Expander graph routing stays strong despite edge failures
Expander Routing under Adversarial Deletions via Temporal Aggregation
Data Structures and Algorithms
Summary
Routing in complex networks involves finding paths that avoid congestion and keep travel times short. This paper tackles the challenge of maintaining efficient routes even when connections in the network are removed unexpectedly. The authors developed an approach that quickly adapts to such changes without making paths much longer or causing traffic jams. Their method works well even when facing an opponent trying to break the network in the worst way possible.
What this means in practice
- •For network schedulers: Keep data routing efficient in networks that lose connections over time while preserving low delay and avoiding overloaded links.
- •For distributed system engineers: Design distributed systems that maintain fast, congestion-resistant communication paths despite ongoing network changes or attacks.
Authors
Bernhard Haeupler, Anton Paramonov
Abstract
In expander routing, we seek to establish paths in the expander graph between given source-target pairs while minimizing both dilation (maximum path length) and congestion (maximum edge load). We study this problem in a decremental dynamic setting where the underlying graph remains an expander despite ongoing edge deletions, and source-target pairs can be added or removed. Our goal is to maintain paths under these updates while keeping dilation and congestion low and performing low computation per update. We present a randomized algorithm that maintains paths with polylogarithmic dilation and congestion against an adaptive adversary, while incurring only polylogarithmic amortized computation per update, all with high probability. Our approach leverages a recent technique called Temporal Aggregation to maintain a collection of low-congestion, low-dilation random walks resilient to adaptive adversaries.