Bratko, Chapter 12: Best First: A Heuristic Search Principle

12.1 Best-First Search
- search from s to t
- expand the node with lowest f(n) = g(n) + h(n)
  - g(n) estimates cost of optimal path from s to n
  - h(n) estimates cost of optimal path form n to t
- A* search if f(n) <= f*(n) for all n
- representation of nodes in a search tree
  - l(N,F/G) is a leaf node N
    - g(N) = G and f(n) = F = G + h(N)
  - t(N,F/G,Subs) is a subtree with root node N
    - list of subtrees Subs ordered by increasing f values
    - G is g(N)
    - F is the most promising f value of the successors in Subs
- best-first search program [Fig12.3]

12.2 Best-First Search applied to the Eight Puzzle
- need to define
  - s(Node,Node1,Cost)
  - goal(Node)
    - goal([2/2,1/3,2/3,3/3,3/2,3/1,2/1,1/1,1/2])
  - h(Node,H) = totdist + 3 * seq
    - totdist = Manhattan distance of all eight tiles
    - seq = 1 for a tile in the center +
            0 for non-center tiles followed by their proper successor +
            2 for non-center tiles not followed by their successor

12.3 Best-First Search applied to Scheduling
- given
  - tasks ti with execution time Di
  - m processors
  - precedence relations between tasks
    - what tasks must be completed before starting this task
- find a schedule for each processor minimizing total run time
- heuristic
  - finall = ((sum Di) + (sum Fj))/m
    - Di = execution times of waiting tasks
    - Fj = finishing times of processors
    - assumes distributed processing
  - Fin = max(Fj)
  - if Finall > Fin then H = Finall - Fin else H = 0