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Computational problem of graph theory
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights
Shortest_path_problem
Algorithm for finding shortest paths
algorithm (/ˈdaɪk.strəz/, DYKE-strəz) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example
Dijkstra's_algorithm
Problem of finding the longest simple path for a given graph
computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph. A path is called simple if it does
Longest_path_problem
Plotting by a computer application
Dijkstra's algorithm for finding the shortest path on a weighted graph. Pathfinding is closely related to the shortest path problem, within graph theory, which
Pathfinding
Computational problem of graph theory
k shortest path routing problem is a generalization of the shortest path routing problem in a given network. It asks not only about a shortest path but
K_shortest_path_routing
Problem optimization method
the shortest path problem is a successive approximation scheme that solves the dynamic programming functional equation for the shortest path problem by
Dynamic_programming
Problem of computing shortest paths around geometric obstacles
The Euclidean shortest path problem is a problem in computational geometry: given a set of polyhedral obstacles in a Euclidean space, and two points, find
Euclidean_shortest_path
Type of spanning tree
computer science, a shortest-path tree rooted at a vertex v of a connected, undirected graph G is a spanning tree T of G, such that the path distance from root
Shortest-path_tree
On short connecting nets with added points
combinatorial optimization problems: the (non-negative) shortest path problem and the minimum spanning tree problem. If a Steiner tree problem in graphs contains
Steiner_tree_problem
Routing protocol for IP networks
Open Shortest Path First (OSPF) is a routing protocol for Internet Protocol (IP) networks. It uses a link state routing (LSR) algorithm and falls into
Open_Shortest_Path_First
Path-finding using high-weight graph edges
edge in the path. The widest path problem is also known as the maximum capacity path problem. It is possible to adapt most shortest path algorithms to
Widest_path_problem
Computational problem of graph theory
A central problem in algorithmic graph theory is the shortest path problem. One of the generalizations of the shortest path problem is known as the
Parallel single-source shortest path algorithm
Parallel_single-source_shortest_path_algorithm
Algorithm for finding the shortest paths in graphs
The Bellman–Ford algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph
Bellman–Ford_algorithm
Computational problem of graph theory
A central problem in algorithmic graph theory is the shortest path problem. Hereby, the problem of finding the shortest path between every pair of nodes
Parallel all-pairs shortest path algorithm
Parallel_all-pairs_shortest_path_algorithm
Sequence of edges which join a sequence of vertices on a given graph
vertex-disjoint paths of length at most k. Glossary of graph theory Path graph Polygonal chain Shortest path problem Longest path problem Dijkstra's algorithm
Path_(graph_theory)
Seidel in 1992 for the all-pairs-shortest-path problem for undirected, unweighted, connected graphs. It solves the problem in O ( V ω log V ) {\displaystyle
Seidel's_algorithm
Pathfinding problem
multi-agent generalization of the pathfinding problem, and it is closely related to the shortest path problem in the context of graph theory. Several algorithms
Multi-agent_pathfinding
Area of discrete mathematics
Hamiltonian path problem Minimum spanning tree Route inspection problem (also called the "Chinese postman problem") Seven bridges of Königsberg Shortest path problem
Graph_theory
Algorithm in graph theory
Roy–Floyd algorithm, or the WFI algorithm) is an algorithm for finding shortest paths in a directed weighted graph with positive or negative edge weights
Floyd–Warshall_algorithm
Graph of intervisible locations in computational geometry
Euclidean shortest path problem may be decomposed into two simpler subproblems: constructing the visibility graph, and applying a shortest path algorithm
Visibility_graph
Dutch computer scientist (1930–2002)
where he worked from 1952 until 1962. He formulated and solved the shortest path problem in 1956, and in 1960 developed the first compiler for the programming
Edsger_W._Dijkstra
NP-hard problem in combinatorial optimization
salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible
Travelling_salesman_problem
Academic field
flow, shortest path problem, transport problem, transshipment problem, location problem, matching problem, assignment problem, packing problem, routing
Network_science
Non-linear partial differential equation encountered in problems of wave propagation
algorithms take advantage of algorithms developed much earlier for shortest path problems on graphs with nonnegative edge lengths. These algorithms take advantage
Eikonal_equation
after the problem is reformulated as an equivalent assignment problem. A later variation of the auction algorithm that solves shortest path problems was introduced
Auction_algorithm
Computational problem
Motion planning, also path planning (also known as the navigation problem or the piano mover's problem) is a computational problem to find a sequence of
Motion_planning
Straight path on a curved surface or a Riemannian manifold
-ˈdiːsɪk, -zɪk/) is a curve representing in some sense the locally shortest path (arc) between two points in a surface, or more generally in a Riemannian
Geodesic
Mathematical optimization problem
problems are special cases of the minimum cost flow problem (we provide brief sketches of each applicable reduction, in turn): Shortest path problem (single-source)
Minimum-cost_flow_problem
Computational graph problem
science and graph theory, the Canadian traveller problem (CTP) is a generalization of the shortest path problem to graphs that are partially observable. In
Canadian_traveller_problem
Method to find shortest paths
technique is also used in a version of the successive shortest paths algorithm for the minimum cost flow problem due to Edmonds and Karp, as well as in Suurballe's
Johnson's_algorithm
Method for finding loopless paths
K-shortest loopless paths for a graph with non-negative edge cost. The algorithm was published by Jin Y. Yen in 1971 and employs any shortest path algorithm
Yen's_algorithm
Method of scheduling activities
This determines the shortest time possible to complete the project. "Total float" (unused time) can occur within the critical path. For example, if a project
Critical_path_method
Problem in computer science
subarray problem in O(n3−ε) time, for any ε>0, would imply a similarly fast algorithm for the all-pairs shortest paths problem. Maximum subarray problems arise
Maximum_subarray_problem
Mathematical operation on matrices
in the min convention. This operation is closely related to the shortest path problem. If W {\displaystyle W} is an n × n {\displaystyle n\times n} matrix
Min-plus matrix multiplication
Min-plus_matrix_multiplication
Shortest path with bounded turning radius
In geometry, the term Dubins path typically refers to the shortest curve that connects two points in the two-dimensional Euclidean plane (i.e. x-y plane)
Dubins_path
Feature of GPS navigation devices
based on the shortest path problem within graph theory, which examines how to identify the path that best meets some criteria (shortest, cheapest, fastest
Turn-by-turn_navigation
Computational problem in graph theory
minimum-cost flow problem of which the maximum flow problem is a particular case. For the single-source shortest path (SSSP) problem with negative weights
Maximum_flow_problem
Optimization problem
two points on the original road network. This is easy to do as shortest path problems are relatively easy to solve. This transforms the sparse original
Vehicle_routing_problem
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
Length of shortest path between two nodes of a graph
of edges in a shortest path (also called a graph geodesic) connecting them. This is also known as the geodesic distance or shortest-path distance. Notice
Distance_(graph_theory)
Part of the automobile controls
based on the shortest path problem, within graph theory, which examines how to identify the path that best meets some criteria (shortest, cheapest, fastest
Automotive_navigation_system
Mathematical model of computation
problem of determining the language accepted by a given acceptor is an instance of the algebraic path problem—itself a generalization of the shortest
Finite-state_machine
Algorithm used for pathfinding and graph traversal
weighted graph, a source node and a goal node, the algorithm finds the shortest path (with respect to the given weights) from source to goal. One major practical
A*_search_algorithm
Method for finding minimum spanning trees
minimum spanning tree problem in a more efficient manner. Dijkstra's algorithm, a very similar algorithm for the shortest path problem Greedoids offer a general
Prim's_algorithm
Combinatorial optimization problem
queues with decrease key in constant time and the single source shortest paths problem". Journal of Computer and System Sciences. Special Issue on STOC
Assignment_problem
Directed graph where edges have a capacity
graph (disambiguation) Max-flow min-cut theorem Oriented matroid Shortest path problem Nowhere-zero flow Active flow network A.V. Goldberg, É. Tardos and
Flow_network
David (2009). "TRANSIT: Ultrafast Shortest-Path Queries with Linear-Time Preprocessing". The Shortest Path Problem: Ninth DIMACS Implementation Challenge
Highway_dimension
Species of slime mold, model organism
the shortest path problem. When grown in a maze with oatmeal at two spots, P. polycephalum retracts from everywhere in the maze, except the shortest route
Physarum_polycephalum
Study of graphs as a representation of relations between discrete objects
flow, shortest path problem, transport problem, transshipment problem, location problem, matching problem, assignment problem, packing problem, routing
Network_theory
Process of monitoring and controlling the movement of a craft or vehicle
roads and navigable routes, and uses algorithms related to the shortest path problem to identify optimal routes. Pedestrian navigation is involved in
Navigation
American computer scientist
algorithm for the all-pairs shortest path problem. date from Author's thesis biographyJohnson, Donald B., Algorithms for shortest paths Death date from author
Donald_B._Johnson
Mathematical theory on behavior of connected clusters in a random graph
Network whose degree distribution follows a power law Shortest path problem – Computational problem of graph theory Swiss cheese model – Model used in risk
Percolation_theory
Fastest curve descent without friction
of a uniform gravitational field to a given end point in the shortest time. The problem was posed by Johann Bernoulli in 1696 and famously solved in one
Brachistochrone_curve
graph Path (graph theory) Seven Bridges of Königsberg Eulerian path Three-cottage problem Shortest path problem Dijkstra's algorithm Open Shortest Path First
List_of_graph_theory_topics
String in combinatorial math
12312 = 312. Any Hamiltonian path through the created graph is a superpermutation, and the problem of finding the path with the smallest weight becomes
Superpermutation
spanning switch say, for a telephone exchange Shortest path problem Bellman–Ford algorithm: computes shortest paths in a weighted graph (where some of the edge
List_of_algorithms
Subexponential bound in computational complexity
the size of the output for some problems; for instance, for the shortest path problem with linearly varying edge weights, the number of distinct solutions
Quasi-polynomial_growth
Center for Discrete Mathematics and Theoretical Computer Science at Rutgers University
Semidefinite and related optimization problems 2001−2001: The traveling salesman problem 2005−2005: The shortest-path problem 2011−2012: Graph partitioning and
DIMACS
Graph path which is an induced subgraph
induced path is sometimes called a snake, and the problem of finding long induced paths in hypercube graphs is known as the snake-in-the-box problem. Similarly
Induced_path
Algorithm that begins on possibly incomplete inputs
worst case for this problem is simply that all of the unreliable edges fail and the problem reduces to the usual shortest path problem. An alternative analysis
Online_algorithm
Longest distance between two vertices
the shortest-path distance in the graph. Diameter may be considered either for weighted or for unweighted graphs. Researchers have studied the problem of
Diameter_(graph_theory)
Any algorithm which solves the search problem
include: Problems in combinatorial optimization, such as: The vehicle routing problem, a form of shortest path problem The knapsack problem: Given a set
Search_algorithm
Constrained Shortest Path First (CSPF) is an extension of shortest path algorithms. The path computed using CSPF is a shortest path fulfilling a set of
Constrained Shortest Path First
Constrained_Shortest_Path_First
Simplified example problem used for research or exposition
In scientific disciplines, a toy problem or a puzzlelike problem is a problem that is not of immediate scientific interest, yet is used as an expository
Toy_problem
Recreational geodesics problem
The spider and the fly problem is a recreational mathematics problem with an unintuitive solution, asking for a shortest path or geodesic between two points
The spider and the fly problem
The_spider_and_the_fly_problem
Automated method for solving mazes
with no prior knowledge of the maze, whereas the dead-end filling and shortest path algorithms are designed to be used by a person or computer program that
Maze-solving_algorithm
Subdivision of the plane by lines
constructing smaller portions of an arrangement, and for problems such as the shortest path problem on the vertices and edges of an arrangement. As an informal
Arrangement_of_lines
Type of heuristic in path-finding problems
same conditions that Dijkstra's algorithm requires in solving the shortest path problem (no negative cost edges). In fact, if the search graph is given
Consistent_heuristic
Least-weight tree connecting graph vertices
design problem is the problem of computing a set, subject to a budget constraint, which contains a spanning tree, such that the sum of shortest paths between
Minimum_spanning_tree
Route planning library and network service
addition to solving the shortest path problem for road networks, OSRM also includes a map matching service and a travelling salesman problem solver for generating
Open_Source_Routing_Machine
Sea route north of North America
route planning under ice uncertainty: A risk-averse stochastic shortest path problem". Transportation Research Part E: Logistics and Transportation Review
Northwest_Passage
Node ordering for directed acyclic graphs
computes the shortest path from some source vertex s to all other vertices: Let d be an array of the same length as V; this will hold the shortest-path distances
Topological_sorting
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 via
Schulze_method
Measure of a graph's centrality, based on shortest paths
centrality in a graph based on shortest paths. Betweenness centrality measures how frequently a node appears on the shortest path between other nodes in the
Betweenness_centrality
Finding shortest walks through all graph edges
optimization, Guan's route problem, the Chinese postman problem, postman tour or route inspection problem is to find a shortest closed path or circuit that visits
Chinese_postman_problem
Method of making choices that maximises utility
each edge), then we can use a standard algorithm for solving the shortest path problem. If we do not know the transmission times, then we have to ask each
Vickrey–Clarke–Groves mechanism
Vickrey–Clarke–Groves_mechanism
Abstract data type
least-weight sub-sequence problem : shortest path problem for a weighted directed graph, paragraph breaking, etc. These problems are said to be convex or
Double-ended_queue
Packet routing strategy
multiple paths in general. Link aggregation Shortest Path Bridging – establishes multiple forward and reverse paths on Ethernet networks. Source routing TRILL –
Equal-cost_multi-path_routing
Class of neural models based on model of a cat's visual cortex
discussed by Kinser, et al. They have also been applied to an all pairs shortest path problem. Zhan, K.; Shi, J.; Wang, H.; Xie, Y.; Li, Q. (2017). "Computational
Pulse-coupled_networks
Property of a computational problem
how the value of the problem starting from t is related to the value of the problem starting from s. Consider finding a shortest path for traveling between
Optimal_substructure
Discipline related to computer vision and cartography
the number of obstacles. Topologically, the problem of path planning is related to the shortest path problem of finding a route between two nodes in a graph
Robotic_mapping
Spanning tree minimizing sum of distances
the tree. It is also called the optimum distance spanning tree, shortest total path length spanning tree, minimum total distance spanning tree, or minimum
Minimum routing cost spanning tree
Minimum_routing_cost_spanning_tree
Vertices connected in pairs by edges
depending on the problem at hand. Such graphs arise in many contexts, for example in shortest path problems such as the traveling salesman problem. One definition
Graph_(discrete_mathematics)
In applied mathematics, a technique to find the shortest path
of contraction hierarchies is a speed-up technique for finding the shortest path in a graph. The most intuitive applications are car-navigation systems:
Contraction_hierarchies
online shortest path problem. In the online shortest path problem, each expert is telling you a different way to drive to work. You pick one path using
Randomized weighted majority algorithm
Randomized_weighted_majority_algorithm
Path in a graph that visits each vertex exactly once
Hamiltonian path. The computational problems of determining whether such paths and cycles exist in graphs are NP-complete; see Hamiltonian path problem for details
Hamiltonian_path
Line tangent to a curve at two locations
the visibility graph approach to solving the Euclidean shortest path problem: the shortest path among a collection of polygonal obstacles may only enter
Bitangent
worst case for this problem is simply that all of the unreliable edges fail and the problem reduces to the usual shortest path problem. An alternative analysis
Online_optimization
Set of all possible values of a system
fields of artificial intelligence and game theory. For instance, the toy problem Vacuum World has a discrete finite state space in which there are a limited
State space (computer science)
State_space_(computer_science)
Topics referred to by the same term
four-letter initialism that may refer to: Single-pair shortest path, in approaches to the shortest path problem Society for Personality and Social Psychology
Spsp
Framework in mathematics
similarities between warping paths by transforming the DTW-equivalent shortest path problem to the maximum flow problem in the dual graph, which can be
Graphical_time_warping
Mathematical operation in linear algebra
although the tropical semiring is also a common choice for graph shortest path problems. Even in the case of matrices over fields, the product is not commutative
Matrix_multiplication
Idempotent semiring endowed with a closure operator
semirings and Kleene algebras appear in algebraic path problems, a generalization of the shortest path problem. Action algebra Algebraic structure Kleene star
Kleene_algebra
Topics referred to by the same term
length of any curve between two points in the plane Shortest path problem, the minimum length of a path between two points in a graph The minimum distance
Minimum_distance
Edge-joined polygons which fold into a polyhedron
the shortest path in each category. The spider and the fly problem is a recreational mathematics puzzle which involves finding the shortest path between
Net_(polyhedron)
Measure of similarity between two graphs
computation of the optimal edit path is cast as a pathfinding search or shortest path problem, often implemented as an A* search algorithm. In addition to exact
Graph_edit_distance
Class of routing protocols
(RIPv1). RIPv1 was formally standardised in 1988. It establishes the shortest path across a network purely on the basis of the hops, that is numbers of
Distance-vector routing protocol
Distance-vector_routing_protocol
Study of algorithms in strategic environments
standard tools of mechanism design to algorithmic problems and in particular to the shortest path problem. This paper coined the term algorithmic mechanism
Algorithmic_game_theory
Optimisation problem in triangle geometry
and even weaker settings. Set TSP problem, a more general task of visiting each of a family of sets by the shortest tour Dörrie, Heinrich (1965), "Fagnano's
Fagnano's_problem
German computer scientist (born 1949)
B.; Tarjan, Robert E. (April 1990), "Faster algorithms for the shortest path problem" (PDF), Journal of the Association for Computing Machinery, 37 (2):
Kurt_Mehlhorn
SHORTEST PATH-PROBLEM
SHORTEST PATH-PROBLEM
Female
English
Short form of English Katherine, KATH means "pure."
Surname or Lastname
English (Bristol and Bath)
English (Bristol and Bath) : unexplained.
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’.
Female
English
English short form of French Catherine, CATH means "pure."
Female
Hebrew
(בַּתש×וּעַ) Variant spelling of Hebrew Bath-Shuwa, BATH-SHUA means "daughter of wealth."Â
Boy/Male
Arabic, Modern
Road; The Way
Surname or Lastname
English (Bath)
English (Bath) : unexplained.
Girl/Female
Australian, British, English
Way
Surname or Lastname
English
English : habitational name from the city of Bath in western England, which is the site of sumptuous, but in the Middle Ages ruined, Roman baths. The place is named with the dative plural of Old English bæð ‘bath’. In some cases the surname may have originated as a metonymic occupational name for an attendant at a public bath house.Scottish : reduced and altered form of McBeth.German : variant of Bathe.Indian (Panjab) : Sikh name based on the name of a Jat clan.
Male
Irish
Short form of Irish Gaelic Parthalán, possibly PARTH means "son of Talmai."
Surname or Lastname
English and Scottish (now mainly found in Ireland)
English and Scottish (now mainly found in Ireland) : variant spelling of Short.
Female
Hebrew
(בַּתש×וּעַ) Hebrew name BATH-SHUWA means "daughter of wealth." In the bible, this is another name Bath-Sheba is known by.
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
Hebrew
(בַּת-ש×ֶבַע) Hebrew name BATH-SHEBA means "daughter of the oath." In the bible, this is the name of a wife of Uriah then later King David, and mother of Solomon. Also spelled Bat-Sheva, Bathsheba, and Bathsheva.
Male
English
English unisex short form of English Patrick and Latin Patricia, PAT means "patrician; of noble birth."
Surname or Lastname
English (mainly Devon)
English (mainly Devon) : variant of Pate 1.
Boy/Male
Muslim/Islamic
Shorter Smaller, Junior
Female
Hebrew
(×Ö¸×¡Ö°× Ö·×ª) Hebrew name of Egyptian origin, ACÄ”NATH means "belonging to the goddess Neith." In the bible, this is the name of Joseph's Egyptian wife.
Boy/Male
Tamil
Sharpest sword of world
Surname or Lastname
English
English : variant of Shore 1 and 2.
SHORTEST PATH-PROBLEM
SHORTEST PATH-PROBLEM
Boy/Male
Indian
Chosen
Surname or Lastname
English
English : variant spelling of Ruston.
Boy/Male
Arabic
Fluency; Eloquence
Male
English
English slang term for someone who breaks things transferred to forename use, originally derived from the verb bust, BUSTER means "to break, smash," hence "breaker, destroyer, smasher."
Boy/Male
Indian
Wealth; Liquid
Girl/Female
Arabic, Muslim
Moon-like Face
Surname or Lastname
English
English : occupational name for a physician’s servant, from Leach 1 + Middle English man ‘manservant’.
Boy/Male
Biblical
Testimony of the assembly.
Male
Japanese
(1-哲雄, 2-哲夫) Japanese name TETSUO means 1) "wise hero" or "wise man."
Boy/Male
Muslim
The giver of life
SHORTEST PATH-PROBLEM
SHORTEST PATH-PROBLEM
SHORTEST PATH-PROBLEM
SHORTEST PATH-PROBLEM
SHORTEST PATH-PROBLEM
n.
A short cut across; a path shorter than by the high road.
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. t.
To mend by sewing on a piece or pieces of cloth, leather, or the like; as, to patch a coat.
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.
n.
Hence: The which contains the strength of life; the vital or essential part; concentrated force; vigor; strength; importance; as, the speech lacked pith.
n.
A small piece of anything used to repair a breach; as, a patch on a kettle, a roof, etc.
v. t.
To mend with pieces; to repair with pieces festened on; to repair clumsily; as, to patch the roof of a house.
n.
The act of exposing the body, or part of the body, for purposes of cleanliness, comfort, health, etc., to water, vapor, hot air, or the like; as, a cold or a hot bath; a medicated bath; a steam bath; a hip bath.
adv.
In a pat manner.
pr.p. & vb. n.
of Path
n.
A small mass, as of butter, shaped by pats.
pl.
of Path
v. t.
To adorn, as the face, with a patch or patches.
n.
Fig.: Anything regarded as a patch; a small piece of ground; a tract; a plot; as, scattered patches of trees or growing corn.
imp. & p. p.
of Path
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.
v. t.
To make a path in, or on (something), or for (some one).
v. i.
To become short or shorter; as, the day shortens in northern latitudes from June to December; a metallic rod shortens by cold.