## Abstract

We consider a multi-level aggregation problem in a weighted rooted tree, studied recently by Bienkowski et al. [7]. In this problem requests arrive over time at the nodes of the tree, and each request specifies a deadline. A request is served by sending it to the root before its deadline at a cost equal to the weight of the path from the node in which it resides to the root. However, requests from different nodes can be aggregated, and served together, so as to save on cost. The cost of serving an aggregated set of requests is equal to the weight of the subtree spanning the nodes in which the requests reside. Thus, the problem is to find a competitive online aggregation algorithm that minimizes the total cost of the aggregated requests. This problem arises naturally in many scenarios, including multicasting, supply- chain management and sensor networks. It is also related to the well studied TCP-acknowledgement problem and the online joint replenishment problem. We present an online O(D)-competitive algorithm for the problem, where D is the depth, or number of levels, of the aggregation tree. This result improves upon the D22D- competitive algorithm obtained recently by Bienkowski et al. [7].

Original language | English |
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Title of host publication | 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017 |

Editors | Philip N. Klein |

Publisher | Association for Computing Machinery |

Pages | 1235-1244 |

Number of pages | 10 |

ISBN (Electronic) | 9781611974782 |

DOIs | |

State | Published - 2017 |

Event | 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017 - Barcelona, Spain Duration: 16 Jan 2017 → 19 Jan 2017 |

### Publication series

Name | Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms |
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Volume | 0 |

### Conference

Conference | 28th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2017 |
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Country/Territory | Spain |

City | Barcelona |

Period | 16/01/17 → 19/01/17 |

### Bibliographical note

Publisher Copyright:Copyright © by SIAM.

## Keywords

- Aggregation of requests
- Competitive analysis
- Online algorithms