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A 10/7-Approximation for Discrete Bamboo Garden Trimming and Continuous Trimming on Star Graphs
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Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: International Conference on Approximation Algorithms for Combinatorial Optimization Problems (APPROX)
Conference: International Conference on Randomization and Computation (RANDOM) - License:
Creative Commons Attribution 4.0 International license
- Publication Date: 2023-09-04
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Felix Höhne and Rob van Stee. A 10/7-Approximation for Discrete Bamboo Garden Trimming and Continuous Trimming on Star Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 16:1-16:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.16
https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2023.16
Abstract
In the discrete bamboo garden trimming problem we are given n bamboo that grow at rates v_1,… ,v_n per day. Each day a robotic gardener cuts down one bamboo to height 0. The goal is to find a schedule that minimizes the height of the tallest bamboo that ever exists.
We present a 10/7-approximation algorithm that is based on a reduction to the pinwheel problem. This is consistent with the approach of earlier algorithms, but some new techniques are used that lead to a better approximation ratio.
We also consider the continuous version of the problem where the gardener travels in a metric space between plants and cuts down a plant each time he reaches one. We show that on the star graph the previously proposed algorithm Reduce-Fastest is a 6-approximation and the known Deadline-Driven Strategy is a (3+2√2)-approximation. The Deadline-Driven Strategy is also a (9+2√5)-approximation on star graphs with multiple plants on each branch.
Subject Classification
ACM Subject Classification
- Theory of computation → Scheduling algorithms
Keywords
- bamboo garden trimming
- approximation algorithms
- scheduling
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