Optimised Search Techniques

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Optimised Search Techniques
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Basic Idea

• BFS brances out to all surrounding nodes
• No discrimination based on direction of target
  node

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BFS example
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E
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BFS example
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BFS example
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BFS example
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BFS example
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Large area needlessly explored
E
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Alternatives

• Best-First Search
• Branch out to nodes which intuitively seem to be
  the closest to the destination
• Use heuristics to estimate distances to
  destination node
• Greedy algorithm
• However, a better solution exists

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A algorithm

• A is an improvement over Best-First Search
• Nodes are given weights based on
• Cost to reach the node
• Estimated cost to reach the end node

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Manhattan Distance

• Manhattan distance - sum of the absolute
  distances between coordinates
• M(x1,y1,x2,y2) x1-x2 y1-y2
• Reflection of distance between points if travel
  only parallel to axes

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Implementation of A

• Using Manhattan distance as an heuristic to
  estimate distance to end point
• w(x,y) c(x,y) M(x,y,xE,yE)
• Item in priority queue with lowest weight popped
  off
• Surrounding nodes added with calculated weights

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A example
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A example
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A example
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A example
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A example
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A example
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Comparison BFS vs A
BFS
A
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E
E
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Special cases of A

• Dijkstra's Algorithm is a case of A with the
  weighting based solely on cost
• w(x,y) c(x,y)
• Breadth-First Search is just A with all nodes
  have a weight of 0
• w(x,y) 0