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The Random Walk Construction of Uniform Spanning Trees and Uniform Labelled Trees

https://doi.org/10.1137/0403039
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Outgoing claims: the papers this work cites, builds on, or argues with.

inferredcites →https://doi.org/10.1002/jgt.3190130604openalex-snapshot
Spanning trees with many leaves in cubic graphs
inferredcites →https://doi.org/10.1007/978-1-4614-1939-6_12openalex-snapshot
Distance-Regular Graphs
inferredcites →https://doi.org/10.1007/978-3-642-74341-2openalex-snapshot
Distance-Regular Graphs
inferredcites →https://doi.org/10.1007/bf01048272openalex-snapshot
Lower bounds for covering times for reversible Markov chains and random walks on graphs
inferredcites →https://doi.org/10.1007/bf01048273openalex-snapshot
Bounds on the cover time
inferredcites →https://doi.org/10.1007/bf01048274openalex-snapshot
On the cover time of random walks on graphs
inferredcites →https://doi.org/10.1007/bfb0071532openalex-snapshot
Distribution of labelled trees by diameter
inferredcites →https://doi.org/10.1016/0167-7152(89)90016-3openalex-snapshot
A proof of the Markov chain tree theorem
inferredcites →https://doi.org/10.1016/0890-5401(89)90067-9openalex-snapshot
Approximate counting, uniform generation and rapidly mixing Markov chains
inferredcites →https://doi.org/10.1016/s0195-6698(83)80045-6openalex-snapshot
Spanning Trees in Regular Graphs
inferredcites →https://doi.org/10.1017/cbo9780511608704openalex-snapshot
Algebraic Graph Theory
inferredcites →https://doi.org/10.1017/s0305004100068079openalex-snapshot
Hitting times for random walks on vertex-transitive graphs
inferredcites →https://doi.org/10.1109/sfcs.1979.34openalex-snapshot
Random walks, universal traversal sequences, and the complexity of maze problems
inferredcites →https://doi.org/10.1109/sfcs.1989.63516openalex-snapshot
Generating random spanning trees
inferredcites →https://doi.org/10.1112/jlms/s2-25.3.564openalex-snapshot
Some Inequalities for Reversible Markov Chains
inferredcites →https://doi.org/10.1214/aop/1176990223openalex-snapshot
Choosing a Spanning Tree for the Integer Lattice Uniformly
inferredcites →https://doi.org/10.1214/aop/1176990534openalex-snapshot
The Continuum Random Tree. I
inferredcites →https://doi.org/10.13182/nse68-a19548openalex-snapshot
The Art of Computer Programming

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Incoming claims: where this work appears in other papers’ reference lists and arguments.

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The diameter of uniform spanning trees in high dimensions
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Copyright Page
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Dedication
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Figure Credits
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Preface
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Prologue
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The Basics
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Insights and Algorithms
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Needles in a Haystack: the Class NP
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Who is the Hardest One of All? NP-Completeness
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The Deep Question: P vs. NP
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The Grand Unified Theory of Computation
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Memory, Paths, and Games
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Optimization and Approximation
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Randomized Algorithms
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Interaction and Pseudorandomness
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Random Walks and Rapid Mixing
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Counting, Sampling, and Statistical Physics
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When Formulas Freeze: Phase Transitions in Computation
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Quantum Computation
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Mathematical Tools
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Exact sampling of spanning trees via fast-forwarded random walks
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An efficient algorithm to find all minimum spanning trees
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Root and community inference on the latent growth process of a network
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Partial recurrence enables robust and efficient computation
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Number of spanning trees as an indicator of critical phenomena: When Kirchhoff meets Ising
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Reformulating nonequilibrium steady states and generalized Hopfield discrimination
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Exact distributions of cover times for N independent random walkers in one dimension
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Universal principles governing multiple random searchers on complex networks: The logarithmic growth pattern and the harmonic law
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Random Walks and Quantum Gravity in Two Dimensions
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Reaction‐diffusion and ant‐based load balancing of communication networks
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Stochastic sensor scheduling in Wireless Sensor Networks with general graph topology
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Enhancing network resilience via self-healing
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A Matrix Chernoff Bound for Strongly Rayleigh Distributions and Spectral Sparsifiers from a few Random Spanning Trees
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Signaling free localization of node failures in all-optical networks
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Distributed Construction of Nested Clusters with Inter-cluster Routing
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Generating random spanning trees
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Markov chains and polynomial time algorithms
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Signaling Free Localization of Node Failures in All-Optical Networks
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Scaling up Electrical Closeness Centrality Computation
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Network-Wide Local Unambiguous Failure Localization (NWL-UFL) via Monitoring Trails
inferred← citeshttps://doi.org/10.1109/tsipn.2017.2668141openalex-snapshot
Temporally Agnostic Rumor-Source Detection
inferred← citeshttps://doi.org/10.1109/tvt.2025.3563236openalex-snapshot
On the Scalability and Coverage of LoRa Mesh for Monitoring Linear Infrastructure
inferred← citeshttps://doi.org/10.1111/biom.12009openalex-snapshot
Exact Goodness‐of‐Fit Tests for Markov Chains
inferred← citeshttps://doi.org/10.1111/gean.12376openalex-snapshot
Probabilistic Regionalization via Evidence Accumulation with Random Spanning Trees as Weak Spatial Representations
inferred← citeshttps://doi.org/10.1111/itor.12626openalex-snapshot
On distance graph coloring problems
inferred← citeshttps://doi.org/10.1112/jlms.70416openalex-snapshot
Random planar trees and the Jacobian conjecture
inferred← citeshttps://doi.org/10.1117/12.3011553openalex-snapshot
A hybrid approach to maze generation algorithms
inferred← citeshttps://doi.org/10.1134/s0040577916060118openalex-snapshot
Fundamental constants in the theory of two-dimensional uniform spanning trees
inferred← citeshttps://doi.org/10.1137/090766632openalex-snapshot
Simulating Size-constrained Galton–Watson Trees
inferred← citeshttps://doi.org/10.1137/1.9781611973075.32openalex-snapshot
An O (log n /log log n )-approximation Algorithm for the Asymmetric Traveling Salesman Problem
inferred← citeshttps://doi.org/10.1137/1.9781611973730.134openalex-snapshot
Fast Generation of Random Spanning Trees and the Effective Resistance Metric
inferred← citeshttps://doi.org/10.1137/1.9781611973730.135openalex-snapshot
Connectivity in Random Forests and Credit Networks
inferred← citeshttps://doi.org/10.1137/120890971openalex-snapshot
Expanders via Random Spanning Trees
inferred← citeshttps://doi.org/10.1137/18m1165979openalex-snapshot
Determinant-Preserving Sparsification of SDDM Matrices
inferred← citeshttps://doi.org/10.1137/22m1524321openalex-snapshot
Optimal Sublinear Sampling of Spanning Trees and Determinantal Point Processes via Average-Case Entropic Independence
inferred← citeshttps://doi.org/10.1137/25m1807344openalex-snapshot
Log-Concave Polynomials for Matroids and Expansion
inferred← citeshttps://doi.org/10.1142/9789812700919_0003openalex-snapshot
NOTES ON PERFECT SIMULATION
inferred← citeshttps://doi.org/10.1142/s1793525309000072openalex-snapshot
RANDOM COMPLEXES AND ℓ2-BETTI NUMBERS
inferred← citeshttps://doi.org/10.1145/129712.129716openalex-snapshot
Balanced matroids
inferred← citeshttps://doi.org/10.1145/1835698.1835745openalex-snapshot
Efficient distributed random walks with applications
inferred← citeshttps://doi.org/10.1145/1963405.1963499openalex-snapshot
Limiting the spread of misinformation in social networks
inferred← citeshttps://doi.org/10.1145/237814.237880openalex-snapshot
Generating random spanning trees more quickly than the cover time
inferred← citeshttps://doi.org/10.1145/2432622.2432624openalex-snapshot
Distributed Random Walks
inferred← citeshttps://doi.org/10.1145/2492517.2500333openalex-snapshot
What do large networks look like?
inferred← citeshttps://doi.org/10.1145/3055399.3055499openalex-snapshot
Sampling random spanning trees faster than matrix multiplication
inferred← citeshttps://doi.org/10.1145/3188745.3188852openalex-snapshot
An almost-linear time algorithm for uniform random spanning tree generation
inferred← citeshttps://doi.org/10.1145/3406325.3451091openalex-snapshot
Log-concave polynomials IV: approximate exchange, tight mixing times, and near-optimal sampling of forests
inferred← citeshttps://doi.org/10.1145/3440749.3442636openalex-snapshot
Generation and Search for the Shortest Path in Two-dimensional Labyrinths as A Model for Optimizing Routing Processes in the Packet Switching Network
inferred← citeshttps://doi.org/10.1145/3514221.3526140openalex-snapshot
Efficient Personalized PageRank Computation: A Spanning Forests Sampling Based Approach
inferred← citeshttps://doi.org/10.1145/3558481.3591101openalex-snapshot
A Simple and Efficient Parallel Laplacian Solver
inferred← citeshttps://doi.org/10.1145/3558481.3591104openalex-snapshot
Quadratic Speedups in Parallel Sampling from Determinantal Distributions
inferred← citeshttps://doi.org/10.1145/3564246.3585207openalex-snapshot
Parallel Discrete Sampling via Continuous Walks
inferred← citeshttps://doi.org/10.1145/3654936openalex-snapshot
Efficient and Provable Effective Resistance Computation on Large Graphs: An Index-based Approach
inferred← citeshttps://doi.org/10.1145/3732772.3733510openalex-snapshot
Sublinear-Time Sampling of Spanning Trees in the Congested Clique
inferred← citeshttps://doi.org/10.1145/3796701.3815944openalex-snapshot
Improved Bounds for Distributed Random Walks and Spanning Trees
inferred← citeshttps://doi.org/10.1184/r1/6475547openalex-snapshot
Detecting Activations over Graphs using Spanning Tree Wavelet Bases
inferred← citeshttps://doi.org/10.1184/r1/6718457openalex-snapshot
Graph Structured Normal Means Inference
inferred← citeshttps://doi.org/10.1186/1471-2105-9-192openalex-snapshot
uShuffle: A useful tool for shuffling biological sequences while preserving the k-let counts
inferred← citeshttps://doi.org/10.1186/1756-0500-7-516openalex-snapshot
An algorithm for score aggregation over causal biological networks based on random walk sampling
inferred← citeshttps://doi.org/10.1201/9781351174664-94openalex-snapshot
Self-healing networks
inferred← citeshttps://doi.org/10.1201/b16132-86openalex-snapshot
Complex Networks
inferred← citeshttps://doi.org/10.1209/0295-5075/108/58003openalex-snapshot
A stronger null hypothesis for crossing dependencies
inferred← citeshttps://doi.org/10.1214/07-ps094openalex-snapshot
A survey of random processes with reinforcement
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