A 12/7-approximation algorithm for the discrete Bamboo Garden Trimming problem

04/24/2020

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by   Martijn van Ee, et al.

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We study the discrete Bamboo Garden Trimming problem (BGT), where we are given n bamboos with different growth rates. At the end of each day, one can cut down one bamboo to height zero. The goal in BGT is to make a perpetual schedule of cuts such that the height of the tallest bamboo ever is minimized. Here, we improve the current best approximation guarantee by designing a 12/7-approximation algorithm. This result is based on a reduction to the Pinwheel Scheduling problem. We show that a guarantee of 12/7 is essentially the best we can hope for if our algorithm is based on this type of reduction.