22C:2 From CAT Scans to Google: Great Ideas in Computing
Homework 3. Due Thursday, September 21, 2006

Alan, Bob, Carl, Dexter, and Ed are notoriously picky rock stars.

Each rock star only plays venues when enticed with appropriate candy
treats in their dressing room (BabyRuth, MilkDuds, ReesesPieces,
Starburst, Twizzlers).

Moreover, each rock star maintains an ordered preference list of candy
treats, along with a "desirability index" for each candy treat on
their list.

A venue's value to a particular rock star is the sum of the product of
the quantities of each candy provided times the rock star's own
desirability index for that candy (this sum of products measures the
rock star's "satisfaction" with that venue).

Assuming a venue can only handle one rock start at a time, how might
you go about finding an assignment of rock stars to concert venues
that maximizes the sum of each rock star's achieved satisfaction?

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1. How is this the same as the stable marriage problem?  How is it
different?

2. How would you solve it? Can you extend the efficient algorithm of
stable marriages to this problem? Who "proposes"? Note that here, the
venues don't directly characterize the desirability of each rock star!

3. Does the "satisfaction index" as described above make sense? What
assumption does it make about the relative happiness of each rock
star?

4. Can you extend your algorithm to cover the case where each venue
gets to pick two rock stars (presumably for successive nights?), and
each rock star gets to pick two venues? What happens if we allow the
venues to repeat (in other words, Bob plays Minneapolis for two
nights)?