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Breadth first search

Breadth first search. Breadth first search. Structures for BFS. Implementation. ( Δ , D) – graph. Breadth first search. BFS by practice. We start from a source node. We want to see if we can reach a target node. We proceed by waves. target. source. Breadth first search.

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Breadth first search

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  1. Breadth first search

  2. Breadth first search Structures for BFS Implementation (Δ, D) – graph Breadth first search

  3. BFS by practice

  4. We start from a source node. We want to see if we can reach a target node. We proceed by waves. target source Breadth first search

  5. We start from a source node. We want to see if we can reach a target node. We proceed by waves. target source 3 waves total. Breadth first search

  6. • a Queue, in which we add neighbours and from which we select the next one to visit • a Dictionary: to each node that we visited we bind as value its predecessor. 2 data structures pred: Danish pred: Awin pred: Shivam target pred: Pranil pred: Pranil pred: Pranil source pred: Robin Breadth first search

  7. Implementation

  8. (Δ, D) – graph

  9. Distance The number of hops it takes to go from A to B is called the distance from A to B and denoted d(A,B). 2 hops 1 hop 3 hops d(Pranil,Som) = 3 Breadth first search

  10. Distance The number of hops it takes to go from A to B is called the distance from A to B and denoted d(A,B). 2 1 We use the shortest path. d(Danish,Aram) = 2 Breadth first search

  11. Diameter The diameter of a graph is the maximum distance between two vertices, and is denoted D. D = 5 Breadth first search

  12. (Δ, D) – graph Let Δ be the maximum degree in a graph, i.e. the largest number of neighbours that any node can have. Let D be the diameter. For a given Δ and D, design the graph having as many nodes as possible. Example: we want to create a good network of workstations. Each workstation can be connected to at most 3, and the diameter must be 1. The best (3, 1) – graph has 4 nodes. Breadth first search

  13. (Δ, D) – graph Let Δ be the maximum degree in a graph, i.e. the largest number of neighbours that any node can have. Let D be the diameter. For a given Δ and D, design the graph having as many nodes as possible. Practice: draw the best (3, 2) – graph possible. The best (3, 1) – graph has 4 nodes. Breadth first search

  14. (Δ, D) – graph Practice: draw the best (3, 2) – graph possible. 5 6 7 8 10 Breadth first search

  15. Breadth first search

  16. Pavol Hell, SFU Jean-Claude Bermond, Université de Nice The network teams from Nice and SFU are associated. Breadth first search

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