144 research outputs found
Minimal chordal sense of direction and circulant graphs
A sense of direction is an edge labeling on graphs that follows a globally
consistent scheme and is known to considerably reduce the complexity of several
distributed problems. In this paper, we study a particular instance of sense of
direction, called a chordal sense of direction (CSD). In special, we identify
the class of k-regular graphs that admit a CSD with exactly k labels (a minimal
CSD). We prove that connected graphs in this class are Hamiltonian and that the
class is equivalent to that of circulant graphs, presenting an efficient
(polynomial-time) way of recognizing it when the graphs' degree k is fixed
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
Shape formation by programmable particles
Shape formation (or pattern formation) is a basic distributed problem for systems of computational mobile entities. Intensively studied for systems of autonomous mobile robots, it has recently been investigated in the realm of programmable matter, where entities are assumed to be small and with severely limited capabilities. Namely, it has been studied in the geometric Amoebot model, where the anonymous entities, called particles, operate on a hexagonal tessellation of the plane and have limited computational power (they have constant memory), strictly local interaction and communication capabilities (only with particles in neighboring nodes of the grid), and limited motorial capabilities (from a grid node to an empty neighboring node); their activation is controlled by an adversarial scheduler. Recent investigations have shown how, starting from a well-structured configuration in which the particles form a (not necessarily complete) triangle, the particles can form a large class of shapes. This result has been established under several assumptions: agreement on the clockwise direction (i.e., chirality), a sequential activation schedule, and randomization (i.e., particles can flip coins to elect a leader). In this paper we provide a characterization of which shapes can be formed deterministically starting from any simply connected initial configuration of n particles. The characterization is constructive: we provide a universal shape formation algorithm that, for each feasible pair of shapes (S0, SF), allows the particles to form the final shape SF (given in input) starting from the initial shape S0, unknown to the particles. The final configuration will be an appropriate scaled-up copy of SF depending on n. If randomization is allowed, then any input shape can be formed from any initial (simply connected) shape by our algorithm, provided that there are enough particles. Our algorithm works without chirality, proving that chirality is computationally irrelevant for shape formation. Furthermore, it works under a strong adversarial scheduler, not necessarily sequential. We also consider the complexity of shape formation both in terms of the number of rounds and the total number of moves performed by the particles executing a universal shape formation algorithm. We prove that our solution has a complexity of O(n2) rounds and moves: this number of moves is also asymptotically worst-case optimal
Robots with Lights: Overcoming Obstructed Visibility Without Colliding
Robots with lights is a model of autonomous mobile computational entities
operating in the plane in Look-Compute-Move cycles: each agent has an
externally visible light which can assume colors from a fixed set; the lights
are persistent (i.e., the color is not erased at the end of a cycle), but
otherwise the agents are oblivious. The investigation of computability in this
model, initially suggested by Peleg, is under way, and several results have
been recently established. In these investigations, however, an agent is
assumed to be capable to see through another agent. In this paper we start the
study of computing when visibility is obstructable, and investigate the most
basic problem for this setting, Complete Visibility: The agents must reach
within finite time a configuration where they can all see each other and
terminate. We do not make any assumption on a-priori knowledge of the number of
agents, on rigidity of movements nor on chirality. The local coordinate system
of an agent may change at each activation. Also, by definition of lights, an
agent can communicate and remember only a constant number of bits in each
cycle. In spite of these weak conditions, we prove that Complete Visibility is
always solvable, even in the asynchronous setting, without collisions and using
a small constant number of colors. The proof is constructive. We also show how
to extend our protocol for Complete Visibility so that, with the same number of
colors, the agents solve the (non-uniform) Circle Formation problem with
obstructed visibility
Parallel Search with no Coordination
We consider a parallel version of a classical Bayesian search problem.
agents are looking for a treasure that is placed in one of the boxes indexed by
according to a known distribution . The aim is to minimize
the expected time until the first agent finds it. Searchers run in parallel
where at each time step each searcher can "peek" into a box. A basic family of
algorithms which are inherently robust is \emph{non-coordinating} algorithms.
Such algorithms act independently at each searcher, differing only by their
probabilistic choices. We are interested in the price incurred by employing
such algorithms when compared with the case of full coordination. We first show
that there exists a non-coordination algorithm, that knowing only the relative
likelihood of boxes according to , has expected running time of at most
, where is the expected running time of the best
fully coordinated algorithm. This result is obtained by applying a refined
version of the main algorithm suggested by Fraigniaud, Korman and Rodeh in
STOC'16, which was designed for the context of linear parallel search.We then
describe an optimal non-coordinating algorithm for the case where the
distribution is known. The running time of this algorithm is difficult to
analyse in general, but we calculate it for several examples. In the case where
is uniform over a finite set of boxes, then the algorithm just checks boxes
uniformly at random among all non-checked boxes and is essentially times
worse than the coordinating algorithm.We also show simple algorithms for Pareto
distributions over boxes. That is, in the case where for
, we suggest the following algorithm: at step choose uniformly
from the boxes unchecked in ,
where . It turns out this algorithm is asymptotically
optimal, and runs about times worse than the case of full coordination
Gathering Anonymous, Oblivious Robots on a Grid
We consider a swarm of 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
rounds and works in the Euclidean plane. The underlying time
model for the algorithm is the fully synchronous 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 .
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 time
bound in the fully synchronous 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
square, because in such configurations cannot be
solved
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 , the rendezvous time can be
exponential in 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 and the size of the smaller of the two agent labels . Our algorithm has a time complexity of
and we show an almost matching lower bound of
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
Mutual visibility by luminous robots without collisions
We consider the Mutual Visibility problem for anonymous dimensionless robots with obstructed visibility moving in a plane: starting from distinct locations, the robots must reach, without colliding, a configuration where no three of them are collinear. We study this problem in the luminous robots model, in which each robot has a visible light that can assume colors from a fixed set. Among other results, we prove that Mutual Visibility can be solved in SSynch with 2 colors and in ASynch with 3 colors. If an adversary can interrupt and stop a robot moving to its computed destination, Mutual Visibility is still solvable in SSynch with 3 colors and, if the robots agree on the direction of one axis, also in ASynch. As a byproduct, we provide the first obstructed-visibility solutions to two classical problems for oblivious robots: collision-less convergence to a point (also known as near-gathering) and circle formation
Occlusal traits in children with neurofibromatosis type 1
Literature is poor of data about the occlusion in children affected by neurofibromatosis type 1 (NF1). This case-control study investigated the occlusal traits in a group of children with NF1
- …