Improved Analysis of Online Balanced Clustering

@inproceedings{Bienkowski2021ImprovedAO,
  title={Improved Analysis of Online Balanced Clustering},
  author={Marcin Bienkowski and Martin B{\"o}hm and Martin Kouteck'y and Thomas Rothvoss and Jir{\'i} Sgall and Pavel Vesel'y},
  booktitle={WAOA},
  year={2021}
}
In the online balanced graph repartitioning problem, one has to maintain a clustering of n nodes into l clusters, each having k = n/l nodes. During runtime, an online algorithm is given a stream of communication requests between pairs of nodes: an inter-cluster communication costs one unit, while the intra-cluster communication is free. An algorithm can change the clustering, paying unit cost for each moved node. This natural problem admits a simple O(l2 ·k2)-competitive algorithm Comp, whose… 

Approximate Dynamic Balanced Graph Partitioning

TLDR
A polynomial-time algorithm which provides an O(log n)-approximation with resource augmentation, based on an integer linear program formulation in a metric space with spreading constraints is presented.

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