Topological Sort of a Directed Acyclic Graph: Difference between revisions
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=Overview= | =Overview= | ||
This is a very useful algorithm when a set of tasks that have precedence constraints between them need to be sequenced - executed in order. The topological sort can be done using [[Searching_a_Graph_and_Finding_a_Path_through_Graphs#Depth-First_Search|Depth-First Search (DFS)]]. | This is a very useful algorithm when a set of tasks that have precedence constraints between them need to be sequenced - executed in order. The topological sort can be done in a straightforward recursive way or using [[Searching_a_Graph_and_Finding_a_Path_through_Graphs#Depth-First_Search|Depth-First Search (DFS)]]. | ||
=Straightforward Algorithm= | =Straightforward Algorithm= | ||
We use the observation that a DAG must have one or more [[Graph#Sync_Vertex|sink vertices]]. The algorithm starts with a sink vertex, assigns to it the largest possible label, deletes the respective sink vertex from the graph, and repeats until there are no more vertices. | We use the observation that a DAG must have one or more [[Graph#Sync_Vertex|sink vertices]]. The algorithm starts with a sink vertex, assigns to it the largest possible label, deletes the respective sink vertex from the graph, and repeats until there are no more vertices. | ||
Revision as of 19:35, 30 September 2021
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Overview
This is a very useful algorithm when a set of tasks that have precedence constraints between them need to be sequenced - executed in order. The topological sort can be done in a straightforward recursive way or using Depth-First Search (DFS).
Straightforward Algorithm
We use the observation that a DAG must have one or more sink vertices. The algorithm starts with a sink vertex, assigns to it the largest possible label, deletes the respective sink vertex from the graph, and repeats until there are no more vertices.
Straightforward_Topological_Sort(Graph G)
let v be a sink vertex of G
set f(v) = n
Straightforward_Topological_Sort(G - {v})