# How Much of a Hypertree can be Captured by Windmills?

 Title: How Much of a Hypertree can be Captured by Windmills? Author: Liang, Percy; Srebro, Nati Other Contributors: Algorithms Issue Date: 2005-01-03 Abstract: 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. URI: http://hdl.handle.net/1721.1/30515 Other Identifiers: MIT-CSAIL-TR-2005-002MIT-LCS-TR-978 Series/Report no.: Massachusetts Institute of Technology Computer Science and Artificial Intelligence Laboratory

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