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We consider the problem of collective exploration of a known n node edgeweighted graph by k mobile agents that have limited energy but are capable of energy transfers. The agents are initially placed at an arbitrary subset of nodes in the graph, and each agent has an initial, possibly different, amount of energy. The goal of the exploration problem is for every edge in the graph to be traversed by at least one agent. The amount of energy used by an agent to travel distance x is proportional to x. In our model, the agents can share energy when colocated: when two agents meet, one can transfer part of its energy to the other. For an nnode path, we give an O(n+k) time algorithm that either nds an exploration strategy, or reports that one does not exist. For an nnode tree with l leaves, we give an O(n+lk^2) algorithm that finds an exploration strategy if one exists. Finally, for the general graph case, we show that the problem of deciding if exploration is possible by energysharing agents is NPhard, even for 3regular graphs. In addition, we show that it is always possible to find an exploration strategy if the totalmore »

Queen Daniela of Sardinia is asleep at the center of a round room at the top of the tower in her castle. She is accompanied by her faithful servant, Eva. Suddenly, they are awakened by cries of "Fire". The room is pitch black and they are disoriented. There is exactly one exit from the room somewhere along its boundary. They must find it as quickly as possible in order to save the life of the queen. It is known that with two people searching while moving at maximum speed 1 anywhere in the room, the room can be evacuated (i.e., with both people exiting) in 1 + (2 pi)/3 + sqrt{3} ~~ 4.8264 time units and this is optimal [Czyzowicz et al., DISC'14], assuming that the first person to find the exit can directly guide the other person to the exit using her voice. Somewhat surprisingly, in this paper we show that if the goal is to save the queen (possibly leaving Eva behind to die in the fire) there is a slightly better strategy. We prove that this "priority" version of evacuation can be solved in time at most 4.81854. Furthermore, we show that any strategy for saving themore »

We introduce and study a new searchtype problem with ( 𝑛+1 )robots on a disk. The searchers (robots) all start from the center of the disk, have unit speed, and can communicate wirelessly. The goal is for a distinguished robot (the queen) to reach and evacuate from an exit that is hidden on the perimeter of the disk in as little time as possible. The remaining n robots (servants) are there to facilitate the queen’s objective and are not required to reach the hidden exit. We provide upper and lower bounds for the time required to evacuate the queen. Namely, we propose an algorithm specifying the trajectories of the robots which guarantees evacuation of the queen in time always better than 2+4(\sqrt{2}1)\pi/n for 𝑛≥4 servants. We also demonstrate that for 𝑛≥4 servants the queen cannot be evacuated in time less than 2 + \pi/n + 2/n^2.

Abstract The EXO200 experiment searched for neutrinoless doublebeta decay of 136 Xe with a singlephase liquid xenon detector. It used an active mass of 110 kg of 80.6%enriched liquid xenon in an ultralow background time projection chamber with ionization and scintillation detection and readout. This paper describes the design and performance of the various support systems necessary for detector operation, including cryogenics, xenon handling, and controls. Novel features of the system were driven by the need to protect the thinwalled detector chamber containing the liquid xenon, to achieve high chemical purity of the Xe, and to maintain thermal uniformity across the detector.Free, publiclyaccessible full text available February 1, 2023