
Random Walks on Dynamic Graphs: Mixing Times, HittingTimes, and Return Probabilities
We establish and generalise several bounds for various random walk quant...
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Towards Exploiting Implicit Human Feedback for Improving RDF2vec Embeddings
RDF2vec is a technique for creating vector space embeddings from an RDF ...
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Rapid mixing in unimodal landscapes and efficient simulatedannealing for multimodal distributions
We consider nearest neighbor weighted random walks on the ddimensional ...
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Complexity and Geometry of Sampling Connected Graph Partitions
In this paper, we prove intractability results about sampling from the s...
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The Pendulum Arrangement: Maximizing the Escape Time of Heterogeneous Random Walks
We identify a fundamental phenomenon of heterogeneous one dimensional ra...
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Multiple Random Walks on Graphs: Mixing Few to Cover Many
Random walks on graphs are an essential primitive for many randomised al...
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Weisfeiler–Leman, Graph Spectra, and Random Walks
The Weisfeiler–Leman algorithm is a ubiquitous tool for the Graph Isomor...
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Random walks on randomly evolving graphs
A random walk is a basic stochastic process on graphs and a key primitive in the design of distributed algorithms. One of the most important features of random walks is that, under mild conditions, they converge to a stationary distribution in time that is at most polynomial in the size of the graph. This fundamental property, however, only holds if the graph does not change over time, while on the other hand many distributed networks are inherently dynamic, and their topology is subjected to potentially drastic changes. In this work we study the mixing (i.e., converging) properties of random walks on graphs subjected to random changes over time. Specifically, we consider the edgeMarkovian random graph model: for each edge slot, there is a twostate Markov chain with transition probabilities p (add a nonexisting edge) and q (remove an existing edge). We derive several positive and negative results that depend on both the density of the graph and the speed by which the graph changes. We show that if p is very small (i.e., below the connectivity threshold of ErdősRényi random graphs), random walks do not mix (fast). When p is larger, instead, we observe the following behavior: if the graph changes slowly over time (i.e., q is small), random walks enjoy strong mixing properties that are comparable to the ones possessed by random walks on static graphs; however, if the graph changes too fast (i.e., q is large), only coarse mixing properties are preserved.
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