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cs.DS updates on arXiv.org

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
Distributed Reconfiguration of Spanning Trees
Siddharth Gupta, Manish Kumar, Shreyas Pai · 2022-11-03 · via cs.DS updates on arXiv.org

In a reconfiguration problem, given a problem and two feasible solutions of the problem, the task is to find a sequence of transformations to reach from one solution to the other such that every intermediate state is also a feasible solution to the problem. In this paper, we study the distributed spanning tree reconfiguration problem and we define a new reconfiguration step, called $k$-simultaneous add and delete, in which every node is allowed to add at most $k$ edges and delete at most $k$ edges such that multiple nodes do not add or delete the same edge. We first observe that, if the two input spanning trees are rooted, then we can do the reconfiguration using a single $1$-simultaneous add and delete step in one round in the CONGEST model. Therefore, we focus our attention towards unrooted spanning trees and show that transforming an unrooted spanning tree into another using a single $1$-simultaneous add and delete step requires $Ω(n)$ rounds in the LOCAL model. We additionally show that transforming an unrooted spanning tree into another using a single $2$-simultaneous add and delete step can be done in $O(\log n)$ rounds in the CONGEST model.