1,904 research outputs found
Search on a Line by Byzantine Robots
We consider the problem of fault-tolerant parallel search on an infinite line by n robots. Starting from the origin, the robots are required to find a target at an unknown location. The robots can move with maximum speed 1 and can communicate in wireless mode among themselves. However, among the n robots, there are f robots that exhibit byzantine faults. A faulty robot can fail to report the target even after reaching it, or it can make malicious claims about having found the target when in fact it has not. Given the presence of such faulty robots, the search for the target can only be concluded when the non-faulty robots have sufficient verification that the target has been found. We aim to design algorithms that minimize the value of S_d (n, f), the time to find a target at a distance d from the origin by n robots among which f are faulty. We give several different algorithms whose running time depends on the ratio f/n, the density of faulty robots, and also prove lower bounds. Our algorithms are optimal for some densities of faulty robots
Certified Impossibility Results for Byzantine-Tolerant Mobile Robots
We propose a framework to build formal developments for robot networks using
the COQ proof assistant, to state and to prove formally various properties. We
focus in this paper on impossibility proofs, as it is natural to take advantage
of the COQ higher order calculus to reason about algorithms as abstract
objects. We present in particular formal proofs of two impossibility results
forconvergence of oblivious mobile robots if respectively more than one half
and more than one third of the robots exhibit Byzantine failures, starting from
the original theorems by Bouzid et al.. Thanks to our formalization, the
corresponding COQ developments are quite compact. To our knowledge, these are
the first certified (in the sense of formally proved) impossibility results for
robot networks
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
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 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 at speed is measured as . 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 , and the evacuation time is at most
, where 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 . For the case , we give an
optimal algorithm, and give upper bounds on the energy for the case .
We also consider the problem of minimizing the evacuation time when the
available energy is bounded by . Surprisingly, when is a
constant, independent of the distance of the exit from the origin, we prove
that evacuation is possible in time , and this is optimal up
to a logarithmic factor. When is linear in , 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
Exploring Graphs with Time Constraints by Unreliable Collections of Mobile Robots
A graph environment must be explored by a collection of mobile robots. Some
of the robots, a priori unknown, may turn out to be unreliable. The graph is
weighted and each node is assigned a deadline. The exploration is successful if
each node of the graph is visited before its deadline by a reliable robot. The
edge weight corresponds to the time needed by a robot to traverse the edge.
Given the number of robots which may crash, is it possible to design an
algorithm, which will always guarantee the exploration, independently of the
choice of the subset of unreliable robots by the adversary? We find the optimal
time, during which the graph may be explored. Our approach permits to find the
maximal number of robots, which may turn out to be unreliable, and the graph is
still guaranteed to be explored.
We concentrate on line graphs and rings, for which we give positive results.
We start with the case of the collections involving only reliable robots. We
give algorithms finding optimal times needed for exploration when the robots
are assigned to fixed initial positions as well as when such starting positions
may be determined by the algorithm. We extend our consideration to the case
when some number of robots may be unreliable. Our most surprising result is
that solving the line exploration problem with robots at given positions, which
may involve crash-faulty ones, is NP-hard. The same problem has polynomial
solutions for a ring and for the case when the initial robots' positions on the
line are arbitrary.
The exploration problem is shown to be NP-hard for star graphs, even when the
team consists of only two reliable robots
Dispersion, Capacitated Nodes, and the Power of a Trusted Shepherd
In this paper, we look at and expand the problems of dispersion and Byzantine
dispersion of mobile robots on a graph, introduced by Augustine and
Moses~Jr.~[ICDCN~2018] and by Molla, Mondal, and Moses~Jr.~[ALGOSENSORS~2020],
respectively, to graphs where nodes have variable capacities. We use the idea
of a single shepherd, a more powerful robot that will never act in a Byzantine
manner, to achieve fast Byzantine dispersion, even when other robots may be
strong Byzantine in nature. We also show the benefit of a shepherd for
dispersion on capacitated graphs when no Byzantine robots are present
Evacuation from a Disk for Robots with Asymmetric Communication
We consider evacuation of two robots from an Exit placed at an unknown location on the perimeter of a unit (radius) disk. The robots can move with max speed 1 and start at the center of the disk at the same time. We consider a new communication model, known as the SR model, in which the robots have communication faults as follows: one of the robots is a Sender and can only send wirelessly at any distance, while the other is a Receiver in that it can only receive wirelessly from any distance. The communication status of each robot is known to the other robot. In addition, both robots can exchange messages when they are co-located, which is known as Face-to-Face (F2F) model.
There have been several studies in the literature concerning the evacuation time when both robots may employ either F2F or Wireless (WiFi) communication. The SR communication model diverges from these two in that the two robots themselves have differing communication capabilities. We study the evacuation time, namely the time it takes until the last robot reaches the Exit, and show that the evacuation time in the SR model is strictly between the F2F and the WiFi models. The main part of our technical contribution is also an evacuation algorithm in which two cooperating robots accomplish the task in worst-case time at most ?+2. Interesting features of the proposed algorithm are the asymmetry inherent in the resulting trajectories, as well as that the robots do not move at full speed for the entire duration of their trajectories
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
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