Fast Two-Robot Disk Evacuation with Wireless Communication

In the fast evacuation problem, we study the path planning problem for two robots who want to minimize the worst-case evacuation time on the unit disk. The robots are initially placed at the center of the disk. In order to evacuate, they need to reach an unknown point, the exit, on the boundary of the disk. Once one of the robots finds the exit, it will instantaneously notify the other agent, who will make a beeline to it. The problem has been studied for robots with the same speed~\cite{s1}. We study a more general case where one robot has speed $1$ and the other has speed $s \geq 1$. We provide optimal evacuation strategies in the case that $s \geq c_{2.75} \approx 2.75$ by showing matching upper and lower bounds on the worst-case evacuation time. For $1\leq s < c_{2.75}$, we show (non-matching) upper and lower bounds on the evacuation time with a ratio less than $1.22$. Moreover, we demonstrate that a generalization of the two-robot search strategy from~\cite{s1} is outperformed by our proposed strategies for any $s \geq c_{1.71} \approx 1.71$.Comment: 18 pages, 10 figure

Communications Biophysics

Contains research objectives and summary of research on five research projects, with ten sub-topics.National Institutes of Health (Grant 1 RO1 NS10916-01)National Institutes of Health (Grant 5 RO1 NS11000-03)National Institutes of Health (Grant 1 RO1 NS11153-01)Harvard-M.I.T. Rehabilitation Engineering CenterU. S. Department of Health, Education, and Welfare (Grant 23-P-55854)National Institutes of Health (Grant 1 RO1 NS11680-01)National Institutes of Health (Grant 5 ROI NS11080-02)M.I.T. Health Sciences FundNational Aeronautics and Space Administration (Grant NSG-2032)National Institutes of Health (Grant 5 TO1 GM01555-09)Massachusetts General Hospital Purchase Order F63853Boston City Hospital Purchase Order 4338-7543

Communications Biophysics

Contains research objectives and summary of research on thirteen research projects split into four section.National Institutes of Health (Grant 1 RO1 NS10737-01)National Institutes of Health (Grant 1 ROI NS10916-01)National Institutes of Health (Grant 5 RO1 NS11000-02)National Institutes of Health (Grant 1 RO1 NS11153-01)Harvard M.I.T. Rehabilitation Engineering CenterU. S. Department of Health, Education, and Welfare, Grant 23-P-55854National Institutes of Health (Grant 1 RO1 NS11680-01)Norlin Music, Inc.Clarence J. LeBel FundNational Institutes of Health (Grant 1 RO1 NS11080-01A1)National Institutes of Health (Grant 5 TO1 GM01555-08)M.I.T. Health Sciences FundBoston City Hospital Purchase Order 1176-05-21335-C