hw1
* more of thinking questions, since will have project0 for coding pretty soon

project0
* put up, start working on next week

students helping with the course material?

sudoku...
* My solver, I basically did what they were talking about for CSP's, which is 
  today's topic, so ...

Outline for today...
* Local search - there are interesting things to say, they can be quite good, 
  but I'm not going to say much more about them now.  Maybe on hw1.
* Main topic today - CSP's and solving methods.

CSP 
* variables (vertices), possible values for variables, constraints/rules.
* types of constraints/rules? (not equal, <=, in range, ...)
  + can convert different kinds, simplify them.
  + for example, in Sudoku can simplify row rule into series of rules on pairs...
  + could also have preference constraints - e.g., class scheduling, job scheduling,
    ...

Examples of CSP problems.
* Sudoku - had that on the board last time.
* SAT
* 8-puzzle
* Others?

Constraint propagation
* pick a value for one of the variables, look at how that reduces the choices
  for other variables - go through the whole graph
  + node consistency
    - none of the choices at that node violate any of the constraints.
  + arc consistency
    - for pair of nodes with constraint between them, for each choice of one there 
      is a choice of the other that is legal.
  + path consistency, k-consistency - check more than two nodes at a time.
* example - sudoku small example.

Backtracking search
* Basically doing DFS but with constraint propagation
* choices - which variable to try assigning first (minimum remaining values), 
  and which order to try the values.
* doing the constraint propagation after each assigned variable - called forward
  checking.

Other observations...
* Local search - yep, could do that for CSP's to.
* Sub-cases that are easier to solve, by looking at what the CSP graph looks like.
  + disconnected components of the graph can be solved separately (that could
    lead to huge saving over just blindly doing backtracking search on the 
    whole graph - see why?)
  + trees are easy to solve - do topological sort to get directed-arc consistent, 
    then ...
    - so another approach for other graphs is to try and make it into a graph
      * by setting a small number of variables, or
      * by decomposing into multiple trees.