CS322 Fall 1999
Module 5 (Search Issues)
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.
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.
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
- 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.
- 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
- Is a backward search more efficient than a forward search
for breadth-first search or A*? Explain why.
- How could a bi-directional search help? Explain. What forward
and backward searches would be useful?
- Give the distance table created by dynamic programming to find a
path from mi to cp.
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
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.
- the nodes are lists of topics that have been
- the arcs are labelled with modules. Suppose L is a node,
and M is a module such that mod(M,P,T), where P is a subset of
L (every element of P is in L), and T is not a subset of L,
then L U T is a neighbour of L, with the arc labelled with M.
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
[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.
For each question in this assignment, say how long you spent on it.
reasonable? What did you learn?
- Draw the search graph to depth four. This should include all
paths from the start node
that contain three or fewer arcs.
- Is loop checking useful? Explain.
- Is multiple path pruning useful? Explain.
- Is backward search better than forward search for this problem? Explain.
- 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.
- Note that here we are representing sets of nodes as
lists sorted alphabetically.