Andrew Beveridge
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View article: The Exact Mixing Time for Trees with Fixed Diameter
The Exact Mixing Time for Trees with Fixed Diameter Open
We characterize the extremal structure for the exact mixing time for random walks on trees $T_{n,d}$ of order $n$ with diameter $d$. Given a graph $G=(V,E)$, let $H(v,π)$ denote the expected length of an optimal stopping rule from vertex $…
View article: Symmetric Rendezvous in Planar Environments With and Without Obstacles
Symmetric Rendezvous in Planar Environments With and Without Obstacles Open
We study the symmetric rendezvous search problem in which two robots that are unaware of each other’s locations try to meet as quickly as possible. In the symmetric version of this problem, the robots are required to execute the same strat…
View article: De Finetti Lattices and Magog Triangles
De Finetti Lattices and Magog Triangles Open
The order ideal $B_{n,2}$ of the Boolean lattice $B_n$ consists of all subsets of size at most $2$. Let $F_{n,2}$ denote the poset refinement of $B_{n,2}$ induced by the rules: $i < j$ implies $\{i \} \prec \{ j \}$ and $\{i,k \} \prec \{j…
View article: Maker-Breaker games on random geometric graphs
Maker-Breaker games on random geometric graphs Open
In a Maker-Breaker game on a graph G, Breaker and Maker alternately claim edges of G. Maker wins if, after all edges have been claimed, the graph induced by his edges has some desired property. We consider four Maker-Breaker games played o…
View article: Pursuit-evasion in a two-dimensional domain
Pursuit-evasion in a two-dimensional domain Open
In a pursuit-evasion game, a team of pursuers attempt to capture an evader. The players alternate turns, move with equal speed, and have full information about the state of the game. We consider the most restrictive capture condition: a pu…
View article: Line-of-Sight Pursuit in Monotone and Scallop Polygons
Line-of-Sight Pursuit in Monotone and Scallop Polygons Open
We study a turn-based game in a simply connected polygonal environment $Q$ between a pursuer $P$ and an adversarial evader $E$. Both players can move in a straight line to any point within unit distance during their turn. The pursuer $P$ w…
View article: Line-of-sight pursuit in strictly sweepable polygons
Line-of-sight pursuit in strictly sweepable polygons Open
We study a turn-based game in a simply connected polygonal environment $Q$ between a pursuer $P$ and an adversarial evader $E$. Both players can move in a straight line to any point within unit distance during their turn. The pursuer $P$ w…
View article: A Pursuit-Evasion Toolkit
A Pursuit-Evasion Toolkit Open
This tutorial contains tools and techniques for designing pursuit and evasion strategies. The material targets a diverse audience including STEM educators as well as robotics researchers interested in applications of pursuit-evasion games.…
View article: A Hitting Time Formula for the Discrete Green's Function
A Hitting Time Formula for the Discrete Green's Function Open
The discrete Green's function (without boundary) $\mathbb{G}$ is a pseudo-inverse of the combinatorial Laplace operator of a graph G = ( V, E ). We reveal the intimate connection between Green's function and the theory of exact stopping ru…
View article: Two-Dimensional Pursuit-Evasion in a Compact Domain with Piecewise Analytic Boundary
Two-Dimensional Pursuit-Evasion in a Compact Domain with Piecewise Analytic Boundary Open
In a pursuit-evasion game, a team of pursuers attempt to capture an evader. The players alternate turns, move with equal speed, and have full information about the state of the game. We consider the most restictive capture condition: a pur…