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08/09/2023
Mean-Biased Processes for Balanced Allocations
We introduce a new class of balanced allocation processes which bias tow...
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07/20/2023
Small But Unwieldy
We show that for any natural number s, there is a constant γ and a subgr...
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03/07/2023
Cops and Robbers on Multi-Layer Graphs
We generalise the popular cops and robbers game to multi-layer graphs, w...
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01/24/2023
Balanced Allocations with Heterogeneous Bins: The Power of Memory
We consider the allocation of m balls (jobs) into n bins (servers). In t...
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07/14/2022
Cover and Hitting Times of Hyperbolic Random Graphs
We study random walks on the giant component of Hyperbolic Random Graphs...
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04/08/2022
The Power of Filling in Balanced Allocations
It is well known that if m balls (jobs) are placed sequentially into n b...
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02/23/2022
Bounds on the Twin-Width of Product Graphs
Twin-width is a graph width parameter recently introduced by Bonnet, Kim...
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02/02/2022
A New Temporal Interpretation of Cluster Editing
The NP-complete graph problem Cluster Editing seeks to transform a stati...
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10/20/2021
Balanced Allocations: Caching and Packing, Twinning and Thinning
We consider the sequential allocation of m balls (jobs) into n bins (ser...
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08/10/2021
Tangled Paths: A Random Graph Model from Mallows Permutations
We introduce the random graph 𝒫(n,q) which results from taking the union...
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02/24/2021
The Cover Time of a (Multiple) Markov Chain with Rational Transition Probabilities is Rational
The cover time of a Markov chain on a finite state space is the expected...
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11/16/2020
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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06/03/2020
Time Dependent Biased Random Walks
We study the biased random walk where at each step of a random walk a "c...
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11/12/2019
The Power of Two Choices for Random Walks
We apply the power-of-two-choices paradigm to random walk on a graph: ra...
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08/28/2018