Graph search algorithms

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Section 9

• Graph search algorithms

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Breadth-first search

• Idea Let n denote a distance of node n from
  the initial node. We visit nodes in order
• All nodes n such that n 1
• All nodes n such that n 2
• All nodes n such that n 3
• All nodes n such that n 4
• All nodes n such that n 5
• ....

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BFS Water analogy

• BFS is similar to pouring water!
• We pour the water on the first node. When there
  is too much water in it, the nodes adjacent to it
  start to fill. And so on...

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BFS
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Depth-first search

• Idea We go as deep as possible.
• Visit recursively all the adjacent nodes of the
  source node.

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DFS Labyrinth analogy

• DFS is similar to going through labyrinth.
• We walk leaving a thread behind us. Whenever we
  have the choice of path, we choose the leftmost
  one. If we reach a dead-end or the place already
  marked, we go back to the first unvisited place.

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DFS
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BFS DFS

• Stunning fact - we can implement both of them
  using the same code, changing only the underlying
  SequenceStructure.

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BFS DFS

• initialize toDo with the node we are starting
  from
• while (!empty(toDo))
• remove a node n from toDo
• visit(n)
• put all unvisited neighbours of
• n on toDo

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BFS DFS
Method toDo implementation
DFS Stack
BFS Queue
Best-first search Priority queue
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Best-first search

• In situation when we have a weight function f on
  nodes, which tells us which node to visit first.
• BFS, but visiting neighbours according to the
  fumction f.
• Just use priority queue!

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WWW as a graph

• Nodes -
• Edges -

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WWW as a graph

• Nodes - webpages
• Edges - links

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WWW as a graph

• How to write a program downloading a whole web
  page?

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WWW as a graph

• How to write a program downloading a whole web
  page?
• Use graph search!
• Which one?

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WWW as a graph

• How to write a program downloading a whole web
  page?
• Use graph search!
• Which one?
• BFS!

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WWW as a graph

• Interesting questions
• What is the diameter of the graph? (probably
  about 20)
• What is its structure?
• What are the efficient search algorithms? -
  Google, Altavista
• What is a typical node?
• Many more...

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Bus/train map as a graph

• Nodes -
• Edges -

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Bus map as a graph

• Nodes - bus/train stops/stations
• Edges - theres an edge from one node to the
  other if there is a bus/train, which takes you
  from one stop to the other.
• www.bahn.de
• How to find how to reach a bus stop/city?

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Survival skills

• How to find a way out in the labyrinth?
• Optimistic version With a thread of string.
• Pessimistic version Without a thread.

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With a thread

• Use DFS - using a thread to go back to the yet
  unvisited paths.

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Without a thread

• A heuristics which often works - always turn
  left.