Bamboo garden trimming problem: (Perpetual maintenance of machines with different attendance urgency factors)

Leszek Gąsieniec, Ralf Klasing, Christos Levcopoulos, Andrzej Lingas, Jie Min, Tomasz Radzik

Research output: Chapter in Book/Report/Conference proceedingConference contribution

8 Scopus citations

Abstract

A garden G is populated by n ≥ 1 bamboos b1, b2, …, bn with the respective daily growth rates h1 ≥ h2 … hn. It is assumed that the initial heights of bamboos are zero. The robotic gardener or simply a robot maintaining the bamboo garden is attending bamboos and trimming them to height zero according to some schedule. The Bamboo Garden Trimming Problem, or simply BGT, is to design a perpetual schedule of cuts to maintain the elevation of bamboo garden as low as possible. The bamboo garden is a metaphor for a collection of machines which have to be serviced with different frequencies, by a robot which can service only one machine during a visit. The objective is to design a perpetual schedule of servicing the machines which minimizes the maximum (weighted) waiting time for servicing. We consider two variants of BGT. In discrete BGT the robot is allowed to trim only one bamboo at the end of each day. In continuous BGT the bamboos can be cut at any time, however, the robot needs time to move from one bamboo to the next one and this time is defined by a weighted network of connections. For discrete BGT, we show a simple 4-approximation algorithm and, by exploiting relationship between BGT and the classical Pinwheel scheduling problem, we obtain also a 2-approximation and even a closer approximation for more balanced growth rates. For continuous BGT, we propose approximation algorithms which achieve approximation ratios O(log(h1/hn)) and O(log n).

Original languageEnglish (US)
Title of host publicationSOFSEM 2017
Subtitle of host publicationTheory and Practice of Computer Science - 43rd International Conference on Current Trends in Theory and Practice of Computer Science, Proceedings
EditorsChristel Baier, Mark van den Brand, Johann Eder, Mike Hinchey, Tiziana Margaria, Bernhard Steffen
PublisherSpringer Verlag
Pages229-240
Number of pages12
ISBN (Print)9783319519623
DOIs
StatePublished - Jan 1 2017
Externally publishedYes
Event43rd Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2017 - Limerick, Ireland
Duration: Jan 16 2017Jan 20 2017

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume10139 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference43rd Conference on Current Trends in Theory and Practice of Computer Science, SOFSEM 2017
CountryIreland
CityLimerick
Period1/16/171/20/17

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Gąsieniec, L., Klasing, R., Levcopoulos, C., Lingas, A., Min, J., & Radzik, T. (2017). Bamboo garden trimming problem: (Perpetual maintenance of machines with different attendance urgency factors). In C. Baier, M. van den Brand, J. Eder, M. Hinchey, T. Margaria, & B. Steffen (Eds.), SOFSEM 2017: Theory and Practice of Computer Science - 43rd International Conference on Current Trends in Theory and Practice of Computer Science, Proceedings (pp. 229-240). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 10139 LNCS). Springer Verlag. https://doi.org/10.1007/978-3-319-51963-0_18