Graph Theory- SC322:
BFS & DFS
Graph Theory- SC322: BFS & DFS
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Graph Theory: Breadth-First Search (BFS) and Depth-First Search (DFS), Lecture notes of Data Structures and Algorithms
An overview of graph searching algorithms, specifically Breadth-First Search (BFS) and Depth-First Search (DFS). It covers the concepts, procedures, and properties of both algorithms, including their differences. BFS explores vertices and edges starting from a specified vertex, looking at vertices closest first, while DFS explores vertices and edges based on the depth of the graph. Both algorithms are essential in understanding graph theory and its applications.
What you will learn
- How does BFS traverse a graph?
- What is the ancestor-descendent property in DFS?
- What is the difference between Breadth-First Search (BFS) and Depth-First Search (DFS) in graph theory?
- What are the advantages and disadvantages of using BFS and DFS?
- What data structures are used in BFS and DFS?
Typology: Lecture notes
2019/2020
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Graph Theory- SC322:
BFS & DFS
Graph searching
Graph seacrhing is the systematic traversal of the vertices and edges of a graph in order to learn useful structural properties of a graph.
Graph searching
Graph seacrhing is the systematic traversal of the vertices and edges of a graph in order to learn useful structural properties of a graph. Graph searching techniques are central to several important graph algorithms. Many advanced algorithms begin by a graph searching routine before proceeding with other computations. The two most common graph searching algorithms are Breadth-First Search (BFS) and Depth-First Search (DFS).
BFS explores the edges and vertices of a graph starting from a specified vertex by looking at vertices closest first and then moving to remote vertices. It performs explorations at all vertices at a distance k from the source before looking at any vertex before doing so for any vertex at distance k + 1.
BFS explores the edges and vertices of a graph starting from a specified vertex by looking at vertices closest first and then moving to remote vertices. It performs explorations at all vertices at a distance k from the source before looking at any vertex before doing so for any vertex at distance k + 1.
DFS explores further and deeper along a path until no further progress is possible and then retraces and branches from an earlier point.
During their course both these algorithms get useful information about the graph. They are used either directly or as prototypes to develop subroutines for many graph algorithms.
BFS (G,s)
(^1) for each vertex u โ V [G ] \ {s}
BFS (G,s)
(^1) for each vertex u โ V [G ] \ {s} (^2) do colour [u] โ white (^3) d[u] โ โ
BFS (G,s)
(^1) for each vertex u โ V [G ] \ {s} (^2) do colour [u] โ white (^3) d[u] โ โ (^4) ฯ[u] โ nil
BFS (G,s)
(^1) for each vertex u โ V [G ] \ {s} (^2) do colour [u] โ white (^3) d[u] โ โ (^4) ฯ[u] โ nil (^5) colour [s] โ grey (^6) d[s] โ s
BFS (G,s)
(^1) for each vertex u โ V [G ] \ {s} (^2) do colour [u] โ white (^3) d[u] โ โ (^4) ฯ[u] โ nil (^5) colour [s] โ grey (^6) d[s] โ s (^7) ฯ[s] โ nil
BFS (G,s)
(^1) for each vertex u โ V [G ] \ {s} (^2) do colour [u] โ white (^3) d[u] โ โ (^4) ฯ[u] โ nil (^5) colour [s] โ grey (^6) d[s] โ s (^7) ฯ[s] โ nil (^8) Q โ โ (^9) ENQUEUE (Q, s)
(^10) while (Q 6 = โ )
(^10) while (Q 6 = โ )
(^11) do u โ DEQUEUE (Q)
(^12) for each v โ Adj[u]
(^10) while (Q 6 = โ )
(^11) do u โ DEQUEUE (Q)
(^12) for each v โ Adj[u]
(^13) do if colour [v ] = white