LCS Publication Details
Publication Title: How Much of a Hypertree can be Captured by Windmills?
Publication Author: Liang, Percy
Additional Authors: Nati Srebro
LCS Document Number: MIT-LCS-TR-978
Publication Date: 1-3-2005
LCS Group: Algorithms
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Current approximation algorithms for maximum weight {\em hypertrees} find heavy {\em windmill farms}, and are based on the fact that a constant ratio (for constant width $k$) of the weight of a $k$-hypertree can be captured by a $k$-windmill farm. However, the exact worst case ratio is not known and is only bounded to be between $1/(k+1)!$ and $1/(k+1)$. We investigate this worst case ratio by searching for weighted hypertrees that minimize the ratio of their weight that can be captured with a windmill farm. To do so, we use a novel approach in which a linear program is used to find ``bad'' inputs to a dynamic program.
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