# Multi-Dimensional Balanced Graph Partitioning via Projected Gradient Descent

## TL;DR

This paper introduces a scalable multi-dimensional balanced graph partitioning method using projected gradient descent, improving distributed graph processing performance on large-scale social networks.

## Contribution

It presents a novel scalable algorithm for multi-dimensional balanced graph partitioning based on randomized projected gradient descent for non-convex relaxations.

## Key findings

- Outperforms state-of-the-art methods on large social networks
- Efficient implementation of the algorithm in practice
- Demonstrates importance of multi-dimensional balance for performance

## Abstract

Motivated by performance optimization of large-scale graph processing systems that distribute the graph across multiple machines, we consider the balanced graph partitioning problem. Compared to the previous work, we study the multi-dimensional variant when balance according to multiple weight functions is required. As we demonstrate by experimental evaluation, such multi-dimensional balance is important for achieving performance improvements for typical distributed graph processing workloads. We propose a new scalable technique for the multidimensional balanced graph partitioning problem. The method is based on applying randomized projected gradient descent to a non-convex continuous relaxation of the objective. We show how to implement the new algorithm efficiently in both theory and practice utilizing various approaches for projection. Experiments with large-scale social networks containing up to hundreds of billions of edges indicate that our algorithm has superior performance compared with the state-of-the-art approaches.