## Abstract

We revisit the design of self-adjusting single-source tree networks. The problem can be seen as a generalization of the classic list update problem to trees, and finds applications in reconfigurable datacenter networks. We are given a balanced binary tree T connecting n nodes V = {v1,..., vn}. A source node v0, attached to the root of the tree, issues communication requests to nodes in V , in an online and adversarial manner; the access cost of a request to a node v, is given by the current depth of v in T. The online algorithm can try to reduce the access cost by performing swap operations, with which the position of a node is exchanged with the position of its parent in the tree; a swap operation costs one unit. The objective is to design an online algorithm which minimizes the total access cost plus adjustment cost (swapping). Avin et al. [12] (LATIN 2020) recently presented RANDOM-PUSH, a constant competitive online algorithm for this problem, based on random walks, together with a sophisticated analysis exploiting the working set property.This paper studies analytically and empirically, online algorithms for this problem. In particular, we explore how to derandomize RANDOM-PUSH. In the analytical part, we consider a simple derandomized algorithm which we call ROTOR-PUSH, as its behavior is reminiscent of rotor walks. Our first contribution is a proof that ROTOR-PUSH is constant competitive: its competitive ratio is 12 and hence by a factor of five lower than the best existing competitive ratio. Interestingly, in contrast to RANDOM-PUSH, the algorithm does not feature the working set property, which requires a new analysis. We further present a significantly improved and simpler analysis for the randomized algorithm, showing that it is 16-competitive.In the empirical part, we compare all self-adjusting single-source tree networks, using both synthetic and real data. In particular, we shed light on the extent to which these self-adjusting trees can exploit temporal and spatial structure in the workload. Our experimental artefacts and source codes are publicly available.

Original language | English |
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Title of host publication | Proceedings - 2022 IEEE 42nd International Conference on Distributed Computing Systems, ICDCS 2022 |

Publisher | Institute of Electrical and Electronics Engineers Inc. |

Pages | 67-77 |

Number of pages | 11 |

ISBN (Electronic) | 9781665471770 |

DOIs | |

State | Published - 1 Jan 2022 |

Event | 42nd IEEE International Conference on Distributed Computing Systems, ICDCS 2022 - Bologna, Italy Duration: 10 Jul 2022 → 13 Jul 2022 |

### Publication series

Name | Proceedings - International Conference on Distributed Computing Systems |
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Volume | 2022-July |

### Conference

Conference | 42nd IEEE International Conference on Distributed Computing Systems, ICDCS 2022 |
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Country/Territory | Italy |

City | Bologna |

Period | 10/07/22 → 13/07/22 |

## Keywords

- competitive analysis
- list update
- online algorithms
- rotor walks
- self adjusting networks

## ASJC Scopus subject areas

- Software
- Hardware and Architecture
- Computer Networks and Communications