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PAC Learning with Bandit Feedback: Sharp Sample Complexity in the Realizable Setting Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications A computational phase transition for learning-to-sample from Ising models Covering vertices by sequential stars Fermi-Dirac machines as quantizations of neurons A Comprehensive Evaluation of Vertex Elimination Algorithms for Algorithmic Differentiation A Tight Bound on Localization of Electrical Flows Optimal Dimension-Free Sampling for Regularized Classification Reducing the Randomness in Partition Oracles for Bounded Degree Minor-Free Graphs Beyond the Half-Approximation: Fair and Efficient Online Class Matching Efficient Uniform Sampling of Surjections via their Profiles Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking Learning-Augmented Online Scheduling with Parsimonious Preemption Entropy Equivalence Testing Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees The Secretary Problem with a Stochastic Precursor Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification Block-Sphere Vector Quantization An Approximation Algorithm for Graph Label Selection Iterative Chow Filtering for Learning with Distribution Shift Complexity of Non-Log-Concave Sampling in Fisher Information Stochastic Matching via Local Sparsification Finite Sample Bounds for Learning with Score Matching What is Learnable in Valiant's Theory of the Learnable? Provable Quantization with Randomized Hadamard Transform Min-Max Optimization Requires Exponentially Many Queries Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm A proximal gradient algorithm for composite log-concave sampling
Maintaining Routing Structures under Deletions via Self-P...
Bernhard Haeupler, Antti Roeyskoe · 2025-07-17 · via cs.DS updates on arXiv.org

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.