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Computational problem of graph theory
algorithmic graph theory is the shortest path problem. One of the generalizations of the shortest path problem is known as the single-source-shortest-paths
Parallel single-source shortest path algorithm
Parallel_single-source_shortest_path_algorithm
Algorithm for finding shortest paths
later. Dijkstra's algorithm finds the shortest path from a given source node to every other node. It can be used to find the shortest path to a specific destination
Dijkstra's_algorithm
Computational problem of graph theory
single-source-shortest-paths (SSSP) problem, which also has parallel approaches: Parallel single-source shortest path algorithm. Let G = ( V , E , w ) {\displaystyle G=(V
Parallel all-pairs shortest path algorithm
Parallel_all-pairs_shortest_path_algorithm
Node ordering for directed acyclic graphs
graph, in topological order. Then the following algorithm computes the shortest path from some source vertex s to all other vertices: Let d be an array
Topological_sorting
Plotting by a computer application
heavily on Dijkstra's algorithm for finding the shortest path on a weighted graph. Pathfinding is closely related to the shortest path problem, within graph
Pathfinding
IEEE standard for Shortest Path Bridging
amendment to the IEEE 802.1Q networking standard which adds support for Shortest Path Bridging (SPB). This technology is intended to simplify the creation
IEEE_802.1aq
Algorithm for computing the maximal flow of a network
that it uses shortest augmenting paths. The introduction of the concepts of the level graph and blocking flow enable Dinic's algorithm to achieve its
Dinic's_algorithm
Algorithm in graph theory
shortest paths in a directed weighted graph with positive or negative edge weights (but with no negative cycles). A single execution of the algorithm
Floyd–Warshall_algorithm
Method for finding minimum spanning trees
similar algorithm for the shortest path problem Greedoids offer a general way to understand the correctness of Prim's algorithm Jarník, V. (1930), "O jistém
Prim's_algorithm
Algorithm for maximum cardinality matching
F} if and only if it ends a shortest augmenting path. The algorithm finds a maximal set of vertex disjoint augmenting paths of length k {\displaystyle
Hopcroft–Karp_algorithm
Minimum spanning forest algorithm that greedily adds edges
Kruskal's algorithm finds a minimum spanning forest of an undirected edge-weighted graph. If the graph is connected, it finds a minimum spanning tree
Kruskal's_algorithm
Sequence of operations for a task
Floyd–Warshall algorithm, the shortest path between a start and goal vertex in a weighted graph can be found using the shortest path to the goal from
Algorithm
Least-weight tree connecting graph vertices
L.; Willard, D. E. (1994), "Trans-dichotomous algorithms for minimum spanning trees and shortest paths", Journal of Computer and System Sciences, 48 (3):
Minimum_spanning_tree
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
Finds likely sequence of hidden states
explain a sequence of observed events. The result of the algorithm is often called the Viterbi path. It is most commonly used with hidden Markov models (HMMs)
Viterbi_algorithm
Optimization technique
memetic algorithm is the use of a local search algorithm instead of or in addition to a basic mutation operator in evolutionary algorithms. A parallel metaheuristic
Metaheuristic
Directed graph with no directed cycles
Section 24.2, Single-source shortest paths in directed acyclic graphs, pp. 592–595. Cormen et al. 2001, Sections 24.1, The Bellman–Ford algorithm, pp. 588–592
Directed_acyclic_graph
NP-hard problem in combinatorial optimization
randomly distributed on a plane, the algorithm on average yields a path 25% longer than the shortest possible path; however, there exist many specially-arranged
Travelling_salesman_problem
Annual conference series on algorithms
The European Symposium on Algorithms (ESA) is an international conference covering the field of algorithms. It has been held annually since 1993, typically
European Symposium on Algorithms
European_Symposium_on_Algorithms
Computational problem in graph theory
For the single-source shortest path (SSSP) problem with negative weights – another particular case of a minimum-cost flow problem – an algorithm running
Maximum_flow_problem
Problem optimization method
algorithm for the shortest path problem is a successive approximation scheme that solves the dynamic programming functional equation for the shortest
Dynamic_programming
Polynomial-time algorithm for the assignment problem
shortest path algorithm". Algorithms for Competitive Programming. Retrieved 14 May 2023. "Solving assignment problem using min-cost-flow". Algorithms
Hungarian_algorithm
Method for finding kth smallest value
In computer science, a selection algorithm is an algorithm for finding the k {\displaystyle k} th smallest value in a collection of orderable values,
Selection_algorithm
Data structure for integer priorities
computer graphics. The first use of the bucket queue was in a shortest path algorithm by Dial (1969). A bucket queue can handle elements with integer
Bucket_queue
Algorithm in mathematical optimization
Ford–Fulkerson algorithm performs global augmentations that send flow following paths from the source all the way to the sink. The push–relabel algorithm is considered
Push–relabel maximum flow algorithm
Push–relabel_maximum_flow_algorithm
Trail in a graph that visits each edge once
vertices Hamiltonian path – a path that visits each vertex exactly once. Route inspection problem, search for the shortest path that visits all edges
Eulerian_path
Measure of similarity between two graphs
minimum cost edit path between the two graphs. The computation of the optimal edit path is cast as a pathfinding search or shortest path problem, often implemented
Graph_edit_distance
Digital workload distribution techniques
is the subject of research in the field of parallel computers. Two main approaches exist: static algorithms, which do not take into account the state of
Load_balancing_(computing)
Study of mathematical algorithms for optimization problems
some way (or even subgradients): Coordinate descent methods: Algorithms which update a single coordinate in each iteration Conjugate gradient methods: Iterative
Mathematical_optimization
Computational problem
changes during path following. Incremental heuristic search algorithms replan fast by using experience with the previous similar path-planning problems
Motion_planning
Routing technique of using multiple alternative paths through a network
for a given network, is a multi-path solution between a pair of source and destination nodes. Unlike shortest-path routing or max-flow routing, for any
Multipath_routing
Tree containing all suffixes of a given text
position, that is, the shortest string starting at i {\displaystyle i} and occurring only once in S {\displaystyle S} . His Algorithm D takes an uncompressed
Suffix_tree
Nonlinear dimensionality reduction method
to be the sum of edge weights along the shortest path between two nodes (computed using Dijkstra's algorithm, for example). The top n eigenvectors of
Isomap
Computer compiler optimization technique
a register. Sethi–Ullman algorithm, an algorithm to produce the most efficient register allocation for evaluating a single expression when the number
Register_allocation
Parallel version of breadth-first search algorithm
runs afterwards. Users can choose to run BFS in kernel 2 and/or Single-Source-Shortest-Path in kernel 3 on the constructed graph. The result of those kernels
Parallel_breadth-first_search
Network that allows computers to share resources and communicate with each other
Most routing algorithms use only one network path at a time. Multipath routing techniques enable the use of multiple alternative paths. Routing can be
Computer_network
Multi-model database
ArangoDB and can be used with predefined algorithms, e.g. PageRank, Single-Source Shortest Path and Connected components. Transactions: ArangoDB supports user-definable
ArangoDB
Algorithm for solving linear programs
Column generation or delayed column generation is an efficient algorithm for solving large linear programs. The overarching idea is that many linear programs
Column_generation
Optimization by removing non-optimal solutions to subproblems
an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists
Branch_and_bound
Network protocol for Ethernet that provides seamless failover
without dedicated switches. This is in contrast to the companion standard Parallel Redundancy Protocol (PRP), with which HSR shares the operating principle
High-availability Seamless Redundancy
High-availability_Seamless_Redundancy
Computational task of sorting whole numbers
L.; Willard, Dan E. (1994), "Trans-dichotomous algorithms for minimum spanning trees and shortest paths", Journal of Computer and System Sciences, 48 (3):
Integer_sorting
Abstract data type in computer science
one method of doing this. Best-first search algorithms, like the A* search algorithm, find the shortest path between two vertices or nodes of a weighted
Priority_queue
Any planar graph can be subdivided by removing a few vertices
technique for the single source shortest path algorithm in planar graphs for nonnegative edge-lengths and proposed a linear time algorithm. Their method generalizes
Planar_separator_theorem
Degree of connectedness within a graph
vertices). In this case, using Brandes' algorithm will divide final centrality scores by 2 to account for each shortest path being counted twice. Eigenvector
Centrality
Algorithm in computer science
a new food source. Onlookers watch the dances of employed bees and choose food sources depending on dances. The main steps of the algorithm are given below:
Artificial bee colony algorithm
Artificial_bee_colony_algorithm
Network traffic shaping and policing algorithm
The leaky bucket is an algorithm based on an analogy of how a bucket with a constant leak will overflow if either the average rate at which water is poured
Leaky_bucket
Optimization algorithm
technique which belongs to the family of local search. It is an iterative algorithm that starts with an arbitrary solution to a problem, then attempts to
Hill_climbing
Subfield of mathematical optimization
sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard. A convex optimization
Convex_optimization
Spore-forming organisms
maze of plastic film. The mold explored all possible paths and solved it for the shortest path. Atsushi Tero and colleagues grew Physarum in a flat wet
Slime_mold
Technique to analyze the infrared spectrum of matter
Hyun Joo; Menke, William (2024-07-26). "PyIRoGlass: An open-source, Bayesian MCMC algorithm for fitting baselines to FTIR spectra of basaltic-andesitic
Fourier-transform infrared spectroscopy
Fourier-transform_infrared_spectroscopy
Mathematical theorem
elementary algorithm for computing conformal maps was discovered. Given points z 0 , … , z n {\displaystyle z_{0},\ldots ,z_{n}} in the plane, the algorithm computes
Riemann_mapping_theorem
Abstract data type
Thus it's possible to modify the standard Dijkstra's algorithm to find single source shortest path in a graph with 0-cost and 1-cost edges. A deque substitutes
Double-ended_queue
Paradox related to increasing roadway capacity
also been reported in Diacamma indicum ants: Leader ants favour the shortest path even when it slows the colony transport. A quantitative model of the
Braess's_paradox
Algorithm for finding zeros of functions
method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes)
Newton's_method
a Fixed Path Routing solution. This algorithm calculates the shortest path using the number of optical routers as the cost function. A single probe is
Routing and wavelength assignment
Routing_and_wavelength_assignment
Misaligned timing signals from different paths
from the source to the destination registers, path min {\displaystyle {\text{path}}_{\text{min}}} is the path with the shortest delay from source to destination
Clock_skew
Method of solving computing problems
Routing Problem Ants drop different pheromones used to compute the "shortest" path from source to destination(s). Agents are encapsulated computer systems that
Lateral_computing
Technique for finding an extremum of a function
but very robust. The technique derives its name from the fact that the algorithm maintains the function values for four points whose three interval widths
Golden-section_search
Optimization algorithm
In operations research, cuckoo search is an optimization algorithm developed by Xin-She Yang and Suash Deb in 2009. It has been shown to be a special
Cuckoo_search
Subdivision of the plane by lines
have studied efficient algorithms for constructing smaller portions of an arrangement, and for problems such as the shortest path problem on the vertices
Arrangement_of_lines
Area of discrete mathematics
unit distance from each other have the same color, and shortest path problem on finding a path between two vertices in a graph that minimizes the sum
Graph_theory
Mathematical algorithm for eliminating variables from a system of linear inequalities
a mathematical algorithm for eliminating variables from a system of linear inequalities. It can output real solutions. The algorithm is named after Joseph
Fourier–Motzkin_elimination
request forgery SSSE—Supplementary Streaming SIMD Extensions SSSP—Single Source Shortest Path SSTC—Security Services Technical Committee SSTP—Secure Socket
List of computing and IT abbreviations
List_of_computing_and_IT_abbreviations
Decentralized distributed system with lookup service
diameter, since the greedy routing algorithm may not find shortest paths. Aside from routing, there exist many algorithms that exploit the structure of the
Distributed_hash_table
Network packet distribution with multiple cores
the hardware supported ones. Receive Packet Steering (RPS) is the RSS parallel implemented in software. All packets received by the NIC are load balanced
Multi-core network packet steering
Multi-core_network_packet_steering
Single-winner electoral system
Computation of the strongest path strengths is the widest path problem. It is a variation of the all-pairs shortest path problem and it can be solved
Schulze_method
Combinatorial optimization problem
"Integer priority queues with decrease key in constant time and the single source shortest paths problem". Journal of Computer and System Sciences. Special Issue
Assignment_problem
Type of extremely powerful computer
thought of as using the maximum computing power to solve a single large problem in the shortest amount of time. Often a capability system is able to solve
Supercomputer
Techniques to study geometric data
"Manhattan" (or "Taxicab") distances where movement is restricted to paths parallel to the axes can be more meaningful than Euclidean distances in urban
Spatial_analysis
Pandurangan. This algorithm runs in O ( D + L log n ) {\displaystyle O(D+L\log n)} time, where L {\displaystyle L} is the local shortest path diameter of
Distributed minimum spanning tree
Distributed_minimum_spanning_tree
Rating of supercomputer systems
kernel does a parallel BFS search of some random vertices (64 search iterations per run); the third kernel runs a single-source shortest paths (SSSP) computation
Graph500
Specialized search engine for travelling
private transport which may leave at any time), an algorithm must therefore not only find a path to a destination, but seek to optimize it so as to minimize
Journey_planner
encompasses the multiple parallel execution of algorithm components that cooperate in some way to solve a problem on a given parallel hardware platform. In
Parallel_metaheuristic
Mathematical operation in linear algebra
algorithm can be parallelized to further improve the performance. As of January 2024[update], the best peer-reviewed matrix multiplication algorithm is
Matrix_multiplication
Project in integrated circuit design
balancing constraints. TritonRoute's core search algorithms, A* and Lee, find each net's shortest legal paths and then routinely resolve conflicts. In every
OpenROAD_Project
Process of monitoring and controlling the movement of a craft or vehicle
navigational map database of roads and navigable routes, and uses algorithms related to the shortest path problem to identify optimal routes. Pedestrian navigation
Navigation
List of concepts in artificial intelligence
and stochastic differential equations. Dijkstra's algorithm An algorithm for finding the shortest paths between nodes in a weighted graph, which may represent
Glossary of artificial intelligence
Glossary_of_artificial_intelligence
Coordinate system for digital imaging
benefits extend to other applications such as finding the shortest path distance and shortest path routing between points in hexagonal interconnection networks
Hexagonal Efficient Coordinate System
Hexagonal_Efficient_Coordinate_System
Identification of which sense of a word is being used
tree (at least in one dictionary). A similar approach searches for the shortest path between two words: the second word is iteratively searched among the
Word-sense_disambiguation
Optimality criterion in phylogeny
, convergent evolution, parallel evolution, and evolutionary reversals). In other words, under this criterion, the shortest possible tree that explains
Maximum_parsimony
the 1930s. Bellman–Ford algorithm for computing the shortest-length path, proposed by Alfonso Shimbel, who presented the algorithm in 1954, but named after
List of examples of Stigler's law
List_of_examples_of_Stigler's_law
Computer storage networking technology
switches manage the state of the Fabric, providing optimized paths via Fabric Shortest Path First (FSPF) data routing protocol. The traffic between two
Fibre_Channel
Concept of social inter-connectedness
Wikipedia" web services have been created, which automatically provide the shortest paths between two Wikipedia articles. A Facebook platform application named
Six_degrees_of_separation
Smooth manifold with an inner product on each tangent space
acceleration. Equivalently, geodesics are curves that locally take the shortest path between two points. They are the generalization of straight lines in
Riemannian_manifold
Systematic representation of the surface of a sphere or ellipsoid onto a plane
relaxes the last constraint entirely. Instead the parallels can be placed according to any algorithm the designer has decided suits the needs of the map
Map_projection
Shortest paths on a bounded deformed sphere-like quadric surface
an oblate ellipsoid, a slightly flattened sphere. A geodesic is the shortest path between two points on a curved surface, analogous to a straight line
Geodesics_on_an_ellipsoid
Collective behaviour of entities that swarm
Routing problem ants drop different pheromones used to compute the "shortest" path from source to destination(s). Rauch, EM; Millonas, MM; Chialvo, DR (1995)
Swarm_behaviour
Crucial concept of quantum information
conditions under which a set of measurements can be performed together on a single quantum system without disturbing each other. This was crucial for understanding
Incompatibility of quantum measurements
Incompatibility_of_quantum_measurements
Network link aggregation technology
routing information to be exchanged allowing protocols such as Open Shortest Path First (OSPF) and Protocol Independent Multicast-Sparse Mode (PIM-SM)
Multi-link_trunking
Data structure for priority queue operations
Applicability of Advanced Implementations of Priority Queues in Finding Shortest Paths". 2019 International Conference on Information and Digital Technologies
Fibonacci_heap
Serial interface for testing integrated circuits
use the shortest path between two states, perhaps constrained by quirks of the adapter. (For example, one adapter[which?] only handles paths whose lengths
JTAG
Signal to a computer processor emitted by hardware or software
well-behaved ISA devices sharing IRQ lines should just work fine. The parallel port also uses edge-triggered interrupts. Many older devices assume that
Interrupt
Computer networking technology
load-balancing (SPB). Shortest Path Bridging includes the use of the link-state routing protocol IS-IS to allow larger networks with shortest path routes between
Ethernet
Protocol for communicating routing information on the Internet
doi:10.17487/RFC2547. RFC 2547. "BGP Best Path Selection Algorithm". Cisco.com. "Understanding BGP Path Selection". Juniper.com. R. Chandra; P. Traina;
Border_Gateway_Protocol
Query language for property graphs
relationships among data entities, such as reachability queries, shortest or cheapest path queries, or centrality analysis. There are two graph models in
Graph_Query_Language
symmetry axis (parallel to the plane of the two equal points). QR algorithm In numerical linear algebra, the QR algorithm is an eigenvalue algorithm: that is
List of inventions and discoveries by women
List_of_inventions_and_discoveries_by_women
Speed of electromagnetic waves in vacuum
Moscow: Nauka. pp. 149–153. Parhami, B. (1999). Introduction to parallel processing: algorithms and architectures. Plenum Press. p. 5. ISBN 978-0-306-45970-2
Speed_of_light
Study of physics on quintillionth-second timescales
potential, given by H ^ {\displaystyle {\hat {H}}} . In parallel, you also have a quantum path that do not perceive the field at all, this trajectory is
Attosecond_physics
Generalization of graph theory
theorems for hypergraphs. In directed hypergraphs: transitive closure, and shortest path problems. Although hypergraphs are more difficult to draw on paper than
Hypergraph
Graph representing faces of another graph
maximum spanning tree of the dual graph. However, this does not work for shortest path trees, even approximately: there exist planar graphs such that, for
Dual_graph
PARALLEL SINGLE-SOURCE-SHORTEST-PATH-ALGORITHM
PARALLEL SINGLE-SOURCE-SHORTEST-PATH-ALGORITHM
Surname or Lastname
English
English : occupational name for someone who laid wooden tiles (shingles) on roofs, from an agent derivative of Middle English schingle ‘shingle’.
Surname or Lastname
English
English : habitational name from a place in Northamptonshire named Dingley, possibly from Middle English dingle ‘hollow’ + Old English lēah ‘woodland clearing’.
Surname or Lastname
English
English : from the Old English personal name Hringwulf.German : from a short form of a Germanic personal name based on hring ‘ring’.German : metonymic occupational name for a ring maker (see Ringler).German : altered spelling of Ringel, an Old Prussian personal name.
Surname or Lastname
English (Bath)
English (Bath) : unexplained.
Surname or Lastname
English
English : patronymic from Middle English sour ‘sour’, ‘tart’, used as a nickname for a sour-tempered, sharp-tongued person.
Female
English
English short form of French Catherine, CATH means "pure."
Surname or Lastname
English
English : from Middle English sengler, syngler ‘singular’ (Old French se(i)ngler), perhaps a nickname for a solitary person.German : topographic name for a valley dweller, from a diminutive of Middle High German senke ‘valley’ + the suffix -er, denoting an inhabitant.German : habitational name for someone from Singeln near Waldshut.German : variant of Sing 1.
Surname or Lastname
English
English : perhaps a metonymic occupational name for a spindle maker, from Middle English spindle, spindel (Old English spinel).Americanized spelling of German and Jewish Spindel.
Surname or Lastname
English
English : metonymic occupational name for a maker of nails or pins, or nickname for a small, thin man, from Middle English tingle, a kind of very small nail (of North German origin).
Surname or Lastname
English (mainly Devon)
English (mainly Devon) : variant of Pate 1.
Male
Norwegian
Norwegian form of Old Norse Sindri, possibly SINDRE means "sparkling."
Surname or Lastname
English and Scottish
English and Scottish : from the personal name Pat(t), Pate, a short form of Patrick.English and Scottish : nickname for a man with a bald head, from Middle English pate ‘head’, ‘skull’.French (Paté) : from Old French pat(t)é ‘with paws’, ‘pawed’ (from pat(t)e ‘paw’), a nickname, applied presumably to a man with large and clumsy hands and feet.German : nickname for a trustworthy man, from Middle High German pate, Middle Low German pade ‘godfather’, ‘male relative’ (see Paeth), or alternatively from a personal name Bado, probably meaning ‘battle’, ‘fight’.
Surname or Lastname
English
English : from the comparative form of Middle English schort ‘short’, hence a distinguishing nickname for the shorter of two closely associated people with the same personal name (for example, members of the same household).
Female
English
Short form of English Katherine, KATH means "pure."
Surname or Lastname
English
English : topographic name for someone who lived in a place cleared of woods by fire, from Middle English sengle ‘burnt clearing’.German : from a pet form of a short form of a Germanic person name formed with sing ‘sing’ as the first element.
Surname or Lastname
English (West Midlands)
English (West Midlands) : occupational name for a worker in the linen or hemp industry, from an agent derivative of Middle English swingle ‘swingle’ (see Swingle).
Surname or Lastname
English
English : metonymic occupational name for a worker in the linen or hemp industry, from Middle English swingle ‘swingle’, a wooden implement used for beating flax or hemp (Middle Dutch swinghel, from the verb ‘to swing’).Possibly an Americanized spelling of German Zwingel, a topographic name from Middle High German zwingel ‘citadel’.
Surname or Lastname
English
English : variant of Ingle.
Surname or Lastname
English
English : topographic name for someone living in a small wooded dell or hollow, Middle English dingle (of uncertain origin). There is a district of Liverpool called Dingle.South German : nickname or status name for a smallholder, from Middle High German dingelīn ‘smallholding’.Americanized spelling of the old Prussian name Dingel or Dyngele, possibly from Germanic thing ‘legal assembly’.
Surname or Lastname
English
English : ethnic name for someone from Prussia, Middle English Spruce, Sprewse. Compare German Preuss. The adjective spruce ‘neat’, ‘dapper’, which probably derives from an attributive use of the name of the country, is not recorded until the late 16th century, too late for it to be a likely source of the surname. The tree (earlier called spruce fir) has likewise only come to be known by this name in the last couple of centuries.
PARALLEL SINGLE-SOURCE-SHORTEST-PATH-ALGORITHM
PARALLEL SINGLE-SOURCE-SHORTEST-PATH-ALGORITHM
Girl/Female
Bengali, Indian, Sanskrit, Telugu
A Small Blossom; A Low Humming Made to a Put a Child to Sleep
Surname or Lastname
English
English : variant of Goucher.
Boy/Male
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sanskrit, Tamil, Telugu
Spirit
Girl/Female
Hindu
Good picture, Beautiful
Girl/Female
Celtic Russian
Pale.
Boy/Male
Arabic
Prayer on Duty
Male
Egyptian
, a royal personage of the XVIIIth or XIXth dynasty.
Boy/Male
German, Swedish
Edge of the Sword; Brave; Hardy
Girl/Female
English
Dearly loved.
Boy/Male
Anglo, Australian, British, Celtic, English
Poet; Wise Warrior
PARALLEL SINGLE-SOURCE-SHORTEST-PATH-ALGORITHM
PARALLEL SINGLE-SOURCE-SHORTEST-PATH-ALGORITHM
PARALLEL SINGLE-SOURCE-SHORTEST-PATH-ALGORITHM
PARALLEL SINGLE-SOURCE-SHORTEST-PATH-ALGORITHM
PARALLEL SINGLE-SOURCE-SHORTEST-PATH-ALGORITHM
v. t.
To make a path in, or on (something), or for (some one).
n.
A line which, throughout its whole extent, is equidistant from another line; a parallel line, a parallel plane, etc.
n.
A way, course, or track, in which anything moves or has moved; route; passage; an established way; as, the path of a meteor, of a caravan, of a storm, of a pestilence. Also used figuratively, of a course of life or action.
a.
Hence, unmarried; as, a single man or woman.
adv.
Without partners, companions, or associates; single-handed; as, to attack another singly.
n.
The quality or state of being short; want of reach or extension; brevity; deficiency; as, the shortness of a journey; the shortness of the days in winter; the shortness of an essay; the shortness of the memory; a shortness of provisions; shortness of breath.
a.
Continuing a resemblance through many particulars; applicable in all essential parts; like; similar; as, a parallel case; a parallel passage.
n.
A unit; one; as, to score a single.
a.
To make short or shorter in measure, extent, or time; as, to shorten distance; to shorten a road; to shorten days of calamity.
v. i.
To take the irrregular gait called single-foot;- said of a horse. See Single-foot.
v. t.
To produce or adduce as a parallel.
imp. & p. p.
of Single
v. t.
To place or set so as to be parallel; to place so as to be parallel to, or to conform in direction with, something else.
pl.
of Path
a.
Extended in the same direction, and in all parts equally distant; as, parallel lines; parallel planes.
imp. & p. p.
of Parallel
v. i.
To be parallel; to correspond; to be like.
a.
Not doubled, twisted together, or combined with others; as, a single thread; a single strand of a rope.
v. i.
To become short or shorter; as, the day shortens in northern latitudes from June to December; a metallic rod shortens by cold.
v. t.
To cover with shingles; as, to shingle a roof.