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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
Computational problem of graph theory
2021-12-11. Hoceini, S.; A. Mellouk; Y. Amirat (2005). "K-Shortest Paths Q-Routing: A New QoS Routing Algorithm in Telecommunication Networks". Networking
Shortest_path_problem
Algorithm for finding shortest paths
used to find the shortest route between one city and all other cities. A common application of shortest path algorithms is network routing protocols, most
Dijkstra's_algorithm
Topics referred to by the same term
Solubility product constant (Ksp); see solubility equilibrium k shortest path routing Kerbal Space Program, a spaceflight simulator game KSP: Kapamilya
KSP
In applied mathematics, transit node routing can be used to speed up shortest-path routing by pre-computing connections between common access nodes to
Transit_node_routing
IEEE standard for Shortest Path Bridging
and all routing is on symmetric shortest paths. The control plane is based on the Intermediate System to Intermediate System (IS-IS) routing protocol
IEEE_802.1aq
Plotting by a computer application
Pathfinding or pathing is the search, by a computer application, for the shortest route between two points. It is a more practical variant on solving mazes
Pathfinding
Algorithm in graph theory
{shortestPath} (i,j,k-1),} s h o r t e s t P a t h ( i , k , k − 1 ) + s h o r t e s t P a t h ( k , j , k − 1 ) ) {\displaystyle \mathrm {shortestPath}
Floyd–Warshall_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
Network routing scheme based on labels identifying paths
IPv6 environment, using appropriate routing protocols. The major goal of MPLS development was the increase of routing speed. This goal is no longer relevant
Multiprotocol_Label_Switching
Optimization problem
vehicle routing problem (VRP) is a combinatorial optimization and integer programming problem which asks "What is the optimal set of routes for a fleet
Vehicle_routing_problem
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
NP-hard problem in combinatorial optimization
yield the shortest route. It was first considered mathematically in the 1930s by Merrill M. Flood, who was looking to solve a school bus routing problem
Travelling_salesman_problem
Internet protocol
Interior Gateway Routing Protocol (EIGRP) is an advanced distance-vector routing protocol that is used on a computer network for automating routing decisions
Enhanced Interior Gateway Routing Protocol
Enhanced_Interior_Gateway_Routing_Protocol
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
Routing technique of using multiple alternative paths through a network
Multipath routing is a routing technique that simultaneously uses multiple alternative paths through a network. This can yield a variety of benefits such
Multipath_routing
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
Category of routing problem minimizing total distance and time
Arc routing problems (ARP) are a category of general routing problems (GRP), which also includes node routing problems (NRP). The objective in ARPs and
Arc_routing
Network routing process
networking, dynamic routing (DR), also called adaptive routing (AR), is a process where a router can forward data via a different route for a given destination
Dynamic_routing
End-to-end connection resiliance
because of the travel time of the FIS notification. Shortest path problem K shortest path routing Shared risk resource group Ireneusz Szcześniak; Ireneusz
Path_protection
Stage of electronic circuit design
In electronic design, wire routing, commonly called simply routing, is a step in the design of printed circuit boards (PCBs) and integrated circuits (ICs)
Routing (electronic design automation)
Routing_(electronic_design_automation)
Protocol for communicating routing information on the Internet
and it makes routing decisions based on paths, network policies, or rule-sets configured by a network administrator. BGP used for routing within an autonomous
Border_Gateway_Protocol
the highway dimension exist, although the one based on approximate shortest paths given below is the most general one. Each definition of the highway
Highway_dimension
Academic field
shortest path problem, transport problem, transshipment problem, location problem, matching problem, assignment problem, packing problem, routing problem
Network_science
Algorithm to search the nodes of a graph
F. Moore, who used it to find the shortest path out of a maze, and later developed by C. Y. Lee into a wire routing algorithm (published in 1961). The
Breadth-first_search
Optimization algorithm
optimization tasks involving some sort of graph, e.g., vehicle routing and internet routing. As an example, ant colony optimization is a class of optimization
Ant colony optimization algorithms
Ant_colony_optimization_algorithms
OSI model layer for packet routing
LLARP, Low Latency Anonymous Routing Protocol OSPF, Open Shortest Path First PIM, Protocol Independent Multicast RIP, Routing Information Protocol "X.225 :
Network_layer
Problem in computer networking
instantaneous end-to-end paths. In these challenging environments, popular ad hoc routing protocols such as AODV and DSR fail to establish routes. This is due to
Routing in delay-tolerant networking
Routing_in_delay-tolerant_networking
Method for finding loopless paths
single-source 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
Aggregation of Internet Protocol networks
a larger network. The new routing prefix for the aggregate network represents the constituent networks in a single routing table entry. The process of
Supernetwork
Type of network topology
E-Cube routing is a static routing method that employs XY-routing algorithm. This is commonly referred to as deterministic, dimension-ordered routing model
Hypercube internetwork topology
Hypercube_internetwork_topology
Property of a computational problem
Longest palindromic substring All-Pairs Shortest Path Any problem that can be solved by dynamic programming. Longest path problem Addition-chain exponentiation
Optimal_substructure
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
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
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
Subfield of mathematical optimization
optimization problems that are covered by this framework are shortest paths and shortest-path trees, flows and circulations, spanning trees, matching, and
Combinatorial_optimization
On short connecting nets with added points
other famous combinatorial optimization problems: the (non-negative) shortest path problem and the minimum spanning tree problem. If a Steiner tree problem
Steiner_tree_problem
IT preservation method
see more Link protection Path Protection P-cycle protection Optical Mesh Networks Shortest Path Problem K shortest path routing Dijkstra's algorithm Saradhi
Segment_protection
Pathfinding problem
generalization of the pathfinding problem, and it is closely related to the shortest path problem in the context of graph theory. Several algorithms have been
Multi-agent_pathfinding
Overview of and topical guide to algorithms
Compare-and-swap Routing algorithm Dijkstra's algorithm Bellman–Ford algorithm Distance-vector routing protocol Link-state routing protocol Congestion
Outline_of_algorithms
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
Chinese_postman_problem
Graph where most nodes are reachable in a small number of steps
as average shortest path length). Purely random graphs, built according to the Erdős–Rényi (ER) model, exhibit a small average shortest path length (varying
Small-world_network
Simple routing algorithm sending incoming packets to all other links than the sender
and since flooding naturally utilizes every path through the network, it will also use the shortest path. Flooding can be costly in terms of wasted bandwidth
Flooding (computer networking)
Flooding_(computer_networking)
The shortest, NM 446, is a quarter-mile (402 m) long and serves to connect Valmora to NM 97. NM 597, the second shortest highway, links U.S. Route 160
List of state roads in New Mexico
List_of_state_roads_in_New_Mexico
Optical network using a mesh topology
including Dijkstra's algorithm; k-shortest path, such as Yen's algorithm; edge and node-diverse or disjoint routing, including Suurballe's algorithm;
Optical_mesh_network
cost of S is the sum, over all pairs (u,v) in E, of the length of the shortest path from u to v, which uses only edges in S. The objective is to find a
Optimal_network_design
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
Protocol - RIPE - RISC OS - Root nameserver - Route analytics - Router (computing) - Routing - Rooster Teeth - Routing information protocol - RSA - RTP - RTSP
Index of Internet-related articles
Index_of_Internet-related_articles
Decentralized distributed system with lookup service
be greater than diameter, since the greedy routing algorithm may not find shortest paths. Aside from routing, there exist many algorithms that exploit
Distributed_hash_table
Radio nodes organized in a mesh topology
Shortest Path First Routing) Routing Protocol for Low-Power and Lossy Networks (IETF ROLL RPL protocol, RFC 6550) PWRP (Predictive Wireless Routing Protocol)
Wireless_mesh_network
extensions (RSVP-TE) signaling protocol. Open Shortest Path First with Traffic Engineering extensions (OSPF-TE) routing protocol. Link Management Protocol (LMP)
Generalized Multi-Protocol Label Switching
Generalized_Multi-Protocol_Label_Switching
Method of drug administration
keratinocytes that constitute the stratum corneum. Although this is the path of shortest distance, the drugs encounter significant resistance to permeation
Transdermal
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
MORE, which stands for MAC independent Opportunistic Routing, is an opportunistic routing protocol designed for wireless mesh networks. The protocol removes
MORE_protocol
Optimized search algorithm
Bidirectional search is a graph search algorithm that finds a shortest path from an initial vertex to a goal vertex in a directed graph. It runs two simultaneous
Bidirectional_search
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
Algorithm
shortest path is evaluated. If the cost for the goal equals infinity, there is no finite-cost path from start to goal. Otherwise, the shortest path can
Lifelong_Planning_A*
Whether one vertex can be reached from another in a graph
{n})} size. This algorithm can also supply approximate shortest path distances, as well as route information. The overall approach is to associate with
Reachability
Directed graph where edges have a capacity
Flow graph (disambiguation) Max-flow min-cut theorem Oriented matroid Shortest path problem Nowhere-zero flow Active flow network Cormen, Thomas; Leiserson
Flow_network
Tree data structure
A set of routing objects NRO. Pointer to Node's parent object Op. Leaf nodes A set of objects NO. Pointer to Node's parent object Op. Routing Object (Feature
M-tree
reducing the overall cost of routing a packet from one node to another by avoiding the need to flood packets. Because the routing metric is supplied by an
Pastry_(DHT)
Heuristic pathfinding algorithm
Iterative deepening A* (IDA*) is a graph traversal and path search algorithm that can find the shortest path between a designated start node and any member of
Iterative_deepening_A*
Logical identifier addressing a specific group of devices on a network
local subnetwork only. For example, the Routing Information Protocol (RIPv2) uses 224.0.0.9, Open Shortest Path First (OSPF) uses 224.0.0.5 and 224.0.0
Multicast_address
Collective behavior of decentralized, self-organized systems
variants existing. Basically, this uses a probabilistic routing table rewarding/reinforcing the route successfully traversed by each "ant" (a small control
Swarm_intelligence
to the Cayley graph of G: the word metric measures the length of the shortest path in the Cayley graph between two elements of G. A generating set for
Word_metric
Optical mesh network routing concept
primary path using a known shortest path algorithm such as Dijkstra's. On computing the primary path, and removing all nodes and links in that path, run
Shared_risk_resource_group
English mathematician (1934–2019)
the Cambridge Philosophical Society in a 1959 article entitled "The Shortest Path Through Many Points", the theorem provides an asymptotic formula for
Jillian_Beardwood
Technology discipline within engineering
and Segment Routing (SR) enhance traffic management and routing efficiency. For intra-domain routing, protocols like Open Shortest Path First (OSPF)
Computer_network_engineering
Undirected graph derived from a hypercube graph
opposite if the shortest path between them has length n.) It can, equivalently, be formed from a hypercube graph (also) of dimension k, which has twice
Folded_cube_graph
Valley in Vestland, Norway
Stemberdøla; in the lower part it is called Aurlandselvi. The route from Aurland to Hol has been the shortest connection between western and eastern Norway since
Aurlandsdalen
Structural analysis of a network
Total number of shortest paths through i Total number of shortest paths {\displaystyle C(i)={\tfrac {{\text{Total number of shortest paths through }}i}{\text{Total
Biased_random_walk_on_a_graph
Technique for drawing non-planar graphs
crossings it forms, one can use a shortest path algorithm in the dual graph of the current embedding, in order to find the shortest sequence of faces of the embedding
Planarization
Study of mathematical algorithms for optimization problems
Simulation-based optimization Test functions for optimization Vehicle routing problem "The Nature of Mathematical Programming Archived 2014-03-05 at
Mathematical_optimization
Specialized search engine for travelling
and ride, etc.). Typical optimizations for car routing are shortest route, fastest route, cheapest route and with constraints for specific waypoints. The
Journey_planner
Any planar graph can be subdivided by removing a few vertices
salesman problem for the shortest path metric on weighted planar graphs; their algorithm uses dynamic programming to find the shortest tour that, at each level
Planar_separator_theorem
Arc crossing all meridians of longitude at the same angle
A rhumb line can be contrasted with a great circle, which is the path of shortest distance between two points on the surface of a sphere. On a great
Rhumb_line
Chinese scientist and revolutionary (born 1961)
for Finding K Shortest Paths Subject to Multiple Constraints". Research Gate. August 2001. Retrieved July 10, 2016. Davis, R. Drew; Kumar, K.; Liu, Gang;
Liu_Gang
Computational problem in graph theory
solutions to the maximum flow problem were discovered, notably the shortest augmenting path algorithm of Edmonds and Karp and independently Dinitz; the blocking
Maximum_flow_problem
Least-weight tree connecting graph vertices
equivalent graphs and minimum spanning arborescences, preserves all max-min shortest paths and De Morgan's law consistency. The dynamic MST problem concerns the
Minimum_spanning_tree
Method for problem solving in optimization
problem a solution can be a route visiting all cities and the goal is to find the shortest route. But a solution can also be a path, and being a cycle is part
Local_search_(optimization)
Tree which includes all vertices of a graph
routing loops, many routing protocols designed for such networks—including the Spanning Tree Protocol, Open Shortest Path First, Link-state routing protocol
Spanning_tree
Section of Interstate Highway in Utah, United States
The 117.38-mile-long (188.90 km) segment in the US state of Utah is the shortest of any of the three states the western I-84 passes through and contains
Interstate_84_in_Utah
Mathematical optimization problem restricted to integers
f} and some constant k {\displaystyle k} , integer programming can be solved in time f ( a , d ) n k {\displaystyle f(a,d)n^{k}} . In particular, the
Integer_programming
Hindu Temple in Uttarakhand, India
road to Chopta is just below this ridge and hence provides the shortest bridle approach path for trekking to the temple from Chopta, over a short distance
Tungnath
President of the United States from 1845 to 1849
sentiment false. At age 53, Polk had the shortest lifespan of any president not assassinated, and the shortest post-presidency among the presidents who
James_K._Polk
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
Search algorithm
contacts MVRRT*, Minimum violation RRT*, an algorithm that finds the shortest route that minimizes the level of unsafety (the "cost" of the environment
Rapidly_exploring_random_tree
Set of related problems in graph theory
multi-robot motion planning (in which the pebbles are robots) and network routing (in which the pebbles are packets of data). The best-known example of a
Pebble_motion_problems
Hypothetical topological feature of spacetime
spacetime should not have any "edges": it should be possible to continue this path arbitrarily far into the particle's future or past for any possible trajectory
Wormhole
German computer scientist
is particularly known for his research on suffix sorting and finding shortest paths in road networks. Sanders earned his Ph.D. from Karlsruhe in 1996, and
Peter Sanders (computer scientist)
Peter_Sanders_(computer_scientist)
Techniques to study geometric data
cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city
Spatial_analysis
State highway in Hawaii County, Hawaii
the road. The highway experiences heavy use as it provides the shortest driving route from Hilo to Kailua-Kona and access to the slopes of Mauna Loa and
Hawaii_Route_200
Search algorithm finding the position of a target value within a sorted array
on the shortest path from the queried vertex to the target. The standard binary search algorithm is simply the case where the graph is a path. Similarly
Binary_search
Optimization by removing non-optimal solutions to subproblems
selection in machine learning Structured prediction in computer vision Arc routing problem, including the Chinese Postman problem Talent Scheduling, scenes-shooting
Branch_and_bound
Mathematical optimization problem
(we provide brief sketches of each applicable reduction, in turn): Shortest path problem (single-source). Require that a feasible solution to the minimum
Minimum-cost_flow_problem
National Trail following the River Thames in England
The Thames Path is a National Trail following the River Thames from one of its sources near Kemble in Gloucestershire to the Woolwich foot tunnel, south
Thames_Path
interval thickness, and vertex separation number Rank coloring k-Chinese postman Shortest total path length spanning tree Slope number two testing Recognizing
List_of_NP-complete_problems
Theorem that curves of bounded curvature contain a unit disk
motion planning. In particular it has been used for finding Dubins paths, shortest routes for vehicles that can move only in a forwards direction and that
Pestov–Ionin_theorem
Street in San Francisco
friar Junipero Serra. Within the city, it forms part of the route of State Route 1, the shortest connection between Interstate 280 and the Golden Gate Bridge
Junipero_Serra_Boulevard
Simulation of wireless network users
{\displaystyle M_{n}} to the next M n + 1 {\displaystyle M_{n+1}} along the shortest path in A {\displaystyle A} between them. In the restricted setting, the
Restricted random waypoint model
Restricted_random_waypoint_model
travel, tourism, insurance
K SHORTEST-PATH-ROUTING
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