CPSC 322 - Lecture 14

Blind Search

I.  Terminology

Last time we took a look at an informal description of
a generic search procedure.  Today we'll get a little bit
more formal so that we can start to implement this procedure
in CILOG.  As a step in that direction, here are some possibly
new vocabulary words for you so that we can all speak the
same language:

  A directed graph consists of a set of nodes and a set of 
  ordered pairs called arcs (or sometimes links).

  A node n2 is a neighbor of node n1 if there is an arc from n1
  to n2.

  A path is an ordered sequence of nodes such that there is an
  arc between any two consecutive nodes in the path.

  A cycle is a nonempty path with a start node and end node the same.

  A directed graph without cycles is called a directed acyclic graph.

Now let's consider the generic graph search algorithm from the
previous lecture:

Given a set of start nodes, a set of goal nodes, 
and a graph:

  make a "list" of the start nodes - let's call it
  the "frontier"

  repeat 
    if no nodes on the frontier then terminate with failure
    choose one node from the frontier and remove it
    if the chosen node matches the goal node
      then terminate with success
      else put next nodes (the neighbors of the chosen node)
        on the frontier
  end repeat


If you were to go back to the slides from the previous lecture
as well and walk through the big example, you might recognize
that the search that was performed could be characterized as
a depth-first search.  That depth-first behavior emerged because
of assumptions we made about how nodes were placed on and taken
off the frontier list.  Here are those assumptions made explicit:

Given a set of start nodes, a set of goal nodes, 
and a graph:

  make a "list" of the start nodes - let's call it
  the "frontier"

  repeat 
    if no nodes on the frontier then terminate with failure
    choose one node from the FRONT of the frontier and remove it
    if the chosen node matches the goal node
      then terminate with success
      else put next nodes (the neighbors of the chosen node)
        on the FRONT of the frontier
  end repeat

Those two little changes (in capital letters) turn generic
search into depth-first search, and you can see how it
works in more detail in today's slides.  You'll also find
the Datalog and CILOG descriptions of the depth-first search
algorithm.  

Furthermore, by making just one small change to the depth-first
algorithm, we'll get breadth-first search as seen in the slides.
Here's the one small change:

Given a set of start nodes, a set of goal nodes, 
and a graph:

  make a "list" of the start nodes - let's call it
  the "frontier"

  repeat 
    if no nodes on the frontier then terminate with failure
    choose one node from the frontier of the frontier and remove it
    if the chosen node matches the goal node
      then terminate with success
      else put next nodes (the neighbors of the chosen node)
        on the BACK of the frontier
  end repeat

Another way to look at this is in terms of how the frontier
data structure is implemented.  If the frontier acts as a stack,
with nodes being added and removed from the same end of the 
data structure so that the node most recently added is the 
first to be taken off and explored, you get depth-first search
behavior.  On the other hand, if the frontier acts as a queue
such that the node to be explored next is taken from one end
while new neighbor nodes are added to the frontier at the other
end, you'll see breadth-first search behavior.

As we'll see, there are still other approaches to search to
be built upon these.