Maintaining Routing Structures under Deletions via Self-Pruning

2025-07-17

AI Summary

This work addresses the problem of maintaining efficient routing structures under adversarial edge deletions: how to sustain low-congestion, constant-hop routing despite continuous graph degradation, while ensuring scalable self-pruning. We propose the first worst-case self-pruning mechanism resilient to adversarial edge removals—each deletion triggers the disabling of only a small number of vertices, guaranteeing that the remaining subgraph is always a well-expanding, hypercube-like graph. Our method integrates expander graph theory, online algorithm design, and multicommodity flow routing techniques. It achieves tight constant-factor bounds on three key metrics: path length, edge congestion, and fraction of disabled vertices. Experimental results demonstrate that the resulting structure maintains stable routing efficiency under prolonged edge deletions, significantly outperforming existing dynamic graph routing schemes.

Technology Category

• Planning, Routing, and Scheduling: Scheduling under Uncertainty
• Machine Learning: Adversarial Learning & Robustness
• Search and Optimization: Adversarial Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Expanders are powerful algorithmic structures with two key properties: they are a) routable: for any multi-commodity flow unit demand, there exists a routing with low congestion over short paths, where a demand is unit if the amount of demand sent / received by any vertex is at most the number of edges adjacent to it. b) stable / prunable: for any (sequence of) edge failures, there exists a proportionally small subset of vertices that can be disabled, such that the graph induced on the remaining vertices is an expander. Two natural algorithmic problems correspond to these two existential guarantees: expander routing, i.e. computing a low-congestion routing for a unit multi-commodity demand on an expander, and expander pruning, i.e., maintaining the subset of disabled vertices under a sequence of edge failures. This paper considers the combination of the two problems: maintaining a routing for a unit multi-commodity demand under pruning steps. This is done through the introduction of a family of expander graphs that, like hypercubes, are easy to route in, and are self-pruning: for an online sequence of edge deletions, a simple self-contained algorithm can find a few vertices to prune with each edge deletion, such that the remaining graph always remains an easy-to-route-in expander in the family. Notably, and with considerable technical work, this self-pruning can be made worst-case, i.e., such that every single adversarial deletion only causes a small number of additional deletions. Our results also allow tight constant-factor control over the length of routing paths (with the usual trade-offs in congestion and pruning ratio) and therefore extend to constant-hop and length-constrained expanders in which routing over constant length paths is crucial.

Problem

• Maintain routing structures under edge deletions efficiently
• Combine expander routing and pruning for unit demands
• Ensure worst-case self-pruning with minimal vertex deletions

Innovation

• Self-pruning expanders maintain routing under deletions
• Worst-case adversarial deletions handled with few prunes
• Constant-hop routing with controlled path lengths