## Abstract

This paper studies a fundamental dynamic clustering problem. The input is an online sequence of pairwise communication requests between n nodes (e.g., tasks or virtual machines). Our goal is to minimize the communication cost by partitioning the communicating nodes into ℓ clusters (e.g., physical servers) of size k (e.g., number of virtual machine slots). We assume that if the communicating nodes are located in the same cluster, the communication request costs 0; if the nodes are located in different clusters, the request is served remotely using inter-cluster communication, at cost 1. Additionally, we can migrate: a node from one cluster to another at cost α≥ 1. We initiate the study of a stochastic problem variant where the communication pattern follows a fixed distribution, set by an adversary. Thus, the online algorithm needs to find a good tradeoff between benefitting from quickly moving to a seemingly good configuration (of low inter-cluster communication costs), and the risk of prematurely ending up in a configuration which later turns out to be bad, entailing high migration costs. Our main technical contribution is a deterministic online algorithm which is O(log n) -competitive with high probability (w.h.p.), for a specific but fundamental class of problems: namely on ring graphs. We also provide first insights in slightly more general models, where the adversary is not restricted to a fixed distribution or the ring.

Original language | English |
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Pages (from-to) | 1369-1390 |

Number of pages | 22 |

Journal | Computing (Vienna/New York) |

Volume | 101 |

Issue number | 9 |

DOIs | |

State | Published - 1 Sep 2019 |

## Keywords

- Clustering
- Migration
- Online algorithms
- Randomization
- Repartition

## ASJC Scopus subject areas

- Software
- Theoretical Computer Science
- Numerical Analysis
- Computer Science Applications
- Computational Theory and Mathematics
- Computational Mathematics