Dijkstra's algorithm

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Running time

Big-O notation Adjacency list Matrix Sparse graphs Self-balancing binary search tree

17 related topics

History

Rotterdam Groningen Amsterdam Mathematical Center in Amsterdam Prim's minimal spanning tree algorithm

7 related topics

Overview

Algorithm Shortest-path algorithm Nodes Graph Road network

24 related topics

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Class: Search algorithm Greedy algorithm Dynamic programming
Data structure: Graph Usually used with priority queue or heap for optimization
Worst-case performance: Θ ( | E | + | V | log ⁡ | V | ) {\displaystyle \Theta (|E|+|V|\log |V|)}

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Overview

Algorithm
Shortest-path algorithm Shortest path problem
Nodes Vertex (graph theory)
Graph Graph (abstract data type)
Road network
Edsger W. Dijkstra
Routing protocols Routing protocol
IS-IS
OSPF Open Shortest Path First
Subroutine
Johnson's algorithm
Min-priority queue Priority queue
Data structure
Time Time complexity
Uniform cost search Dijkstra's algorithm
Fibonacci heap
Asymptotically Asymptotic computational complexity
Directed graphs Directed graph
Contraction hierarchies Contraction hierarchy
Orders of magnitude
Partially ordered Partially ordered set
Monotonically Monotonic function
Artificial intelligence
Best-first search

History

Rotterdam
Groningen
Amsterdam
Mathematical Center in Amsterdam Centrum Wiskunde & Informatica
Prim's minimal spanning tree algorithm Prim's algorithm
Jarník Vojtěch Jarník
Prim Robert C. Prim

Algorithm

Set Set (abstract data type)

Description

Intersections Intersection (road)
Neighbor Neighbourhood (graph theory)
Relabeling Graph labeling

Pseudocode

Proof

Correctness Correctness (computer science)
Mathematical induction

Running time

Big-O notation
Adjacency list
Matrix Adjacency matrix
Sparse graphs Sparse graph
Self-balancing binary search tree
Binary heap
Pairing heap
Average case Best, worst and average case
Probability distribution
Bidirectional Bidirectional search
A* algorithm
Transit nodes Transit Node Routing
Tarjan Robert Tarjan
Comparison-based Comparison sort
Bucket queue
Van Emde Boas tree
Radix heap

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Map overview Semantic statistics

Nodes81

Edges80

Triples177

Avg. degree1.98

Density0.024691

Components1

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Dijkstra's algorithm

Top relations

related to References · 88

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related to Algorithm · 13

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related to External links · 11

Dijkstra's algorithm → Charles Babbage Institute, Dijkstra, Dijkstra's, Edsger, MinneapolisImplementation, Minnesota, Oral, Robert Cecil Martin, TDD, The Clean Code Blog, University

related to Bidirectional Dijkstra · 9

Dijkstra's algorithm → Bidirectional Dijkstra, Dijkstra's, Each, Qb, Qf, Sb, Sf, The, Two

related to Optimality for comparison-sorting by distance · 9

Dijkstra's algorithm → As, Dijkstra's, Haeupler, Hladík, In, Rozhoň, Tarjan, To, Tětek

related to Practical performance considerations · 9

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related to Related problems and algorithms · 7

Dijkstra's algorithm → Dijkstra's, Each, For, IS-IS, OSPF, The, To

related to Practical optimizations and infinite graphs · 6

Dijkstra's algorithm → Dijkstra's, In, Moreover, The, This, UCS

related to Proof · 5

Dijkstra's algorithm → Dijkstra's, For, Invariant, Note, To

related to Running time · 5

Dijkstra's algorithm → Bounds, Dijkstra's, For, In, The

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Important terminology

algorithm shortest path dijkstra's distance nodes graph node queue priority source graphs time search displaystyle current one edges edge weights

Entity relationships Subject–Predicate–Object triples

Subject	Predicate	Object	Confidence	Src
Dijkstra's algorithm	Class	Search algorithm Greedy algorithm Dynamic programming	1.00	infobox
Dijkstra's algorithm	Data structure	Graph Usually used with priority queue or heap for optimization	1.00	infobox
Dijkstra's algorithm	Worst-case performance	Θ ( \| E \| + \| V \| log ⁡ \| V \| ) {\displaystyle \Theta (\|E\|+\|V\|\log \|V\|)}	1.00	infobox
Dijkstra's algorithm	is a	successive approximation scheme that solves the dynamic programming functional equation for the shortest path problem by the Reaching method.In fact	0.90	text
Johnson's algorithm.The algorithm uses a min-priority queue data structure for selecting the shortest paths known so far	instance of	It is also employed as a subroutine in algorithms	0.80	text
contraction hierarchies can be up to seven orders of magnitude faster.Dijkstra's algorithm is commonly used on graphs where the edge weights are positive integers or real numbers	instance of	algorithms	0.80	text
the A	instance of	goal-directed variants	0.80	text
the ALT	instance of	sometimes reducing the explored region from an exponential-size ball to two smaller half-balls.The method is widely used in point-to-point routing for maps and navigation softwa…	0.80	text
contraction hierarchies	instance of	sometimes reducing the explored region from an exponential-size ball to two smaller half-balls.The method is widely used in point-to-point routing for maps and navigation softwa…	0.80	text
and reach-based routing.If the actual shortest path	instance of	sometimes reducing the explored region from an exponential-size ball to two smaller half-balls.The method is widely used in point-to-point routing for maps and navigation softwa…	0.80	text
Fibonacci heaps provide better theoretical bounds but often perform worse in real applications because of large constant factors.Graph structure also plays a major role	instance of	Alternatives	0.80	text
Dijkstra's algorithm	related to Algorithm	The	0.60	section

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