# 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…

## One Citation

### Approximate Dynamic Balanced Graph Partitioning

- Computer ScienceSPAA
- 2022

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.

## References

SHOWING 1-10 OF 16 REFERENCES

### Optimal Online Balanced Graph Partitioning

- Computer ScienceIEEE INFOCOM 2021 - IEEE Conference on Computer Communications
- 2021

This paper revisits the online balanced partitioning problem that asks for an algorithm that strikes an optimal tradeoff between the benefits of collocation and its costs and improves the deterministic lower bound of Ω(k • ℓ) on the competitive ratio.

### Online Balanced Repartitioning

- Computer ScienceDISC
- 2016

It is proved that any deterministic online algorithm has a competitive ratio of at least k, even with augmentation, which is attractive as, in contrast to \(\ell \), k is likely to be small in practice.

### Dynamic Balanced Graph Partitioning

- Computer ScienceSIAM J. Discret. Math.
- 2020

It is proved that any deterministic online algorithm has a competitive ratio of at least $k$, even with significant augmentation, which is a constant competitive algorithm for the maximum matching variant.

### Brief Announcement: Deterministic Lower Bound for Dynamic Balanced Graph Partitioning

- Computer SciencePODC
- 2020

This paper revisits the online balanced partitioning problem and provides a significantly improved deterministic lower bound of Ω(k · ℓ) on the competitive ratio and an asymptotically tight upper bound for the general model in which the communication pattern can change arbitrarily over time.

### Optimal hierarchical decompositions for congestion minimization in networks

- Computer Science, MathematicsSTOC
- 2008

This paper shows how to construct cut-based decompositions that only result in a logarithmic loss in performance, which is asymptotically optimal and shows an interesting relationship between these seemingly different decomposition techniques.

### Tight Bounds for Online Graph Partitioning

- Computer Science, MathematicsSODA
- 2021

An improved lower bound as well as a deterministic polynomial-time online algorithm, that is asymptotically optimal, and an upper bound of $O(\log \ell + \log k)$ on its competitive ratio and show that no randomized online algorithm can achieve a competitive ratio of less than $Omega$.

### Efficient Distributed Workload (Re-)Embedding

- Computer ScienceAbstracts of the 2019 SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Systems
- 2019

This paper studies a fundamental model which captures the tradeoff between the benefits and costs of dynamically collocating communication partners on l servers, in an online manner and produces a distributed online algorithm which is asymptotically almost optimal, i.e., almost matches the lower bound on the competitive ratio of any (distributed or centralized) online algorithm.

### Amortized efficiency of list update and paging rules

- Computer ScienceCACM
- 1985

This article shows that move-to-front is within a constant factor of optimum among a wide class of list maintenance rules, and analyzes the amortized complexity of LRU, showing that its efficiency differs from that of the off-line paging rule by a factor that depends on the size of fast memory.

### Managing data transfers in computer clusters with orchestra

- Computer Science, BusinessSIGCOMM
- 2011

This work proposes a global management architecture and a set of algorithms that improve the transfer times of common communication patterns, such as broadcast and shuffle, and allow scheduling policies at the transfer level,such as prioritizing a transfer over other transfers.

### A polylogarithmic approximation of the minimum bisection

- Computer Science, MathematicsProceedings 41st Annual Symposium on Foundations of Computer Science
- 2000

An algorithm is presented that finds a bisection whose cost is within ratio of O(log/sup 2/ n) from the optimal, and for graphs excluding any fixed graph as a minor (e.g. planar graphs) the previously known approximation ratio was roughly /spl radic/n.