Optimal Local Algorithms via Topology-Sensitivity

Introduction

Considering the rapid growth of data sets and network sizes over the past decade, there is little doubt that the future of computation is distributed. One central aspect lying at the heart of distributed algorithms is the question of locality: what can be computed using only local information, and how much information is needed?

Importance of Locality

While answering this question is essential for obtaining highly efficient algorithms for many important distributed problems—such as load balancing in massive networks—locality is a fundamentally important concept also in many other fields of algorithmics, such as:

• Classical sequential algorithms
• Massively parallel algorithms
• Dynamic algorithms
• Sublinear algorithms
• Streaming algorithms
• Online algorithms

Challenges in Distributed Algorithms

In the context of distributed algorithms, a careful analysis of recent research on impossibilities reveals the key challenges in understanding locality—and therefore in designing optimal algorithms—for many graph problems. These challenges include:

1. Understanding how to solve tree-like structures efficiently.
2. Understanding how to explicitly exploit any deviations from a tree-like topology algorithmically.

Project Goals

The goal of this proposal is to gain a fundamental understanding of locality via the novel concept of topology-sensitive algorithms. This approach precisely addresses the key challenges by explicitly exploiting local topological features in the input instance.

Expected Outcomes

Such an understanding will result in:

• Optimal algorithms
• Tight complexity bounds for many important distributed problems

This will help resolve central questions in distributed algorithms that have been open for decades, laying the foundations for highly efficient and scalable algorithms in massive networks. It will also imply significant improvements over the state-of-the-art in a variety of other algorithmic fields.

Conclusion

In a nutshell, the proposed project aims at a world in which everything that can be done locally will be done locally.