1. Optimised Search Techniques

2. Basic Idea BFS brances out to all surrounding nodes
No discrimination based on direction of target node

3. BFS example S E

4. BFS example S E

5. BFS example S E

6. BFS example S E

7. BFS example S
Large area needlessly explored E

8. 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

9. 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

10. 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

11. 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

12. A* example S E

13. A* example S 9 7 E

14. A* example S 9 7 9 7 E

15. A* example S 9 7 9 7 7 E

16. A* example S 9 7 9 7 7 7 7 E

17. A* example 11 S 9 11 11 9 7 9 11 9 7 7 7 9 7 7 9 9 E

18. Comparison: BFS vs A*
BFS A* S S E E

19. 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