Collaborative Delivery with Energy-Constrained Mobile Robots

We consider the problem of collectively delivering some message from a specified source to a designated target location in a graph, using multiple mobile agents. Each agent has a limited energy which constrains the distance it can move. Hence multiple agents need to collaborate to move the message, each agent handing over the message to the next agent to carry it forward. Given the positions of the agents in the graph and their respective budgets, the problem of finding a feasible movement schedule for the agents can be challenging. We consider two variants of the problem: in non-returning delivery, the agents can stop anywhere; whereas in returning delivery, each agent needs to return to its starting location, a variant which has not been studied before. We first provide a polynomial-time algorithm for returning delivery on trees, which is in contrast to the known (weak) NP-hardness of the non-returning version. In addition, we give resource-augmented algorithms for returning delivery in general graphs. Finally, we give tight lower bounds on the required resource augmentation for both variants of the problem. In this sense, our results close the gap left by previous research.Comment: 19 pages. An extended abstract of this paper was published at the 23rd International Colloquium on Structural Information and Communication Complexity 2016, SIROCCO'1

Rendezvous of Distance-aware Mobile Agents in Unknown Graphs

We study the problem of rendezvous of two mobile agents starting at distinct locations in an unknown graph. The agents have distinct labels and walk in synchronous steps. However the graph is unlabelled and the agents have no means of marking the nodes of the graph and cannot communicate with or see each other until they meet at a node. When the graph is very large we want the time to rendezvous to be independent of the graph size and to depend only on the initial distance between the agents and some local parameters such as the degree of the vertices, and the size of the agent's label. It is well known that even for simple graphs of degree $\Delta$, the rendezvous time can be exponential in $\Delta$ in the worst case. In this paper, we introduce a new version of the rendezvous problem where the agents are equipped with a device that measures its distance to the other agent after every step. We show that these \emph{distance-aware} agents are able to rendezvous in any unknown graph, in time polynomial in all the local parameters such the degree of the nodes, the initial distance $D$ and the size of the smaller of the two agent labels $l = \min(l_1, l_2)$. Our algorithm has a time complexity of $O(\Delta(D+\log{l}))$ and we show an almost matching lower bound of $\Omega(\Delta(D+\log{l}/\log{\Delta}))$ on the time complexity of any rendezvous algorithm in our scenario. Further, this lower bound extends existing lower bounds for the general rendezvous problem without distance awareness

Laser-induced electron emission from a tungsten nanotip: identifying above threshold photoemission using energy-resolved laser power dependencies

We present an experiment studying the interaction of a strongly focused 25 fs laser pulse with a tungsten nanotip, investigating the different regimes of laser-induced electron emission. We study the dependence of the electron yield with respect to the static electric field applied to the tip. Photoelectron spectra are recorded using a retarding field spectrometer and peaks separated by the photon energy are observed with a 45 % contrast. They are a clear signature of above threshold photoemission (ATP), and are confirmed by extensive spectrally resolved studies of the laser power dependence. Understanding these mechanisms opens the route to control experiment in the strong-field regime on nanoscale objects.Comment: 9 pages, 6 figure

A general lower bound for collaborative tree exploration

We consider collaborative graph exploration with a set of $k$ agents. All agents start at a common vertex of an initially unknown graph and need to collectively visit all other vertices. We assume agents are deterministic, vertices are distinguishable, moves are simultaneous, and we allow agents to communicate globally. For this setting, we give the first non-trivial lower bounds that bridge the gap between small ($k \leq \sqrt n$) and large ($k \geq n$) teams of agents. Remarkably, our bounds tightly connect to existing results in both domains. First, we significantly extend a lower bound of $\Omega(\log k / \log\log k)$ by Dynia et al. on the competitive ratio of a collaborative tree exploration strategy to the range $k \leq n \log^c n$ for any $c \in \mathbb{N}$. Second, we provide a tight lower bound on the number of agents needed for any competitive exploration algorithm. In particular, we show that any collaborative tree exploration algorithm with $k = Dn^{1+o(1)}$ agents has a competitive ratio of $\omega(1)$, while Dereniowski et al. gave an algorithm with $k = Dn^{1+\varepsilon}$ agents and competitive ratio $O(1)$, for any $\varepsilon > 0$ and with $D$ denoting the diameter of the graph. Lastly, we show that, for any exploration algorithm using $k = n$ agents, there exist trees of arbitrarily large height $D$ that require $\Omega(D^2)$ rounds, and we provide a simple algorithm that matches this bound for all trees

Optimal online and offline algorithms for robot-assisted restoration of barrier coverage

Cooperation between mobile robots and wireless sensor networks is a line of research that is currently attracting a lot of attention. In this context, we study the following problem of barrier coverage by stationary wireless sensors that are assisted by a mobile robot with the capacity to move sensors. Assume that $n$ sensors are initially arbitrarily distributed on a line segment barrier. Each sensor is said to cover the portion of the barrier that intersects with its sensing area. Owing to incorrect initial position, or the death of some of the sensors, the barrier is not completely covered by the sensors. We employ a mobile robot to move the sensors to final positions on the barrier such that barrier coverage is guaranteed. We seek algorithms that minimize the length of the robot's trajectory, since this allows the restoration of barrier coverage as soon as possible. We give an optimal linear-time offline algorithm that gives a minimum-length trajectory for a robot that starts at one end of the barrier and achieves the restoration of barrier coverage. We also study two different online models: one in which the online robot does not know the length of the barrier in advance, and the other in which the online robot knows the length of the barrier. For the case when the online robot does not know the length of the barrier, we prove a tight bound of $3/2$ on the competitive ratio, and we give a tight lower bound of $5/4$ on the competitive ratio in the other case. Thus for each case we give an optimal online algorithm.Comment: 20 page

Deterministic meeting of sniffing agents in the plane

Two mobile agents, starting at arbitrary, possibly different times from arbitrary locations in the plane, have to meet. Agents are modeled as discs of diameter 1, and meeting occurs when these discs touch. Agents have different labels which are integers from the set of 0 to L-1. Each agent knows L and knows its own label, but not the label of the other agent. Agents are equipped with compasses and have synchronized clocks. They make a series of moves. Each move specifies the direction and the duration of moving. This includes a null move which consists in staying inert for some time, or forever. In a non-null move agents travel at the same constant speed, normalized to 1. We assume that agents have sensors enabling them to estimate the distance from the other agent (defined as the distance between centers of discs), but not the direction towards it. We consider two models of estimation. In both models an agent reads its sensor at the moment of its appearance in the plane and then at the end of each move. This reading (together with the previous ones) determines the decision concerning the next move. In both models the reading of the sensor tells the agent if the other agent is already present. Moreover, in the monotone model, each agent can find out, for any two readings in moments t1 and t2, whether the distance from the other agent at time t1 was smaller, equal or larger than at time t2. In the weaker binary model, each agent can find out, at any reading, whether it is at distance less than \r{ho} or at distance at least \r{ho} from the other agent, for some real \r{ho} > 1 unknown to them. Such distance estimation mechanism can be implemented, e.g., using chemical sensors. Each agent emits some chemical substance (scent), and the sensor of the other agent detects it, i.e., sniffs. The intensity of the scent decreases with the distance.Comment: A preliminary version of this paper appeared in the Proc. 23rd International Colloquium on Structural Information and Communication Complexity (SIROCCO 2016), LNCS 998

Byzantine Gathering in Networks

This paper investigates an open problem introduced in [14]. Two or more mobile agents start from different nodes of a network and have to accomplish the task of gathering which consists in getting all together at the same node at the same time. An adversary chooses the initial nodes of the agents and assigns a different positive integer (called label) to each of them. Initially, each agent knows its label but does not know the labels of the other agents or their positions relative to its own. Agents move in synchronous rounds and can communicate with each other only when located at the same node. Up to f of the agents are Byzantine. A Byzantine agent can choose an arbitrary port when it moves, can convey arbitrary information to other agents and can change its label in every round, in particular by forging the label of another agent or by creating a completely new one. What is the minimum number M of good agents that guarantees deterministic gathering of all of them, with termination? We provide exact answers to this open problem by considering the case when the agents initially know the size of the network and the case when they do not. In the former case, we prove M=f+1 while in the latter, we prove M=f+2. More precisely, for networks of known size, we design a deterministic algorithm gathering all good agents in any network provided that the number of good agents is at least f+1. For networks of unknown size, we also design a deterministic algorithm ensuring the gathering of all good agents in any network but provided that the number of good agents is at least f+2. Both of our algorithms are optimal in terms of required number of good agents, as each of them perfectly matches the respective lower bound on M shown in [14], which is of f+1 when the size of the network is known and of f+2 when it is unknown

Le référentiel taxonomique Florical et les caractéristiques de la flore vasculaire indigène de la Nouvelle-Calédonie

The taxonomic reference base Florical and characteristics of the native vascular flora of New Caledonia. The floristic inventory presented here comprises the evolving computerised database Florical (http://www.botanique.nc/herbier/florical). As of the date of publication, it lists all native vascular plant species (as well as infraspecific taxa) present in the territory of New Caledonia, whether validly published or in press, along with their basionym, organised according to the most recent classifications systems (APG III 2009 for the angiosperms, Smith et at [2006] for the ferns and lycophytes, and Mabberley [2009] for the gymnosperms), accompanied by their status (native or endemic) and the various vegetation types in which they occur. After a brief historical review of our knowledge of New Caledonian botany, the characteristics (richness, composition and endemism) of the different taxonomic groups (ferns and lycophytes, gymnosperms and then angiosperms -mono- and dicotyledons) are analyzed, followed by an assessment of the distribution of these groups among the vegetation types. The vascular flora of New Caledonia is characterised by its high level of richness (3371 species, including 3099 for the flowering plants alone), despite the absence or under-representation of some taxa that are abundantly represented elsewhere in the tropics, and especially by its remarkable distinctiveness (with endemism at the species level reaching 74,7%, and 77.8% for the flowering plants). The flora stands out by the presence of several relictual taxa and a high level of speciation among certain groups, despite the fact that the island was re-colonised relatively recently following the total submersion of its much older basement during the Paleocene and the Oligocene. Details of the measures taken to conserve this extraordinary natural heritage show that only 3.4% of the territory's total surface area is effectively protected. Despite the undeniable progress made in recent years by the authorities concerned, significant work remains to be done, especially in the northern Province

Gathering in Dynamic Rings

The gathering problem requires a set of mobile agents, arbitrarily positioned at different nodes of a network to group within finite time at the same location, not fixed in advanced. The extensive existing literature on this problem shares the same fundamental assumption: the topological structure does not change during the rendezvous or the gathering; this is true also for those investigations that consider faulty nodes. In other words, they only consider static graphs. In this paper we start the investigation of gathering in dynamic graphs, that is networks where the topology changes continuously and at unpredictable locations. We study the feasibility of gathering mobile agents, identical and without explicit communication capabilities, in a dynamic ring of anonymous nodes; the class of dynamics we consider is the classic 1-interval-connectivity. We focus on the impact that factors such as chirality (i.e., a common sense of orientation) and cross detection (i.e., the ability to detect, when traversing an edge, whether some agent is traversing it in the other direction), have on the solvability of the problem. We provide a complete characterization of the classes of initial configurations from which the gathering problem is solvable in presence and in absence of cross detection and of chirality. The feasibility results of the characterization are all constructive: we provide distributed algorithms that allow the agents to gather. In particular, the protocols for gathering with cross detection are time optimal. We also show that cross detection is a powerful computational element. We prove that, without chirality, knowledge of the ring size is strictly more powerful than knowledge of the number of agents; on the other hand, with chirality, knowledge of n can be substituted by knowledge of k, yielding the same classes of feasible initial configurations

Anonymous Graph Exploration with Binoculars

International audienceWe investigate the exploration of networks by a mobile agent. It is long known that, without global information about the graph, it is not possible to make the agent halts after the exploration except if the graph is a tree. We therefore endow the agent with binoculars, a sensing device that can show the local structure of the environment at a constant distance of the agent current location.We show that, with binoculars, it is possible to explore and halt in a large class of non-tree networks. We give a complete characterization of the class of networks that can be explored using binoculars using standard notions of discrete topology. This class is much larger than the class of trees: it contains in particular chordal graphs, plane triangulations and triangulations of the projective plane. Our characterization is constructive, we present an Exploration algorithm that is universal; this algorithm explores any network explorable with binoculars, and never halts in non-explorable networks