## Abstract

Reordering buffer management (RBM) is an elegant theoretical model that captures the tradeoff between buffer size and switching costs for a variety of reordering/sequencing problems. In this problem, colored items arrive over time, and are placed in a buffer of size k. When the buffer becomes full, an item must be removed from the buffer. A penalty cost is incurred each time the sequence of removed items switches colors. In the non-uniform cost model, there is a weight wc associated with each color c, and the cost of switching to color c is wc. The goal is to minimize the total cost of the output sequence, using the buffer to rearrange the input sequence. Recently, a randomized O(log log k)-competitive online algorithm was given for the case that all colors have the same weight (FOCS 2013). This is an exponential improvement over the nearly tight bound of O(√ log k) on the deterministic competitive ratio of that version of the problem (Adamaszek et al., STOC 2011). In this paper, we give an O((log log kγ)^{2})-competitive algorithm for the non-uniform case, where γ is the ratio of the maximum to minimum color weight. Our work demonstrates that randomness can achieve exponential improvement in the competitive ratio even for the non-uniform case.

Original language | American English |
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Title of host publication | Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings |

Editors | Magnus M. Halldorsson, Naoki Kobayashi, Bettina Speckmann, Kazuo Iwama |

Publisher | Springer Verlag |

Pages | 78-90 |

Number of pages | 13 |

ISBN (Print) | 9783662476710 |

DOIs | |

State | Published - 2015 |

Event | 42nd International Colloquium on Automata, Languages and Programming, ICALP 2015 - Kyoto, Japan Duration: 6 Jul 2015 → 10 Jul 2015 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9134 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 42nd International Colloquium on Automata, Languages and Programming, ICALP 2015 |
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Country/Territory | Japan |

City | Kyoto |

Period | 6/07/15 → 10/07/15 |

### Bibliographical note

Funding Information:Sungjin Im—Supported in part by NSF grant CCF-1409130.

Publisher Copyright:

© Springer-Verlag Berlin Heidelberg 2015.