# Efficient Distributed Workload (Re-)Embedding

## TL;DR

This paper introduces a distributed online algorithm for dynamic workload embedding in reconfigurable networked systems, balancing the benefits of collocation against re-embedding costs, and nearly matches the theoretical optimal performance.

## Contribution

It presents a novel distributed online algorithm for workload embedding that is asymptotically almost optimal, addressing the challenge of dynamic, demand-aware reconfiguration.

## Key findings

- Algorithm is asymptotically almost optimal in competitive ratio.
- The approach effectively balances reconfiguration costs and performance benefits.
- Application demonstrated in distributed union find problem.

## Abstract

Modern networked systems are increasingly reconfigurable, enabling demand-aware infrastructures whose resources can be adjusted according to the workload they currently serve. Such dynamic adjustments can be exploited to improve network utilization and hence performance, by moving frequently interacting communication partners closer, e.g., collocating them in the same server or datacenter. However, dynamically changing the embedding of workloads is algorithmically challenging: communication patterns are often not known ahead of time, but must be learned. During the learning process, overheads related to unnecessary moves (i.e., re-embeddings) should be minimized. This paper studies a fundamental model which captures the tradeoff between the benefits and costs of dynamically collocating communication partners on $\ell$ servers, in an online manner. Our main contribution is a distributed online algorithm which is asymptotically almost optimal, i.e., almost matches the lower bound (also derived in this paper) on the competitive ratio of any (distributed or centralized) online algorithm. As an application, we show that our algorithm can be used to solve a distributed union find problem in which the sets are stored across multiple servers.