and by Tarjan's algorithm in reverse topological order. For each component in the reverse topological order, if its variables
2-satisfiability
Overview of and topical guide to algorithms
Pigeonhole sort Selection algorithm Quickselect Median of medians Order statistic tree Depth-first search Breadth-first search Topological sorting Flood fill
Outline_of_algorithms
elements, add it to the end of the sorted list Smoothsort Other Bitonic sorter Pancake sorting Spaghetti sort Topological sort Unknown class Samplesort Longest
List_of_algorithms
Computational problem
terms of time complexity, it can be solved in linear time simply by a topological sort. The Boolean formula value problem (or Boolean formula evaluation problem)
Circuit_value_problem
Software for handling software deployment
installs it. However, both kinds of tools have many commonalities: Topological sorting of the dependency graph used in a package manager to handle dependencies
Package_manager
Python library for graphs and networks
NetworkX Releases Version Release date Major Changes 0.22 17 June 2005 Topological sorting for testing directed acyclic graphs (DAGs). Integration of Dijkstra's
NetworkX
Bellman–Ford algorithm A* algorithm Floyd–Warshall algorithm Topological sorting Pre-topological order Adjacency list Adjacency matrix Adjacency algebra –
List_of_graph_theory_topics
Type of mathematical space
the cover containing it. The corresponding topological property is used to define compactness: a topological space is compact if every open cover has a
Compact_space
necessarily avoiding crossings). 2. Topological graph theory is the study of graph embeddings. 3. Topological sorting is the algorithmic problem of arranging
Glossary_of_graph_theory
Compiler optimization technique
left out, the dependency graph is a directed acyclic graph. Then, any topological sort of this graph is a valid instruction schedule. The edges of the graph
Instruction_scheduling
Collection of standard, Unix-based utilities from GNU
characters tsort – Performs a topological sort unexpand – Converts spaces to tabs uniq – Removes duplicate lines from a sorted file wc – Reports the number
GNU_Core_Utilities
Way of storing data in a computer
are also key building blocks for many efficient algorithms, such as topological sort and set union-find. A linked list is a collection of structures ordered
Linked_data_structure
Class of algorithms
traverse the current node's right subtree. The pre-order traversal is a topologically sorted one, because a parent node is processed before any of its child nodes
Tree_traversal
Collection of Unix tools in single executable file
extending sparsely if necessary. ts — timestamp standard input. tsort — Topologically sort for dependency resolution. tty — Show filename of terminal connected
Toybox
Mathematical description of mixing substances
weak topological mixing is one that has no non-constant continuous (with respect to the topology) eigenfunctions of the shift operator. Topological mixing
Mixing_(mathematics)
Computer science algorithm
step. DFS is the basis for many graph-related algorithms, including topological sorts and planarity testing. Input: A graph G and a vertex v of G. Output:
Graph_traversal
Mathematical idealization of the trace left by a moving point
finite union of topological curves. When complex zeros are considered, one has a complex algebraic curve, which, from the topological point of view, is
Curve
Collection of open sets used to define a topology
(or basis; pl.: bases) for the topology τ {\displaystyle \tau } of a topological space ( X , τ ) {\displaystyle (X,\tau )} is a family B {\displaystyle
Base_(topology)
Limited form of tree data structure
search trees and binary heaps, and are used for efficient searching and sorting. The designation of non-root nodes as left or right child even when there
Binary_tree
Method of analyzing variables in software
straightforward. The control-flow graph can then be topologically sorted; running in the order of this sort, the entry states can be computed at the start
Data-flow_analysis
Number of "holes" of a surface
itself on a sphere with n cross-caps or on a sphere with n/2 handles. In topological graph theory there are several definitions of the genus of a group. Arthur
Genus_(mathematics)
with status 0 Version 7 AT&T UNIX tsort Text processing Mandatory Topological sort Version 7 AT&T UNIX tty Misc Mandatory Report user's terminal name
List_of_POSIX_commands
Algebraic theory
algebraic theory of topological quantum information is a collection of algebraic techniques developed and applied to topological aspects of condensed
Algebraic theory of topological quantum information
Algebraic_theory_of_topological_quantum_information
Quantum computing chip by Microsoft
processor developed by Microsoft. It uses topological superconductors in an attempt to enable topological quantum computing, which is designed to offer
Majorana_1
Partition of vertices of a directed graph
this condensation is topologically sorted, then each weak component necessarily appears as a consecutive subsequence of the topological order of the strong
Weak_component
Software engineering
history has the structure of a directed acyclic graph which can be topologically sorted. This makes it possible to use a divide and conquer search algorithm
Bisection (software engineering)
Bisection_(software_engineering)
Structure in computing
graph) into a picture. tsort Command-line utility that performs a topological sort. A sample call graph generated from gprof analyzing itself: index called
Call_graph
Class in computational complexity theory
instance, the circuit value problem can be solved in linear time by a topological sort. Of course, because the reductions to a P-complete problem may have
P-complete
topological topos, or more recent incarnations such as condensed sets or pyknotic sets. These attempt to embed the category of (certain) topological spaces
Generalized_space
Mathematical result in differential geometry
dimension of the space of solutions) is equal to the topological index (defined in terms of some topological data). It includes many other theorems, such as
Atiyah–Singer_index_theorem
Generalization of finite-dimensional Euclidean spaces different from Hilbert spaces
finite-dimensional ones. In practice a sort of converse to this is often true: if a "naturally occurring" topological vector space is not a Banach space,
Nuclear_space
Sorting algorithms for quantum computers
A quantum sort is any sorting algorithm that runs on a quantum computer. Any comparison-based quantum sorting algorithm would take at least Ω ( n log
Quantum_sort
Topological space with a dense countable subset
In mathematics, a topological space is called separable if it contains a countable dense subset; that is, there exists a sequence ( x n ) n = 1 ∞ {\displaystyle
Separable_space
Tool to track locally defined data attached to the open sets of a topological space
{\displaystyle F} arises from a natural topological situation, E {\displaystyle E} may not have any clear topological interpretation. For example, if F {\displaystyle
Sheaf_(mathematics)
Study of discrete mathematical structures
metric spaces, there are more general discrete topological spaces, finite metric spaces, finite topological spaces. The time scale calculus is a unification
Discrete_mathematics
lexicographically ordered topological sort of a given directed acyclic graph in linear time; this lexicographic topological ordering is one of the key
Partition_refinement
In the field of computer science, a pre-topological order or pre-topological ordering of a directed graph is a linear ordering of its vertices such that
Pre-topological_order
Topological space in which all singleton sets are closed
every pair of topologically distinguishable points. The properties T1 and R0 are examples of separation axioms. Let X be a topological space and let x
T1_space
Theorem on extension of bounded linear functionals
its real part. Continuity A linear functional F {\displaystyle F} on a topological vector space is continuous if and only if this is true of its real part
Hahn–Banach_theorem
Concept in topology
the underlying topological space of any scheme. Given any topological space one can construct a T0 space by identifying topologically indistinguishable
Kolmogorov_space
Russian mathematician (1927–2003)
problems in other areas of mathematics including linear algebra and topological sorting of graphs. O'Connor, John J.; Robertson, Edmund F., "Alexander Skopin"
Alexander_Skopin
Theorem in geometric topology
two-dimensional topological manifolds, which was understood in various forms since the 1860s. In higher dimensions, the closed and connected topological manifolds
Poincaré_conjecture
Class of algorithms which use a moving line to solve geometrical problems
polygons. Topological sweeping is a form of plane sweep with a simple ordering of processing points, which avoids the necessity of completely sorting the points;
Sweep_line_algorithm
Broad concept generalizing scalars in mathematics and physics
with a non-degenerate, skew-symmetric, bilinear form Topological vector space, a blend of topological structure with the algebraic concept of a vector space
Vector (mathematics and physics)
Vector_(mathematics_and_physics)
Algorithm in mathematical optimization
into a linked list and maintains the invariant that the list is topologically sorted with respect to the admissible network. The algorithm scans the list
Push–relabel maximum flow algorithm
Push–relabel_maximum_flow_algorithm
Manifold upon which it is possible to perform calculus
a differentiable manifold is a topological manifold with a globally defined differential structure. Any topological manifold can be given a differential
Differentiable_manifold
Graph layout on multiple half-planes
include abstract algebra and knot theory. The notion of a book, as a topological space, was defined by C. A. Persinger and Gail Atneosen in the 1960s
Book_embedding
Type of monoidal category
algebraic theory of topological quantum information, as they are used to store the algebraic data describing anyons in topological quantum phases of matter
Modular_tensor_category
Algorithm for visible surface determination in 3D graphics
algorithm's time-complexity depends on the sorting algorithm used to order the polygons. Assuming an optimal sorting algorithm, painter's algorithm has a worst-case
Painter's_algorithm
British-Lebanese mathematician (1929–2019)
contributions include the Atiyah–Singer index theorem and co-founding topological K-theory. He was awarded the Fields Medal in 1966 and the Abel Prize
Michael_Atiyah
Real-valued number of spatial dimensions
dimension of a set exceeds its topological dimension, the set is considered to have fractal geometry. Unlike topological dimensions, the fractal index
Fractal_dimension
Quotient of two integers
{Q} .} All three topologies coincide and turn the rationals into a topological field. The rational numbers are an important example of a space which
Rational_number
Left-invariant (or right-invariant) measure on locally compact topological group
measure assigns an "invariant volume" to subsets of locally compact topological groups, consequently defining an integral for functions on those groups
Haar_measure
Mathematical object
compactification of R3. In general, any topological space that is homeomorphic to the 3-sphere is called a topological 3-sphere. The homology groups of the
3-sphere
Measure of magnetic field topology
other sorts of magnetic structures, such as helical magnetic field lines. Magnetic helicity is a continuous generalization of the topological concept
Magnetic_helicity
Product of any collection of compact topological spaces is compact
Tychonoff's theorem states that the product of any collection of compact topological spaces is compact with respect to the product topology. The theorem is
Tychonoff's_theorem
the properties of topological spaces and structures defined on them. It differs from other branches of topology as the topological spaces do not have
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Property that is not changed by mathematical transformations
a linear change of variables. The dimension and homology groups of a topological object are invariant under homeomorphism. The number of fixed points
Invariant_(mathematics)
Embedding a topological space into a compact space as a dense subset
embedding of a topological space X as a dense subset of a compact space is called a compactification of X. It is often useful to embed topological spaces in
Compactification (mathematics)
Compactification_(mathematics)
Mathematical category
abundance of situations in mathematics where topological heuristics are very effective, but an honest topological space is lacking; it is sometimes possible
Topos
Branch of mathematics that studies the properties of groups
between infinite abstract groups and topological groups: whenever a group Γ can be realized as a lattice in a topological group G, the geometry and analysis
Group_theory
Branch of mathematics
of smooth topological invariants of such manifolds, such as de Rham cohomology or the intersection form, as well as smoothable topological constructions
Differential_topology
Problem in computer science
S2CID 263324404. Katriel, Irit; Bodlaender, Hans L. (2006), "Online topological ordering", ACM Transactions on Algorithms, 2 (3): 364–379, CiteSeerX 10
List-labeling_problem
occasionally heard a clank of "switching noise." This algorithm is a form of topological sort, and is the heart of the algorithm that controls a minimal spanning
Nonblocking minimal spanning switch
Nonblocking_minimal_spanning_switch
Hypothetical particle with one magnetic pole
group at long distances, there are magnetic monopoles. The argument is topological: The holonomy of a gauge field maps loops to elements of the gauge group
Magnetic_monopole
Sheaf cohomology on the étale site
a topological space, and its objects can be thought of informally as "étale open subsets" of X. The intersection of two open sets of a topological space
Étale_cohomology
Equivalence class of objects sharing local properties at a point in a topological space
In mathematics, the notion of a germ of an object in/on a topological space is an equivalence class of that object and others of the same kind that captures
Germ_(mathematics)
splitting problem Scheduling to minimize weighted completion time Block Sorting (Sorting by Block Moves) Sparse approximation Variations of the Steiner tree
List_of_NP-complete_problems
Algorithm for finding shortest paths
ISBN 0-262-03293-7. Dial, Robert B. (1969). "Algorithm 360: Shortest-path forest with topological ordering [H]". Communications of the ACM. 12 (11): 632–633. doi:10.1145/363269
Dijkstra's_algorithm
German mathematician (1885–1955)
discovered in 2015, in a form of crystals known as Weyl semimetals, a type of topological material. The question for the ultimate foundations and the ultimate
Hermann_Weyl
Matching of coordinates to physical locations
problem based on similarity between points' curve and the road curve. Topological map matching aligns GPS points with a road network by considering the
Map_matching
Fundamental space of geometry
The inner product and the norm allow expressing and proving metric and topological properties of Euclidean geometry. The next subsection describe the most
Euclidean_space
{a+bi}}=a-b\ i~.} 2. Topological closure: If S is a subset of a topological space T, then S ¯ {\displaystyle {\overline {S}}} is its topological closure, that
Glossary of mathematical symbols
Glossary_of_mathematical_symbols
Mathematical object that generalizes the standard notions of sets and functions
the category of rings and ring homomorphisms; and Top, the category of topological spaces and continuous maps. All of the preceding categories have the
Category_(mathematics)
Data structures used in spatial indexing
are sorted by their first coordinate ("X") and then split into pages of the desired size. Packed Hilbert R-tree: variation of Nearest-X, but sorting using
R-tree
which is specified below. The first part of the algorithm does a topological ordering of the resolution graph (considering that edges goes from antecedentes
Resolution proof reduction via local context rewriting
Resolution_proof_reduction_via_local_context_rewriting
measure whose domain is the Borel σ-algebra. 2. The Borel σ-algebra on a topological space is the smallest σ-algebra containing all open sets. 3. Borel's
Glossary of real and complex analysis
Glossary_of_real_and_complex_analysis
Sequence of operations for a task
discovered improved sorting and hashing algorithms. In a paper published in Nature, AlphaDev was reported to have discovered small sorting algorithms that
Algorithm
Type of formal logic
interpreted using topological structures. For instance, the Interior Semantics interprets formulas of modal logic as follows. A topological model is a tuple
Modal_logic
Speculative feature of the early universe
0-dimensional topological defect: magnetic monopole 2-dimensional topological defect: domain wall (example of 1-dimensional topological defect: a cosmic
Cosmic_string
Concept in natural language processing
Computationally, semantic similarity can be estimated by defining a topological similarity, by using ontologies to define the distance between terms/concepts
Semantic_similarity
Triangulation method
2010-02-23. Edelsbrunner, Herbert; Shah, Nimish (1996). "Incremental Topological Flipping Works for Regular Triangulations". Algorithmica. 15 (3): 223–241
Delaunay_triangulation
Computing company founded in 2014
distillation, and the first demonstration of the creation and control of topological qubits whose linking properties can help make quantum computing fault-tolerant
Quantinuum
Global nonprofit technology consortium
urn:ogc:def:dataType:geoxacml:1.0:geometry and several geographic functions such as topological, bag, set, geometric and conversion functions. KMIP — The Key Management
OASIS_Open
Postcode area within the United Kingdom
followed, alphabetically, by their most important parish, chapelry, topological or built environment feature names, up to 10. Similarly as to the Battersea
SW_postcode_area
TOPOLOGICAL SORTING
TOPOLOGICAL SORTING
Surname or Lastname
English and French
English and French : from a medieval personal name, ultimately from Greek Basileios ‘royal’. The name was borne by a 4th-century bishop of Caesarea in Cappadocia, regarded as one of the four Fathers of the Eastern Church; he wrote important theological works and established a rule for religious orders of monks. Various other saints are also known under these and cognate names. The popularity of Vasili as a Russian personal name is largely due to the fact that this was the ecclesiastical name of St. Vladimir (956–1015), Prince of Kiev, who was chiefly responsible for the introduction of Christianity to Russia. As an American surname, this has also absorbed some Greek, Russian, and other derivatives of Greek Vasili.
Surname or Lastname
English
English : regional name from the district around Middlesbrough named Cleveland ‘the land of the cliffs’, from the genitive plural (clifa) of Old English clif ‘bank’, ‘slope’ + land ‘land’.Americanized spelling of Norwegian Kleiveland or Kleveland, habitational names from any of five farmsteads in Agder and Vestlandet named with Old Norse kleif ‘rocky ascent’ or klefi ‘closet’ (an allusion to a hollow land formation) + land ‘land’.Grover Cleveland (1837–1908), 22nd and 24th president of the U.S., was the fifth child of a country Presbyterian clergyman. His father, Richard Falley Cleveland, a graduate of Yale College and of the theological seminary at Princeton, was descended from a certain Moses Cleaveland who arrived in MA in 1635.
Surname or Lastname
English
English : variant of Sewell.Samuel Sewall (1652–1730) came with his parents from Bishop Stoke, Hampshire, England, to Newbury, MA, as a nine-year-old boy. In 1676 he married Hannah Hull, a wealthy heiress, and in 1681 he was appointed printer to the Council in Boston. He served as a judge in the infamous Salem witchcraft trials of 1692—the only one of the judges to admit publicly that he had been wrong. In 1700 he published The Selling of Joseph, which argues that all men are created equal and presents theological arguments against slavery.
TOPOLOGICAL SORTING
TOPOLOGICAL SORTING
Boy/Male
American, Chinese, German, Teutonic
Gifted Ruler; The People's Ruler; Variant of Dedrick; King of Nations
Boy/Male
Gaelic Irish Scottish American
Form of Michael 'Who is like God?'.
Girl/Female
Tamil
Prasansha | பà¯à®°à®¸à®‚ஷா
Happy
Girl/Female
Indian, Telugu
Pure
Girl/Female
Hindu, Indian
Having Knowledge of the Subject
Girl/Female
Indian
Variant of Fatima (A daughter of the prophet (SAW))
Girl/Female
Arabic, Muslim
Respect; Honour; Sanctity
Boy/Male
Tamil
Sukhamay | ஸூக஼மயÂ
Pleasurable
Girl/Female
Bengali, Gujarati, Hindu, Indian, Kannada, Marathi, Mythological, Sanskrit, Sindhi, Telugu
Wife of the Sage Kashyap; Arohi; Earth Goddess: Idea
Girl/Female
Australian, Danish, Greek
Wisdom
TOPOLOGICAL SORTING
TOPOLOGICAL SORTING
TOPOLOGICAL SORTING
TOPOLOGICAL SORTING
TOPOLOGICAL SORTING
a.
Of or pertaining to theology, or the science of God and of divine things; as, a theological treatise.
a.
Pertaining to posology.
a.
Of or pertaining tootology.
a.
Theological.
adv.
In a zoological manner; according to the principles of zoology.
v. i.
To introduce innovations in doctrine, esp. in theological doctrine.
n.
A student in a theological seminary.
a.
Of or pertaining to zoology, or the science of animals.
a.
Of or pertaining to pomology.
a.
Alt. of Posological
a.
Alt. of Tropological
a.
Of or pertaining to oology.
a.
Characterized by tropes; varied by tropes; tropical.
a.
Of or pertaining to nosology.
a.
Of or pertaining to orology.
a.
Of or pertaining to noology.
v. t.
To use in a tropological sense, as a word; to make a trope of.
a.
Pertaining to doxology; giving praise to God.
a.
Pertaining to homology; having a structural affinity proceeding from, or base upon, that kind of relation termed homology.
a.
Relating to a horologe, or to horology.