Study questions and advice for Chapter 8 Contemporary Mathematics Fall '09

• General:
• Give a brief discussion - what is the problem or type of problem being discussed in chapter 8?
• Go into a bit of detail - what kind of information is one likely to be given, and what are the things one has to be able to do with it?  Include things like project digraphs and making a schedule.
• Making digraphs:
  
• In a project digraph, we draw an arrow from task "A" to task "B" under what conditions?  (How do we decide where to put the arrows in a project digraph?)
• The "Start" vertex should have arrows from it to which vertices/tasks?
• The "End" vertex should have arrows to it from which vertices/tasks?
  
• Making a schedule from a digraph and a priority list:
• Suppose we are given a project digraph and a priority list.  We're working our way through making the schedule.  Suppose a processor has just finished a task, but the other processor(s) are still working.  What steps will you take to decide what the just-finished processor should do next?  (Don't forget to check whether some additional tasks are now "ready").
• What is the critical time of a project, and how is it related to the actual finishing time?
• Can/will adding processors change the critical time?
• Can/will adding processors change the actual finishing time?
• Is there always a priority list (whether or not we find it) that leads to a finishing time equal to the critical time?
• Is there always a priority list (whether or not we find it) that leads to a schedule without idle time?
  
• How to pick a good priority list (when one isn't chosen for you):
  
• How many different priority lists could a project with n tasks have?
• What's the sure way to find the priority list that gets the project finished as quickly as possble?  What are its advantages and disadvantages?
• What is the other way to find a priority list that we've studied (and the only one we've used in class)?
  
• The Critical-Path algorithm
• What is a task's critical time?  What is a project's critical time?
• How does the Backflow algorithm work, and what does it give?
• How do we get a priority list from a list of the tasks' critical times? (and what do we call this particular priority list?)
• If we use the critical-path algorithm, are we guaranteed to find a priority list that finishes the project in the critical time?  If yes, why?  If no, is there any way to build a priority list guaranteed to finish the project in the critical time?
  

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