A unified approach for Gathering and Exclusive Searching on rings under weak assumptions

International audienceConsider a set of mobile robots placed on distinct nodes of a discrete, anonymous, and bidirectional ring. Asynchronously, each robot takes a snapshot of the ring, determining the size of the ring and which nodes are either occupied by robots or empty. Based on the observed configuration, it decides whether to move to one of its adjacent nodes or not. In the first case, it performs the computed move, eventually. This model of computation is known as Look-Compute-Move. The computation depends on the required task. In this paper, we solve both the well-known Gathering and Exclusive Searching tasks. In the former problem, all robots must simultaneously occupy the same node, eventually. In the latter problem, the aim is to clear all edges of the graph. An edge is cleared if it is traversed by a robot or if both its endpoints are occupied. We consider the exclusive searching where it must be ensured that two robots never occupy the same node. Moreover, since the robots are oblivious, the clearing is perpetual, i.e., the ring is cleared infinitely often.In the literature, most contributions are restricted to a subset of initial configurations. Here, we design two different algorithms and provide acharacterization of the initial configurations that permit the resolution of the problems under very weak assumptions. More precisely, we provide a full characterization (except for few pathological cases) of the initial configurations for which gathering can be solved. The algorithm relies on thenecessary assumption of the local-weak multiplicity detection. This means that during the Look phase a robot detects also whether the node it occupies is occupied by other robots, without acquiring the exact number.For the exclusive searching, we characterize all (except for few pathological cases) aperiodic configurations from which the problem is feasible. Wealso provide some impossibility results for the case of periodic configurations

Robot Searching and Gathering on Rings under Minimal Assumptions

Consider a set of mobile robots with minimal capabilities placed over distinct nodes of a discrete anonymous ring. They operate on the basis of the so called \emph{Look}-\emph{Compute}-\emph{Move} cycle. Asynchronously, each robot takes a snapshot of the ring, determining which nodes are either occupied by robots or empty. Based on the observed configuration, it decides whether to move to one of its adjacent nodes or to stay idle. In the first case, it performs the computed move, eventually. The computation also depends on the required task. In this paper, we solve both the well-known \emph{Searching} and \emph{Gathering} tasks. In the literature, most contributions are restricted to a subset of initial configurations. Here, we design two different algorithms and provide a full characterization of the initial configurations that permit the resolution of the problems under minimal assumptions.Nous considérons un ensemble de robots mobiles qui sont placés sur distincts sommets d'un réseau en anneau. Le réseau est anonyme et les robots ont des aptitudes minimales. Ils opérent par des cycles \emph{Observer}-\emph{Calculer}-\emph{Bouger}. Nous résolvons les problémes de la réunion et du nettoyage de graphe dans ce modéle

Randomized Byzantine Gathering in Rings

We study the problem of gathering k anonymous mobile agents on a ring with n nodes. Importantly, f out of the k anonymous agents are Byzantine. The agents operate synchronously and in an autonomous fashion. In each round, each agent can communicate with other agents co-located with it by broadcasting a message. After receiving all the messages, each agent decides to either move to a neighbouring node or stay put. We begin with the k agents placed arbitrarily on the ring, and the task is to gather all the good agents in a single node. The task is made harder by the presence of Byzantine agents, which are controlled by a single Byzantine adversary. Byzantine agents can deviate arbitrarily from the protocol. The Byzantine adversary is computationally unbounded. Additionally, the Byzantine adversary is adaptive in the sense that it can capitalize on information gained over time (including the current round) to choreograph the actions of Byzantine agents. Specifically, the entire state of the system, which includes messages sent by all the agents and any random bits generated by the agents, is known to the Byzantine adversary before all the agents move. Thus the Byzantine adversary can compute the positioning of good agents across the ring and choreograph the movement of Byzantine agents accordingly. Moreover, we consider two settings: standard and visual tracking setting. With visual tracking, agents have the ability to track other agents that are moving along with them. In the standard setting, agents do not have such an ability. In the standard setting we can achieve gathering in ?(nlog nlog k) rounds with high probability and can handle ?(k/(log k)) number of Byzantine agents. With visual tracking, we can achieve gathering faster in ?(n log n) rounds whp and can handle any constant fraction of the total number of agents being Byzantine

Optimal torus exploration by oblivious robots

International audienceWe deal with a team of autonomous robots that are endowed with motion actuators and visibility sensors. Those robots are weak and evolve in a discrete environment. By weak, we mean that they are anonymous, uniform, unable to explicitly communicate, and oblivious. We first show that it is impossible to solve the terminating exploration of a simple torus of arbitrary size with less than 4 or 5 such robots, respectively depending on whether the algorithm is probabilistic or deterministic. Next, we propose in the SSYNC model a probabilistic solution for the terminating exploration of torus-shaped networks of size ℓ×L, where 7≤ℓ≤L, by a team of 4 such weak robots. So, this algorithm is optimal w.r.t. the number of robots

Asynchronous Gathering in a Torus

We consider the gathering problem for asynchronous and oblivious robots that cannot communicate explicitly with each other but are endowed with visibility sensors that allow them to see the positions of the other robots. Most investigations on the gathering problem on the discrete universe are done on ring shaped networks due to the number of symmetric configurations. We extend in this paper the study of the gathering problem on torus shaped networks assuming robots endowed with local weak multiplicity detection. That is, robots cannot make the difference between nodes occupied by only one robot from those occupied by more than one robot unless it is their current node. Consequently, solutions based on creating a single multiplicity node as a landmark for the gathering cannot be used. We present in this paper a deterministic algorithm that solves the gathering problem starting from any rigid configuration on an asymmetric unoriented torus shaped network

On the Synthesis of Mobile Robots Algorithms: the Case of Ring Gathering

International audienceRecent advances in Distributed Computing highlight models and algorithms for autonomous swarms of mobile robots that self-organize and cooperate to solve global objectives. The overwhelming majority of works so far considers handmade algorithms and correctness proofs.This paper is the first to propose a formal framework to automatically design distributed algorithms that are dedicated to autonomous mobile robots evolving in a discrete space. As a case study, we consider the problem of gathering all robots at a particular location, not known beforehand. Our contribution is threefold. First, we propose an encoding of the gathering problem as a reachability game. Then, we automatically generate an optimal distributed algorithm for three robots evolving on a fixed size uniform ring. Finally, we prove by induction that the generated algorithm is also correct for any ring size except when an impossibility result holds (that is, when the number of robots divides the ring size)

Using crowdsourced geospatial data to aid in nuclear proliferation monitoring

In 2014, a Defense Science Board Task Force was convened in order to assess and explore new technologies that would aid in nuclear proliferation monitoring. One of their recommendations was for the director of National Intelligence to explore ways that crowdsourced geospatial imagery technologies could aid existing governmental efforts. Our research builds directly on this recommendation and provides feedback on some of the most successful examples of crowdsourced geospatial data (CGD). As of 2016, Special Operations Command (SOCOM) has assumed the new role of becoming the primary U.S. agency responsible for counter-proliferation. Historically, this institution has always been reliant upon other organizations for the execution of its myriad of mission sets. SOCOM's unique ability to build relationships makes it particularly suited to the task of harnessing CGD technologies and employing them in the capacity that our research recommends. Furthermore, CGD is a low cost, high impact tool that is already being employed by commercial companies and non-profit groups around the world. By employing CGD, a wider whole-of-government effort can be created that provides a long term, cohesive engagement plan for facilitating a multi-faceted nuclear proliferation monitoring process.http://archive.org/details/usingcrowdsource1094551570Major, United States ArmyMajor, United States ArmyApproved for public release; distribution is unlimited

Parameterized Analysis of the Cops and Robber Game

Pursuit-evasion games have been intensively studied for several decades due to their numerous applications in artificial intelligence, robot motion planning, database theory, distributed computing, and algorithmic theory. Cops and Robber (CnR) is one of the most well-known pursuit-evasion games played on graphs, where multiple cops pursue a single robber. The aim is to compute the cop number of a graph, k, which is the minimum number of cops that ensures the capture of the robber. From the viewpoint of parameterized complexity, CnR is W[2]-hard parameterized by k [Fomin et al., TCS, 2010]. Thus, we study structural parameters of the input graph. We begin with the vertex cover number (vcn). First, we establish that k ? vcn/3+1. Second, we prove that CnR parameterized by vcn is FPT by designing an exponential kernel. We complement this result by showing that it is unlikely for CnR parameterized by vcn to admit a polynomial compression. We extend our exponential kernels to the parameters cluster vertex deletion number and deletion to stars number, and design a linear vertex kernel for neighborhood diversity. Additionally, we extend all of our results to several well-studied variations of CnR