Add a slightly cleaned-up version of the paper, superseding the "notes"

[match/match.git] / notes

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-Assignment problems arise in a variety of settings.  
-For funding agencies such as NSF program directors 
-that co-ordinate panels, assigning proposals to 
-reviewers is a major challenge. It is important that each proposal be
-reviewed by qualified experts, and at the same time we would like the
-workload across different reviewers to be roughly balanced. The same
-issue arises for a program committee chair, who may have to assign
-literally hundreds of papers to a program committee consisting of
-thirty to forty program committee members. 
-
-{\em What does CMT use? What does Easychair use?}
-
-From now on we will focus on the problem of assigning papers to
-reviewers. 
-We assume that each reviewer is given access to the
-list of papers to be reviewed, and provides input on their
-preferences by giving a ``desirability'' score to each paper.
-We also assume that each paper  has to be reviewed by $r$
-reviewers. 
-
-We do not consider stable marriage type preference lists,
-because a strict ranking of papers would be rather tedious
-to produce. In this scheme, the papers are essentially grouped
-into a few categories.
-
-
-Ideally, from the perspective of the papers, we would like to
-assign each paper the $r$ ``best'' reviewers for the paper.
-Ofcourse, this would lead to a load imbalanced solution where
-the load on some program committee members is very high, and the
-load on others is low. On the other hand, we could insist 
-on a perfectly load balanced solution in which the number
-of papers assigned to each program committee member do not
-exceed $\lceil rN/P  \rceil$, where $N$ is the number of
-submissions and $P$ is the number of program committee members.
-Recall that each paper needs $r$ reviewers, so a total of $rN$
-reviews need to be generated. However this may lead to a solution
-which is not optimal from the perspective of the papers.
-
-One of our goals is to study precisely this tradeoff, and allow each
-reviewer to have upto $\lceil rN/P  \rceil + C$ papers assigned to
-them, where $C$ is the {\em imbalance factor}. The main question
-we consider is: is it possible to obtain a high quality
-assignment with a fairly low value of $C$?
-
-One can ask the same question from the perspective of the reviewers
-as well. Each reviewer would ideally like papers
-that are the ``most desirable'' from their point of view.
-
-{\em Stinkers} are papers that pretty much no-one wanted to review. 
-We would like to spread the load of the stinkers as evenly as possible.
- 
-\section{Formulation as a Min Cost Flow Problem}
-
-\section{Experimental Results} 
- 
-\section{Conclusions}
-