CS322 Fall 1999
Module 5 (Search Issues)
Assignment 5

Due: 1:30pm, Wednesday 13 October 1999.

The aim of this assignment is to learn more about search, both advanced search techniques as well as how to represent an abstract problem as a search problem.

Question 1

The graph mod5gr1999, available from the web site in both CILog format as well as for the graph-drawing applet, is meant to be part of the road network for a city. For this graph, the aim is find a path from node mi to the location cp that can only be reached by round-about methods.
  1. Which of the following methods will find a path from mi to cp without loop detection or multiple-path pruning: depth-first search, A* search, breadth-first search, best-first search.
  2. For A* search, how much saving (in the number of nodes expanded) is obtained by using loop detection and using Multiple-path pruning? (Give the number of nodes selected from the frontier with and without each of the two pruning methods).
  3. Is a backward search more efficient than a forward search for breadth-first search or A*? Explain why.
  4. How could a bi-directional search help? Explain. What forward and backward searches would be useful?
  5. Give the distance table created by dynamic programming to find a path from mi to cp.

Question 2

Publish-on demand for textbooks and online courses is becoming more commonplace. We want to be able to deliver custom versions of cs322 for use at other places who may only want to use a subset of the modules, perhaps in different orders. Here we consider the problem of delivering a course to suit the goals of an instructor as a search problem.

Suppose mod(Mod,Prereqs,Teaches) is true if module Mod covers the elements of the list Teaches and requires that the students have already covered the elements of the list Prereqs.

Suppose we decide to represent the problem of designing custom courses as a search problem where The start node is labelled with the empty list []. A goal node is a node that includes all of the topics the instructor wants to cover.

For example, suppose an instructor wants to cover nnlearning, and proofs, then any node that contains both nnlearning and proofs is a goal node. Then a solution is the path that starts with [], then has arc labelled with m1 to node [intro], then has arc m4 to node1 [intro, search], then has arc m2 to node [intro, search, semantics, symbols], then has arc m6 to node [csp, intro, search, semantics, symbols], then has arc m12 to [csp, intro, nnlearning, search, semantics, symbols], then has arc m3 to node [csp, intro, nnlearning, proofs, search, semantics, symbols], which is a goal node.

  1. Draw the search graph to depth four. This should include all paths from the start node that contain three or fewer arcs.
  2. Is loop checking useful? Explain.
  3. Is multiple path pruning useful? Explain.
  4. Is backward search better than forward search for this problem? Explain.
  5. Suppose we want to use A* search. Give a non-trivial heuristic function that is an underestimate of the actual distance from a node to a goal.

Question 3

For each question in this assignment, say how long you spent on it. Was this reasonable? What did you learn?


Note that here we are representing sets of nodes as lists sorted alphabetically.

David Poole