Time-Energy Tradeoffs for Evacuation by Two Robots in the Wireless Model

Two robots stand at the origin of the infinite line and are tasked with searching collaboratively for an exit at an unknown location on the line. They can travel at maximum speed $b$ and can change speed or direction at any time. The two robots can communicate with each other at any distance and at any time. The task is completed when the last robot arrives at the exit and evacuates. We study time-energy tradeoffs for the above evacuation problem. The evacuation time is the time it takes the last robot to reach the exit. The energy it takes for a robot to travel a distance $x$ at speed $s$ is measured as $xs^2$. The total and makespan evacuation energies are respectively the sum and maximum of the energy consumption of the two robots while executing the evacuation algorithm. Assuming that the maximum speed is $b$, and the evacuation time is at most $cd$, where $d$ is the distance of the exit from the origin, we study the problem of minimizing the total energy consumption of the robots. We prove that the problem is solvable only for $bc \geq 3$. For the case $bc=3$, we give an optimal algorithm, and give upper bounds on the energy for the case $bc>3$. We also consider the problem of minimizing the evacuation time when the available energy is bounded by $\Delta$. Surprisingly, when $\Delta$ is a constant, independent of the distance $d$ of the exit from the origin, we prove that evacuation is possible in time $O(d^{3/2}\log d)$, and this is optimal up to a logarithmic factor. When $\Delta$ is linear in $d$, we give upper bounds on the evacuation time.Comment: This is the full version of the paper with the same title which will appear in the proceedings of the 26th International Colloquium on Structural Information and Communication Complexity (SIROCCO'19) L'Aquila, Italy during July 1-4, 201

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

Evacuating Two Robots from a Disk: A Second Cut

We present an improved algorithm for the problem of evacuating two robots from the unit disk via an unknown exit on the boundary. Robots start at the center of the disk, move at unit speed, and can only communicate locally. Our algorithm improves previous results by Brandt et al. [CIAC'17] by introducing a second detour through the interior of the disk. This allows for an improved evacuation time of $5.6234$. The best known lower bound of $5.255$ was shown by Czyzowicz et al. [CIAC'15].Comment: 19 pages, 5 figures. This is the full version of the paper with the same title accepted in the 26th International Colloquium on Structural Information and Communication Complexity (SIROCCO'19

Revisiting the Problem of Searching on a Line

We revisit the problem of searching for a target at an unknown location on a line when given upper and lower bounds on the distance D that separates the initial position of the searcher from the target. Prior to this work, only asymptotic bounds were known for the optimal competitive ratio achievable by any search strategy in the worst case. We present the first tight bounds on the exact optimal competitive ratio achievable, parameterized in terms of the given bounds on D, along with an optimal search strategy that achieves this competitive ratio. We prove that this optimal strategy is unique. We characterize the conditions under which an optimal strategy can be computed exactly and, when it cannot, we explain how numerical methods can be used efficiently. In addition, we answer several related open questions, including the maximal reach problem, and we discuss how to generalize these results to m rays, for any m >= 2

NF-κB: A lesson in family values

A set of mobile robots (represented as points) is distributed in the Cartesian plane. The collection contains an unknown subset of byzantine robots which are indistinguishable from the reliable ones. The reliable robots need to gather, i.e., arrive to a configuration in which at the same time, all of them occupy the same point on the plane. The robots are equipped with GPS devices and at the beginning of the gathering process they communicate the Cartesian coordinates of their respective positions to the central authority. On the basis of this information, without the knowledge of which robots are faulty, the central authority designs a trajectory for every robot. The central authority aims to provide the trajectories which result in the shortest possible gathering time of the healthy robots. The efficiency of a gathering strategy is measured by its competitive ratio, i.e., the maximal ratio between the time required for gathering achieved by the given trajectories and the optimal time required for gathering in the offline case, i.e., when the faulty robots are known to the central authority in advance. The role of the byzantine robots, controlled by the adversary, is to act so that the gathering is delayed and the resulting competitive ratio is maximized. The objective of our paper is to propose efficient algorithms when the central authority is aware of an upper bound on the number of byzantine robots. We give optimal algorithms for collections of robots known to contain at most one faulty robot. When the proportion of byzantine robots is known to be less than one half or one third, we provide algorithms with small constant competitive ratios. We also propose algorithms with bounded competitive ratio in the case where the proportion of faulty robots is arbitrary

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

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

Consistency of service composition

We address the problem of ensuring that, when an application executing a service binds to a service that matches required functional properties, both the application and the service can work together, i.e., their composition is consistent. Our approach is based on a component algebra for service-oriented computing in which the configurations of applications and of services are modelled as asynchronous relational nets typed with logical interfaces. The techniques that we propose allow for the consistency of composition to be guaranteed based on properties of service orchestrations (implementations) and interfaces that can be checked at design time, which is essential for supporting the levels of dynamicity required by run-time service binding. © 2012 Springer-Verlag Berlin Heidelberg

Recurrent and High‐frequency Use of the Emergency Department by Pediatric Patients

Objectives The authors sought to describe the epidemiology of and risk factors for recurrent and high‐frequency use of the emergency department (ED) by children. Methods This was a retrospective cohort study using a database of children aged 0 to 17 years, inclusive, presenting to 22 EDs of the Pediatric Emergency Care Applied Research Network (PECARN) during 2007, with 12‐month follow‐up after each index visit. ED diagnoses for each visit were categorized as trauma, acute medical, or chronic medical conditions. Recurrent visits were defined as any repeat visit; high‐frequency use was defined as four or more recurrent visits. Generalized estimating equations (GEEs) were used to measure the strength of associations between patient and visit characteristics and recurrent ED use. Results A total of 695,188 unique children had at least one ED visit each in 2007, with 455,588 recurrent ED visits in the 12 months following the index visits. Sixty‐four percent of patients had no recurrent visits, 20% had one, 8% had two, 4% had three, and 4% had four or more recurrent visits. Acute medical diagnoses accounted for most visits regardless of the number of recurrent visits. As the number of recurrent visits per patient rose, chronic diseases were increasingly represented, with asthma being the most common ED diagnosis. Trauma‐related diagnoses were more common among patients without recurrent visits than among those with high‐frequency recurrent visits (28% vs. 9%; p < 0.001). High‐frequency recurrent visits were more often within the highest severity score classifications. In multivariable analysis, recurrent visits were associated with younger age, black or Hispanic race or ethnicity, and public health insurance. Conclusions Risk factors for recurrent ED use by children include age, race and ethnicity, and insurance status. Although asthma plays an important role in recurrent ED use, acute illnesses account for the majority of recurrent ED visits. Resumen Objetivos Describir la epidemiología y los factores de riesgo de revista e hiperfrecuentación del servicio de urgencias (SU) por parte de los pacientes pediátricos. Metodología Estudio de cohorte retrospectivo mediante una base de datos de niños entre 0 y 17 años inclusive, que acudieron a 22 SU de la Pediatric Emergency Care Applied Research Network durante 2007, con un seguimiento de 12 meses tras cada visita índice. Los diagnósticos del SU de cada visita se clasificaron como traumatológico, médico agudo o enfermedades médicas crónicas. Las revisitas se definieron como cualquier visita repetida; la hiperfrecuentación se definió como cuatro o más revisitas. Se utilizaron ecuaciones de estimación generalizada para medir la fuerza de las asociaciones entre las características al paciente y la visita y la revisita del SU. Resultados Un total de 695.188 niños tuvieron al menos una visita al SU en 2007, con 455.588 revisitas al SU en los 12 meses tras las visitas índice. Un 64% de los pacientes no tuvieron revisitas, un 20% tuvo una, un 8% tuvo dos, un 4% tuvo tres y un 4% tuvo cuatro o más revisitas. Los diagnósticos médicos agudos representan la mayoría de las visitas, con independencia del número de revisitas. A medida que el número de revisitas por paciente aumentaba, las enfermedades crónicas estaban más representadas, y el asma fue el diagnóstico más común en el SU. Los diagnósticos relacionados con lo traumatológico fueron más frecuentes entre los pacientes sin revisitas que entre aquéllos con hiperfrecuentación (28% vs. 9%; p < 0,001). La alta frecuencia de revisitas fue más frecuente en las clasificaciones de gravedad más altas. En el análisis multivariable, las revisitas se asociaron con una edad más joven, raza o etnia negra o hispana, y la tenencia de un seguro de salud público. Conclusiones Los factores de riesgo para la revisita al SU por los niños incluyen la edad, la raza o etnia, y el tipo de seguro médico. Aunque el asma juega un papel importante en la revisita al SU, las enfermedades agudas representan la mayoría de la revistas al SU.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106853/1/acem12347.pd

Variation in Ancillary Testing among Pediatric Asthma Patients Seen in Emergency Departments

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72605/1/j.aem.2007.01.016.pd