GENERAL GRAPH SEARCH

• Many interesting and useful problems cannot be handled solely by dynamic programming. For example, consider the traveling salesman problem - finding the shortest distance tour covering N cities and only visiting each city once:
  
  
  The complexity of an exhaustive search solution to such problems can be O(N^T) - which is prohibitive for speech recognition.
  
  
• A search tree solution to the traveling salesman problem is show below:
  
  
  
• The search space is defined by a triplet (S,O,G), where S is the set of initial states, O is a set of operators or rules, and G is a set of goal states.
  
  
• A general algorithm for searching such spaces can be defined as follows:
  
  
• An important part of any search algorithm is the successor operator which generates the list of all possible nodes that can follow a given node, and computes the distance associated with each of these arcs.