17 citations · 26 across the 7 of their papers we have counts for
7 papers
Linearly Bounded Liars, Adaptive Covering Codes, and Deterministic Random Walks
Joshua N. Cooper, Robert B. Ellis
We analyze a deterministic form of the random walk on the integer line called the {\em liar machine}, similar to the rotor-router model, finding asymptotically tight pointwise and…
Two-batch liar games on a general bounded channel
Robert B. Ellis, Kathryn L. Nyman
We consider an extension of the 2-person Rényi-Ulam liar game in which lies are governed by a channel , a set of allowable lie strings of maximum length . Carole selects $x\i…
Random Geometric Graph Diameter in the Unit Ball
Robert B. Ellis, Jeremy L. Martin, Catherine Yan
The unit ball random geometric graph has as its vertices points distributed independently and uniformly in the -dimensional unit ball, with two vertices adjac…
Density of normal binary covering codes
Robert B. Ellis
A binary code with covering radius is a subset of the hypercube such that every is within Hamming distance of some codeword , where $…
The Renyi-Ulam pathological liar game with a fixed number of lies
Robert B. Ellis, Vadim Ponomarenko, Catherine H. Yan
The -round Renyi-Ulam pathological liar game with lies on the set is a 2-player perfect information zero sum game. In each round Paul chooses a subset $A\…
Discrete Green's functions for products of regular graphs
Robert B. Ellis
Discrete Green's functions are the inverses or pseudo-inverses of combinatorial Laplacians. We present compact formulas for discrete Green's functions, in terms of the eigensystems…