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

Gathering Anonymous, Oblivious Robots on a Grid

We consider a swarm of $n$ autonomous mobile robots, distributed on a 2-dimensional grid. A basic task for such a swarm is the gathering process: All robots have to gather at one (not predefined) place. A common local model for extremely simple robots is the following: The robots do not have a common compass, only have a constant viewing radius, are autonomous and indistinguishable, can move at most a constant distance in each step, cannot communicate, are oblivious and do not have flags or states. The only gathering algorithm under this robot model, with known runtime bounds, needs $\mathcal{O}(n^2)$ rounds and works in the Euclidean plane. The underlying time model for the algorithm is the fully synchronous $\mathcal{FSYNC}$ model. On the other side, in the case of the 2-dimensional grid, the only known gathering algorithms for the same time and a similar local model additionally require a constant memory, states and "flags" to communicate these states to neighbors in viewing range. They gather in time $\mathcal{O}(n)$. In this paper we contribute the (to the best of our knowledge) first gathering algorithm on the grid that works under the same simple local model as the above mentioned Euclidean plane strategy, i.e., without memory (oblivious), "flags" and states. We prove its correctness and an $\mathcal{O}(n^2)$ time bound in the fully synchronous $\mathcal{FSYNC}$ time model. This time bound matches the time bound of the best known algorithm for the Euclidean plane mentioned above. We say gathering is done if all robots are located within a $2\times 2$ square, because in $\mathcal{FSYNC}$ such configurations cannot be solved

Rendezvous on a Line by Location-Aware Robots Despite the Presence of Byzantine Faults

A set of mobile robots is placed at points of an infinite line. The robots are equipped with GPS devices and they may communicate their positions on the line to a central authority. The collection contains an unknown subset of "spies", i.e., byzantine robots, which are indistinguishable from the non-faulty ones. The set of the non-faulty robots need to rendezvous in the shortest possible time in order to perform some task, while the byzantine robots may try to delay their rendezvous for as long as possible. The problem facing a central authority is to determine trajectories for all robots so as to minimize the time until the non-faulty robots have rendezvoused. The trajectories must be determined without knowledge of which robots are faulty. Our goal is to minimize the competitive ratio between the time required to achieve the first rendezvous of the non-faulty robots and the time required for such a rendezvous to occur under the assumption that the faulty robots are known at the start. We provide a bounded competitive ratio algorithm, where the central authority is informed only of the set of initial robot positions, without knowing which ones or how many of them are faulty. When an upper bound on the number of byzantine robots is known to the central authority, we provide algorithms with better competitive ratios. In some instances we are able to show these algorithms are optimal

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

Constitutive innate immunity of tropical House Wrens varies with season and reproductive activity

In lowland Neotropical regions, where air temperature and day length remain relatively constant year round, seasonality is determined primarily by changes in rainfall. The wet season triggers the start of breeding for many Neotropical birds but also alters the antigenic environment, likely increasing the risk of disease transmission. We explored 2 hypotheses about temporal variation in constitutive innate immunity of a Neotropical bird, the House Wren (Troglodytes aedon). The antigen response hypothesis proposes that Neotropical wrens upregulate their immune function in the wet season either in anticipation of or in response to vectors that become more prevalent. The resource constraint hypothesis proposes that during periods of putative high resource demand, such as when parents are feeding young, immune function should be compromised and downregulated. Controlling for reproductive stage, we found that microbicidal capacity of blood against Escherichia coli was higher in the wet than the dry season, consistent with the antigen response hypothesis. Phagocytosis of E. coli and Staphylococcus aureus did not differ between wet and dry seasons. Microbicidal capacity and H/L ratio of tropical House Wrens did not vary among reproductive stages, and our data offered no support for the idea that immune function is compromised during the period when parents are feeding young

Effect of transport length on in vivo oxidative status and breast meat characteristics in outdoor-reared chicken genotypes

The aim of the study was to evaluate the effect of transport length on in vivo oxidative status and breast meat characteristics in two chicken genotypes reared under free range conditions. A total of 200 male chicks, 100 from fast-growing (Ross 308) and 100 from medium-growing (Naked Neck) strain were used. Fifty-six of these, 28 for genotype, before slaughtering, were randomly allocated to 2 pre-slaughter conditions: absence (0 h) or 4 h of transport. The transport length significantly affected the in vivo oxidative status of broiler greatly reducing the α and δ-tocopherol, retinol and lutein + zeaxanthin content of plasma, and increased the oxidative stress (thiobarbituric acid reactive substances, TBARS) in both strains. Concerning meat quality, the pH (0, 2 and 24 h post-mortem) of breast muscles of chickens transported for 4 h, showed higher values, and respect to strains, Naked Neck had lower values. The pH values were negatively correlated with the lightness (2–24 h) and the shear force of meat. The transport length significantly affected the fatty acid profile of breast muscle, with a decrease in polyunsaturated fatty acids and an increase in TBARS value. Even the antioxidants content of breast was reduced by chicken transport (α-tocotrienol, α-, δ-tocopherol and lutein + zeaxanthin), especially in Naked Neck birds. In conclusion, the results indicate that transport for 4 h prior to slaughter, negatively affect the meat quality of poultry. Slow-growing chickens seem more sensible to stress transport due to the higher kinetic behaviour of these strains

Almost optimal asynchronous rendezvous in infinite multidimensional grids

Two anonymous mobile agents (robots) moving in an asynchronous manner have to meet in an infinite grid of dimension δ> 0, starting from two arbitrary positions at distance at most d. Since the problem is clearly infeasible in such general setting, we assume that the grid is embedded in a δ-dimensional Euclidean space and that each agent knows the Cartesian coordinates of its own initial position (but not the one of the other agent). We design an algorithm permitting the agents to meet after traversing a trajectory of length O(d δ polylog d). This bound for the case of 2d-grids subsumes the main result of [12]. The algorithm is almost optimal, since the Ω(d δ) lower bound is straightforward. Further, we apply our rendezvous method to the following network design problem. The ports of the δ-dimensional grid have to be set such that two anonymous agents starting at distance at most d from each other will always meet, moving in an asynchronous manner, after traversing a O(d δ polylog d) length trajectory. We can also apply our method to a version of the geometric rendezvous problem. Two anonymous agents move asynchronously in the δ-dimensional Euclidean space. The agents have the radii of visibility of r1 and r2, respectively. Each agent knows only its own initial position and its own radius of visibility. The agents meet when one agent is visible to the other one. We propose an algorithm designing the trajectory of each agent, so that they always meet after traveling a total distance of O( ( d)), where r = min(r1, r2) and for r ≥ 1. r)δpolylog ( d r

How to gather asynchronous oblivious robots on anonymous rings

A set of robots arbitrarily placed on the nodes of an anonymous graph have to meet at one common node and remain in there. This problem is known in the literature as the \emph{gathering}. Robots operate in Look-Compute-Move cycles; in one cycle, a robot takes a snapshot of the current configuration (Look), decides whether to stay idle or to move to one of its neighbors (Compute), and in the latter case makes the computed move instantaneously (Move). Cycles are performed asynchronously for each robot. Moreover, each robot is empowered by the so called \emph{multiplicity detection} capability, that is, a robot is able to detect during its Look operation whether a node is empty, or occupied by one robot, or occupied by an undefined number of robots greater than one. The described problem has been extensively studied during the last years. However, the known solutions work only for specific initial configurations and leave some open cases. In this paper, we provide an algorithm which solves the general problem, and is able to detect all the non-gatherable configurations. It is worth noting that our new algorithm makes use of a unified and general strategy for any initial configuration.Un ensemble de robots placés arbitrairement sur les sommets d'un graphe anonyme doivent se rencontrer sur un sommet commun. Ce problème est connu dans la littérature comme le \emph{gathering}. Les robots utilisent des cycles Look-Compute-Move; dans un cycle, un robot prend un instantané de la configuration actuelle (Look), décide de rester inactif ou de se déplacer sur l'un de ses voisins (Compute), et dans ce cas, fait le déplacement (Move). Les cycles sont exécutés de manière asynchrone pour chaque robot. Chaque robot possède la capacité de \emph{multiplicity detection}: un robot est capable de détecter au cours de son opération Look si un sommet est vide, occupé par un robot, ou occupé par un nombre indéfini de robots. Le problème décrit a été largement étudié au cours des dernières années. Toutefois, les solutions connues ne sont valides que pour des configurations initiales spécifiques. Nous fournissons un algorithme qui résout le problème général, et est capable de détecter toutes les configurations initiales pour lesquelles le problème est impossible. Il est intéressant de noter que notre nouvel algorithme utilise une stratégie unifiée et générale pour chaque configuration initiale

Gathering of Robots on Anonymous Grids without multiplicity detection

International audienceThe paper studies the gathering problem on grid networks. A team of robots placed at different nodes of a grid, have to meet at some node and remain there. Robots operate in Look-Compute-Move cycles; in one cycle, a robot perceives the current configuration in terms of occupied nodes (Look), decides whether to move towards one of its neighbors (Compute), and in the positive case makes the computed move instantaneously (Move). Cycles are performed asynchronously for each robot. The problem has been deeply studied for the case of ring networks. However, the known techniques used on rings cannot be directly extended to grids. Moreover, on rings, another assumption concerning the so-called multiplicity detection capability was required in order to accomplish the gathering task. That is, a robot is able to detect during its Look operation whether a node is empty, or occupied by one robot, or occupied by an undefined number of robots greater than one. In this paper, we provide a full characterization about gatherable configurations for grids. In particular, we show that in this case, the multiplicity detection is not required. Very interestingly, sometimes the problem appears trivial, as it is for the case of grids with both odd sides, while sometimes the involved techniques require new insights with respect to the well-studied ring case. Moreover, our results reveal the importance of a structure like the grid that allows to overcome the multiplicity detection with respect to the ring case