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Understanding Breadth-First Search: Networking Algorithms Seminar

Join us for an enlightening seminar on Breadth-First Search (BFS) presented by Mohammad Reza Akhavan at the Computer Science and Electrical Engineering Department, Luleå University of Technology. The seminar covers fundamental topics such as rooted trees, spanning trees, and the BFS algorithm. Attendees will learn how to visit all nodes and edges in a graph, determine its connectivity, compute connected components, and find shortest paths. Gain insights into BFS applications while enriching your understanding of essential networking algorithms.

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Understanding Breadth-First Search: Networking Algorithms Seminar

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  1. Breadth-First Search Seminar – Networking Algorithms CS and EE Dept. Lulea University of Technology 27 Jan. 2005 Mohammad Reza Akhavan

  2. Outline (BFS) • Rooted Tree • Spanning Tree • Breadth-First Search • BFS Algorithm • Example

  3. Rooted Tree • A rooted tree is a tree in which a special node is singled out. This node is called the "root“. A tree which is not rooted is sometimes called a free tree. Rooted Tree Free Tree

  4. Spanning Tree A spanning tree in a graph G with n nodes and m edges: • A sub-graph that connects all the nodes. • A sub-graph with no cycles. • A sub-graph with m=n-1 edges.

  5. Breadth-First Search • Visits all the nodes and edges of G • Determines whether G is connected • Computes the connected components of G • Find and report a path with the minimum number of edges between two given nodes • Find a simple cycle, if there is one • Provide the shortest path from a given root to all other nodes of the network

  6. BFS for Shortest Path (i=0) s 0 • The algorithm uses a mechanism for setting and getting “labels” of nodes and edges. • Nodes whose distance from s is 0 are labeled.

  7. BFS for Shortest Path (i=1) s 1 0 1 1 Nodes whose distance from s is 1 are labeled.

  8. BFS for Shortest Path (i=2) 1 s 0 2 2 1 2 1 Nodes whose distance from s is 2 are labeled.

  9. 1 s 0 2 2 3 1 2 1 BFS for Shortest Path (i=3) Nodes whose distance from s is 3 are labeled. The next iteration finds out that the whole graph is labeled and therefore the procedure stops.

  10. 1 s 0 2 2 3 1 2 1 s 1 0 2 2 3 1 2 1 The BFS Tree

  11. BFS Algorithm • The algorithm uses a mechanism for setting and getting “labels” of nodes and edges • Search a graph by increasing distance from the starting vertex (or from the starting vertices in case of several connected components). • Can think of creating one level after the other (by increasing depth).

  12. BFS – Asynchronies Mode 0 1 1 1 3 2 3 2 2 2 4 2 3 3 4 3 4 2 3 4 4 5 4 3 7 5 7 7 4 6 6

  13. References: • Introduction to Distributed Algorithms by Gerard Tel. • Google !

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