Exploring an unknown graph to locate a black hole using tokens

Consider a team of (one or more) mobile agents operating in a graph G. Unaware of the graph topology and starting from the same node, the team must explore the graph. This problem, known as graph exploration, was initially formulated by Shannon in 1951, and has been extensively studied since under a variety of conditions. The existing investigations have all assumed that the network is safe for the agents, and the solutions presented in the literature succeed in their task only under this assumption. Recently, the exploration problem has been examined also when the network is unsafe. The danger examined is the presence in the network of a black hole, a node that disposes of any incoming agent without leaving any observable trace of this destruction. The goal is for at least one agent to survive and to have all the surviving agents to construct a map of the network, indicating the edges leading to the black hole. This variant of the problem is also known as black hole search. This problem has been investigated assuming powerful inter-agent communication mechanisms: whiteboards at all nodes. Indeed, in this model, the black hole search problem can be solved with a minimal team size and performing a polynomial number of moves. In this paper, we consider a less powerful token model.We constructively prove that the black hole search problem can be solved also in this model; furthermore, this can be done using a minimal team size and performing a polynomial number of moves. Our algorithm works even if the agents are asynchronous and if both the agents and the nodes are anonymous.4th IFIP International Conference on Theoretical Computer ScienceRed de Universidades con Carreras en Informática (RedUNCI

Exploration of High-Dimensional Grids by Finite Automata

We consider the problem of finding a treasure at an unknown point of an n-dimensional infinite grid, n >= 3, by initially collocated finite automaton agents (scouts/robots). Recently, the problem has been well characterized for 2 dimensions for deterministic as well as randomized agents, both in synchronous and semi-synchronous models [S. Brandt et al., 2018; Y. Emek et al., 2015]. It has been conjectured that n+1 randomized agents are necessary to solve this problem in the n-dimensional grid [L. Cohen et al., 2017]. In this paper we disprove the conjecture in a strong sense: we show that three randomized synchronous agents suffice to explore an n-dimensional grid for any n. Our algorithm is optimal in terms of the number of the agents. Our key insight is that a constant number of finite automaton agents can, by their positions and movements, implement a stack, which can store the path being explored. We also show how to implement our algorithm using: four randomized semi-synchronous agents; four deterministic synchronous agents; or five deterministic semi-synchronous agents. We give a different algorithm that uses 4 deterministic semi-synchronous agents for the 3-dimensional grid. This is provably optimal, and surprisingly, matches the result for 2 dimensions. For n >= 4, the time complexity of the solutions mentioned above is exponential in distance D of the treasure from the starting point of the agents. We show that in the deterministic case, one additional agent brings the time down to a polynomial. Finally, we focus on algorithms that never venture much beyond the distance D. We describe an algorithm that uses O(sqrt{n}) semi-synchronous deterministic agents that never go beyond 2D, as well as show that any algorithm using 3 synchronous deterministic agents in 3 dimensions, if it exists, must travel beyond Omega(D^{3/2}) from the origin

Exploring an unknown graph to locate a black hole using tokens

Consider a team of (one or more) mobile agents operating in a graph G. Unaware of the graph topology and starting from the same node, the team must explore the graph. This problem, known as graph exploration, was initially formulated by Shannon in 1951, and has been extensively studied since under a variety of conditions. The existing investigations have all assumed that the network is safe for the agents, and the solutions presented in the literature succeed in their task only under this assumption. Recently, the exploration problem has been examined also when the network is unsafe. The danger examined is the presence in the network of a black hole, a node that disposes of any incoming agent without leaving any observable trace of this destruction. The goal is for at least one agent to survive and to have all the surviving agents to construct a map of the network, indicating the edges leading to the black hole. This variant of the problem is also known as black hole search. This problem has been investigated assuming powerful inter-agent communication mechanisms: whiteboards at all nodes. Indeed, in this model, the black hole search problem can be solved with a minimal team size and performing a polynomial number of moves. In this paper, we consider a less powerful token model.We constructively prove that the black hole search problem can be solved also in this model; furthermore, this can be done using a minimal team size and performing a polynomial number of moves. Our algorithm works even if the agents are asynchronous and if both the agents and the nodes are anonymous.4th IFIP International Conference on Theoretical Computer ScienceRed de Universidades con Carreras en Informática (RedUNCI

Impact of Water Withdrawals from Groundwater and Surface Water on Continental Water Storage Variations

Humans have strongly impacted the global water cycle, not only water flows but also water storage. We have performed a first global-scale analysis of the impact of water withdrawals on water storage variations, using the global water resources and use model WaterGAP. This required estimation of fractions of total water withdrawals from groundwater, considering five water use sectors. According to our assessment, the source of 35% of the water withdrawn worldwide (4300 cubic km/yr during 1998-2002) is groundwater. Groundwater contributes 42%, 36% and 27% of water used for irrigation, households and manufacturing, respectively, while we assume that only surface water is used for livestock and for cooling of thermal power plants. Consumptive water use was 1400 cubic km/yr during 1998-2002. It is the sum of the net abstraction of 250 cubic km/yr of groundwater (taking into account evapotranspiration and return flows of withdrawn surface water and groundwater) and the net abstraction of 1150 km3/yr of surface water. Computed net abstractions indicate, for the first time at the global scale, where and when human water withdrawals decrease or increase groundwater or surface water storage. In regions with extensive surface water irrigation, such as Southern China, net abstractions from groundwater are negative, i.e. groundwater is recharged by irrigation. The opposite is true for areas dominated by groundwater irrigation, such as in the High Plains aquifer of the central USA, where net abstraction of surface water is negative because return flow of withdrawn groundwater recharges the surface water compartments. In intensively irrigated areas, the amplitude of seasonal total water storage variations is generally increased due to human water use; however, in some areas, it is decreased. For the High Plains aquifer and the whole Mississippi basin, modeled groundwater and total water storage variations were compared with estimates of groundwater storage variations based on groundwater table observations, and with estimates of total water storage variations from the GRACE satellites mission. Due to the difficulty in estimating area-averaged seasonal groundwater storage variations from point observations of groundwater levels, it is uncertain whether WaterGAP underestimates actual variations or not. We conclude that WaterGAP possibly overestimates water withdrawals in the High Plains aquifer where impact of human water use on water storage is readily discernible based on WaterGAP calculations and groundwater observations. No final conclusion can be drawn regarding the possibility of monitoring water withdrawals in the High Plains aquifer using GRACE. For the less intensively irrigated Mississippi basin, observed and modeled seasonal groundwater storage reveals a discernible impact of water withdrawals in the basin, but this is not the case for total water storage such that water withdrawals at the scale of the whole Mississippi basin cannot be monitored by GRACE