Optimised Search Techniques

Basic Idea

BFS brances out to all surrounding nodesNo discrimination based on direction of

target node

BFS example

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BFS example

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BFS example

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Large area needlessly explored

Alternatives

Best-First Search:Branch out to nodes which intuitively seem to be the closest to the destinationUse heuristics to estimate distances to destination nodeGreedy algorithm

However, a better solution exists

A* algorithm

A* is an improvement over Best-First SearchNodes are given weights based on:

Cost to reach the nodeEstimated cost to reach the end node

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

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

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*

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BFS A*

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