24. Topological Ordering of Directed Acyclic Graphs (DAG)
The chapter focuses on the topological sorting of directed acyclic graphs (DAGs), detailing the process of labeling vertices by their in-degrees and demonstrating the elimination of vertices to determine a valid sequence of tasks. A specific algorithm involving adjacency lists is discussed, highlighting how it improves efficiency to linear time complexity for identifying in-degrees and processing vertices. The chapter concludes with pseudocode to illustrate the implemented algorithm and its complexity analysis.
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What we have learnt
- Topological sorting is essential for ordering tasks based on dependencies in a directed acyclic graph.
- The in-degree of a vertex is crucial for determining its eligibility for processing within the topological sort.
- Using an adjacency list enhances the efficiency of the topological sorting algorithm by allowing linear time complexity rather than quadratic.
Key Concepts
- -- Directed Acyclic Graph (DAG)
- A directed graph with no cycles, meaning that it is impossible to return to the same vertex after following the directions of the edges.
- -- Indegree
- The number of incoming edges to a vertex, used to determine a vertex's readiness for processing in topological sorting.
- -- Topological Sort
- An algorithm that orders the vertices of a DAG linearly in such a way that for every directed edge from vertex A to vertex B, vertex A comes before vertex B in the ordering.
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