Deterministic walks with choice

Beeler, Katy E.; Berenhaut, Kenneth S.; Cooper, Joshua; Hunter, Meagan N.; Barr, Peter S.

doi:10.1016/j.dam.2013.08.031

Cited by 3 publications

(4 citation statements)

References 22 publications

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“…This model is well studied for expanders [8,17]. The power of choice has also been studied in the context of deterministic random walks and the rotor-router model [7,18].…”

Section: Related Literaturementioning

confidence: 99%

The power of two choices for random walks

Georgakopoulos

Haslegrave

Sauerwald

et al. 2021

Combinator. Probab. Comp.

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We apply the power-of-two-choices paradigm to a random walk on a graph: rather than moving to a uniform random neighbour at each step, a controller is allowed to choose from two independent uniform random neighbours. We prove that this allows the controller to significantly accelerate the hitting and cover times in several natural graph classes. In particular, we show that the cover time becomes linear in the number n of vertices on discrete tori and bounded degree trees, of order $${\mathcal O}(n\log \log n)$$ on bounded degree expanders, and of order $${\mathcal O}(n{(\log \log n)^2})$$ on the Erdős–Rényi random graph in a certain sparsely connected regime. We also consider the algorithmic question of computing an optimal strategy and prove a dichotomy in efficiency between computing strategies for hitting and cover times.

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“…This model is well studied for expanders [8,17]. The power of choice has also been studied in the context of deterministic random walks and the rotor-router model [7,18].…”

Section: Related Literaturementioning

confidence: 99%

The power of two choices for random walks

Georgakopoulos

Haslegrave

Sauerwald

et al. 2021

Combinator. Probab. Comp.

View full text Add to dashboard Cite

show abstract

“…This model is well studied for expanders [7,16]. The power of choice has also been studied in the context of deterministic random walks and the rotor-router model [6,17].…”

Section: Related Literaturementioning

confidence: 99%

The Power of Two Choices for Random Walks

Georgakopoulos,

Haslegrave,

Sauerwald

et al. 2019

Preprint

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We apply the power-of-two-choices paradigm to random walk on a graph: rather than moving to a uniform random neighbour at each step, a controller is allowed to choose from two independent uniform random neighbours. We prove that this allows the controller to significantly accelerate the hitting and cover times in several natural graph classes. In particular, we show that the cover time becomes linear in the number n of vertices on discrete tori and bounded degree trees, of order O(n log log n) on expanders, and of order O(n(log log n) 2 ) on the Erdős-Rényi random graph in a certain sparsely connected regime.We also consider the algorithmic question of computing an optimal strategy, and prove a dichotomy in efficiency between computing strategies for hitting and cover times.

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“…Fairness and choice have been considered in the past, notably in the context of social welfare and information processing. The interested reader might like to consult, for instance [2][3][4][9][10][11][12][13]. Figure 5 provides an example of a (9, 5) choice-hypergraph with vertex set V = {1, 2, .…”

Section: Theorem 2 If (H C) Is a Choice-hypergraph With A Zero-edgementioning

confidence: 99%

“…For various considerations of choice functions, see for instance [2,3]. For some recent work related to choice in the context of Cayley graphs, see [4].…”

Section: Introductionmentioning

confidence: 99%