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...

algorithm (/ˈdaɪkstrəz/ DYKE-strəz) is an algorithm for finding the shortest paths between nodes in a weighted graph, which may represent, for example...

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...

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...

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...

the shortest path problem is a successive approximation scheme that solves the dynamic programming functional equation for the shortest path problem by...

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...

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...

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...

combinatorial optimization problems: the (non-negative) shortest path problem and the minimum spanning tree problem. If a Steiner tree problem in graphs contains...

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...

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...

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...

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...

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...

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...

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...

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...

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...

after the problem is reformulated as an equivalent assignment problem. A later variation of the auction algorithm that solves shortest path problems was introduced...

flow, shortest path problem, transport problem, transshipment problem, location problem, matching problem, assignment problem, packing problem, routing...

algorithms take advantage of algorithms developed much earlier for shortest path problems on graphs with nonnegative edge lengths. These algorithms take advantage...

Euclidean shortest path problem may be decomposed into two simpler subproblems: constructing the visibility graph, and applying a shortest path algorithm...

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...

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...

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...

-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...

Tree Protocol for wireless sensor networks Canadian traveller problem, a shortest path problem Cambridge Technology Partners, US consulting company 1991-2001...

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...

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)...