Outline

• Using Slidy
• Probabilistic Analysis - The Hiring Problem
• Review Probability

Using Slidy

• The slides for this class are HTML files.
• They are made to look like slides using a Javascript called Slidy.
• The following keystrokes do useful things in Slidy:
  • h - help (see all the commands)
  • f - fullscreen (gets rid of the links at the bottom of the window
  • space - advance a slide
  • left/right arrows - forward or back a slide
  • up/down arrows - scroll within a slide
  • a - show all slides at once for printing

The Hiring Problem

We will now begin our investigation of randomized algorithms with a toy problem:

• You want to hire an office assistant from an employment agency.
• You want to interview candidates and determine if they are better than the current assistant and if so replace the current assistant.
• You are going to eventually interview every candidate from a pool of `n` candidates.
• You want to always have the best person for this job, so you will replace an assistant with a better one as soon as you are done the interview.
• However, there is a cost to fire and then hire someone.
• You want to know the expected price of following this strategy until all `n` candidates have been interviewed.

Pseudo-Code

Hire-Assistant(n)
1 best := dummy candidate
2 for i := 1 to n
3     do interview of candidate i
4         if i is better than best
5             best := i
6             hire candidate i

Total Cost and Cost of Hiring

• Interviewing has a low cost `c_i`.
• Hiring has a high cost `c_h`.
• Let `n` be the number of candidates to be interviewed and let `m` be the number of people hired.
• The total cost then goes as `O(n cdot c_i+m cdot c_h)`
• The number of candidates is fixed so the part of the algorithm we want to focus on is the `m cdot c_h` term.
• This term governs the cost of hiring.

Worst-case Analysis

• In the worst case, everyone we interview turns out to be better than the person we currently have.
• In this case, the hiring cost for the algorithm will be `O(n cdot c_h)`.
• This bad situation presumably doesn't typically happen so it is interesting to ask what happens in the average case.