Breadth first search

Breadth first search

Breadth first search

Structures for BFS

Implementation

(Δ, D) – graph

BFS by practiceBFS by practice

target

Breadth first search

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

source

target

Breadth first search

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

source

3 waves total.

target

Breadth first search

source

• 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: Robin

pred:

Pranil

pred:

Pranilpred:

Pranil

pred:

Shivam

pred:

Danishpred:

Awin

ImplementationImplementation

((ΔΔ, D) – graph , D) – graph

Distance

Breadth first search

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).

1 hop

2 hops

3 hops

d(Pranil,Som) = 3

Distance

Breadth first search

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

d(Danish,Aram) = 2

1

We use the shortest path.

Diameter

Breadth first search

The diameter of a graph is the maximum distance between two vertices, and is denoted D.

D = 5

(Δ, D) – graph

Breadth first search

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.

(Δ, D) – graph

Breadth first search

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.

The best (3, 1) – graph has 4 nodes.

Practice: draw the best (3, 2) – graph possible.

(Δ, D) – graph

Breadth first search

Practice: draw the best (3, 2) – graph possible.

5 6 7

8 10

Breadth first search

Breadth first search

Pavol Hell, SFU

Jean-Claude Bermond, Université de Nice

The network teams from Nice and SFU are associated.