Time-Energy Tradeoffs for Evacuation by Two Robots in the Wireless Model

Two robots stand at the origin of the infinite line and are tasked with searching collaboratively for an exit at an unknown location on the line. They can travel at maximum speed $b$ and can change speed or direction at any time. The two robots can communicate with each other at any distance and at any time. The task is completed when the last robot arrives at the exit and evacuates. We study time-energy tradeoffs for the above evacuation problem. The evacuation time is the time it takes the last robot to reach the exit. The energy it takes for a robot to travel a distance $x$ at speed $s$ is measured as $xs^2$. The total and makespan evacuation energies are respectively the sum and maximum of the energy consumption of the two robots while executing the evacuation algorithm. Assuming that the maximum speed is $b$, and the evacuation time is at most $cd$, where $d$ is the distance of the exit from the origin, we study the problem of minimizing the total energy consumption of the robots. We prove that the problem is solvable only for $bc \geq 3$. For the case $bc=3$, we give an optimal algorithm, and give upper bounds on the energy for the case $bc>3$. We also consider the problem of minimizing the evacuation time when the available energy is bounded by $\Delta$. Surprisingly, when $\Delta$ is a constant, independent of the distance $d$ of the exit from the origin, we prove that evacuation is possible in time $O(d^{3/2}\log d)$, and this is optimal up to a logarithmic factor. When $\Delta$ is linear in $d$, we give upper bounds on the evacuation time.Comment: This is the full version of the paper with the same title which will appear in the proceedings of the 26th International Colloquium on Structural Information and Communication Complexity (SIROCCO'19) L'Aquila, Italy during July 1-4, 201

Gathering of robots in a ring with mobile faults

In this paper, we consider the problem of gathering mobile agents in a graph in the presence of mobile faults that can appear anywhere in the graph. Faults are modeled as a malicious mobile agent that attempts to block the path of the honest agents and prevents them from gathering. The problem has been previously studied by a subset of the authors for asynchronous agents in the ring and in the grid graphs. Here, we consider synchronous agents and we present new algorithms for the unoriented ring graphs that solve strictly more cases than the ones solvable with asynchronous agents. We also show that previously known solutions for asynchronous agents in the oriented ring can be improved when agents are synchronous. We finally provide a proof-of-concept implementation of the synchronous algorithms using real Lego Mindstorms EV3 robots.In this paper, we consider the problem of gathering mobile agents in a graph in the presence of mobile faults that can appear anywhere in the graph. Faults are modeled as a malicious mobile agent that attempts to block the path of the honest agents and prevents them from gathering. The problem has been previously studied by a subset of the authors for asynchronous agents in the ring and in the grid graphs. Here, we consider synchronous agents and we present new algorithms for the unoriented ring graphs that solve strictly more cases than the ones solvable with asynchronous agents. We also show that previously known solutions for asynchronous agents in the oriented ring can be improved when agents are synchronous. We finally provide a proof-of-concept implementation of the synchronous algorithms using real Lego Mindstorms EV3 robots

Time-energy tradeoffs for evacuation by two robots in the wireless model

Two robots stand at the origin of the infinite line and are tasked with searching collaboratively for an exit at an unknown location on the line. They can travel at maximum speed b and can change speed or direction at any time. The two robots can communicate with each other at any distance and at any time. The task is completed when the last robot arrives at the exit and evacuates. We study time-energy tradeoffs for the above evacuation problem. The evacuation time is the time it takes the last robot to reach the exit. Th