Is there a name and theory for "arrangement/packing" problems?
- From: Chris F Clark <cfc@xxxxxxxxxxxxxxxxxxxx>
- Date: Fri, 25 Apr 2008 15:08:19 -0400
Yesterday, I needed to arrange a set of reviewers to look at
proposals. I'll give the details below. However, it occured to me
that this kind of discrete arrangement/packing might be well studied
and even have a name and branch of mathematics devoted to its study,
like Diophantine equations are a part of Number Theory that captures
systems of algerbraic equations with integral solutions. If there is
such a name for these problems and some relevant theory I can start to
read, I'd appreciate a pointer.
Here's the problem I was facing.
I have 8 reviewers and 24 papers and I would like each paper to be
reviewed by 3 reviewers, but with as many unique combinations of
reviewer pairs as possible. That works out because 24 papers * 3
reviews/paper = 72 reviews = 8 reviewers * 9 reviews/reviewer. Thus,
with each reviewer reviewing 9 papers, the numbers work out perfectly.
However, actually assigning the reviewers to the papers was hard. I
haven't even yet come up with a scheme that achieve's the kind of
balance I want (not even close), and I simply took an initial
approximate scheme and used that. I would consider an assignment of
reviewers to papers successful if no pair of reviewers did more than 3
papers together (and each paper had a unique tripplet of reviers). I
think such an assignment should be possible. Moreover, it seems like
there should be some relatively elegant pattern that approximates and
even balance. And, that is why I'm wondering if such problems have
names and what area researches them. In the mean itme, I may try
writing a brute force program to try to find different combinations
that work.
Thanks,
Chris
.
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