X-Git-Url: https://mattmccutchen.net/match/match.git/blobdiff_plain/56b2309d91ad118a6758b8e5d904b3ac4edc49ce..5d419061ba673a5658e0f7485f73babb72491852:/paper/paper.tex diff --git a/paper/paper.tex b/paper/paper.tex index 088ca17..a332681 100644 --- a/paper/paper.tex +++ b/paper/paper.tex @@ -139,8 +139,8 @@ Flow can pass from $s$ through one or more of the nodes $r^t_i$ and one or more of the nodes $p^t_j$ to the sink to represent a review by reviewer $i$ of paper $j$. -Each paper has an edge of capacity $r$ to -the sink, indicating that it needs $r$ reviews. In general, these +Each paper has an edge of capacity $q$ to +the sink, indicating that it needs $q$ reviews. In general, these edges will constitute the min cut, so any max flow will saturate them and thereby provide all the required reviews. We take the min-cost max flow in order to provide the reviews in the ``best'' possible way. @@ -204,8 +204,8 @@ unit-capacity edge of cost $-c_1$ from $p^1_j$ to $p^3_j$. In addition to the bonus edges, there are edges of zero cost and unlimited capacity that reviews can follow from $p^1_j$ to $p^2_j$ and from $p^2_j$ to $p^3_j$ in order to reach the sink. -The choice to offer bonuses for two reviews was based on the value $r = 3$; -this would be easy to change for other values of $r$. +The choice to offer bonuses for two reviews was based on the value $q = 3$; +this would be easy to change for other values of $q$. In the example in Figure~\ref{flow-fig}, paper 1 is interesting to reviewer 1 and boring to reviewers 2 and 3.