249 research outputs found
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 . The best known lower bound of 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
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
Collaborative Delivery with Energy-Constrained Mobile Robots
We consider the problem of collectively delivering some message from a
specified source to a designated target location in a graph, using multiple
mobile agents. Each agent has a limited energy which constrains the distance it
can move. Hence multiple agents need to collaborate to move the message, each
agent handing over the message to the next agent to carry it forward. Given the
positions of the agents in the graph and their respective budgets, the problem
of finding a feasible movement schedule for the agents can be challenging. We
consider two variants of the problem: in non-returning delivery, the agents can
stop anywhere; whereas in returning delivery, each agent needs to return to its
starting location, a variant which has not been studied before.
We first provide a polynomial-time algorithm for returning delivery on trees,
which is in contrast to the known (weak) NP-hardness of the non-returning
version. In addition, we give resource-augmented algorithms for returning
delivery in general graphs. Finally, we give tight lower bounds on the required
resource augmentation for both variants of the problem. In this sense, our
results close the gap left by previous research.Comment: 19 pages. An extended abstract of this paper was published at the
23rd International Colloquium on Structural Information and Communication
Complexity 2016, SIROCCO'1
Single-photon entanglement generation by wavefront shaping in a multiple-scattering medium
We demonstrate the control of entanglement of a single photon between several
spatial modes propagating through a strongly scattering medium. Measurement of
the scattering matrix allows the wavefront of the photon to be shaped to
compensate the distortions induced by multiple scattering events. The photon
can thus be directed coherently to a single or multi-mode output. Using this
approach we show how entanglement across different modes can be manipulated
despite the enormous wavefront disturbance caused by the scattering medium.Comment: 4 pages, 3 figures, reference adde
A general lower bound for collaborative tree exploration
We consider collaborative graph exploration with a set of agents. All
agents start at a common vertex of an initially unknown graph and need to
collectively visit all other vertices. We assume agents are deterministic,
vertices are distinguishable, moves are simultaneous, and we allow agents to
communicate globally. For this setting, we give the first non-trivial lower
bounds that bridge the gap between small () and large () teams of agents. Remarkably, our bounds tightly connect to existing results
in both domains.
First, we significantly extend a lower bound of
by Dynia et al. on the competitive ratio of a collaborative tree exploration
strategy to the range for any . Second,
we provide a tight lower bound on the number of agents needed for any
competitive exploration algorithm. In particular, we show that any
collaborative tree exploration algorithm with agents has a
competitive ratio of , while Dereniowski et al. gave an algorithm
with agents and competitive ratio , for any
and with denoting the diameter of the graph. Lastly, we
show that, for any exploration algorithm using agents, there exist
trees of arbitrarily large height that require rounds, and we
provide a simple algorithm that matches this bound for all trees
Laser-induced electron emission from a tungsten nanotip: identifying above threshold photoemission using energy-resolved laser power dependencies
We present an experiment studying the interaction of a strongly focused 25 fs
laser pulse with a tungsten nanotip, investigating the different regimes of
laser-induced electron emission. We study the dependence of the electron yield
with respect to the static electric field applied to the tip. Photoelectron
spectra are recorded using a retarding field spectrometer and peaks separated
by the photon energy are observed with a 45 % contrast. They are a clear
signature of above threshold photoemission (ATP), and are confirmed by
extensive spectrally resolved studies of the laser power dependence.
Understanding these mechanisms opens the route to control experiment in the
strong-field regime on nanoscale objects.Comment: 9 pages, 6 figure
Node Labels in Local Decision
The role of unique node identifiers in network computing is well understood
as far as symmetry breaking is concerned. However, the unique identifiers also
leak information about the computing environment - in particular, they provide
some nodes with information related to the size of the network. It was recently
proved that in the context of local decision, there are some decision problems
such that (1) they cannot be solved without unique identifiers, and (2) unique
node identifiers leak a sufficient amount of information such that the problem
becomes solvable (PODC 2013).
In this work we give study what is the minimal amount of information that we
need to leak from the environment to the nodes in order to solve local decision
problems. Our key results are related to scalar oracles that, for any given
, provide a multiset of labels; then the adversary assigns the
labels to the nodes in the network. This is a direct generalisation of the
usual assumption of unique node identifiers. We give a complete
characterisation of the weakest oracle that leaks at least as much information
as the unique identifiers.
Our main result is the following dichotomy: we classify scalar oracles as
large and small, depending on their asymptotic behaviour, and show that (1) any
large oracle is at least as powerful as the unique identifiers in the context
of local decision problems, while (2) for any small oracle there are local
decision problems that still benefit from unique identifiers.Comment: Conference version to appear in the proceedings of SIROCCO 201
Deterministic meeting of sniffing agents in the plane
Two mobile agents, starting at arbitrary, possibly different times from
arbitrary locations in the plane, have to meet. Agents are modeled as discs of
diameter 1, and meeting occurs when these discs touch. Agents have different
labels which are integers from the set of 0 to L-1. Each agent knows L and
knows its own label, but not the label of the other agent. Agents are equipped
with compasses and have synchronized clocks. They make a series of moves. Each
move specifies the direction and the duration of moving. This includes a null
move which consists in staying inert for some time, or forever. In a non-null
move agents travel at the same constant speed, normalized to 1. We assume that
agents have sensors enabling them to estimate the distance from the other agent
(defined as the distance between centers of discs), but not the direction
towards it. We consider two models of estimation. In both models an agent reads
its sensor at the moment of its appearance in the plane and then at the end of
each move. This reading (together with the previous ones) determines the
decision concerning the next move. In both models the reading of the sensor
tells the agent if the other agent is already present. Moreover, in the
monotone model, each agent can find out, for any two readings in moments t1 and
t2, whether the distance from the other agent at time t1 was smaller, equal or
larger than at time t2. In the weaker binary model, each agent can find out, at
any reading, whether it is at distance less than \r{ho} or at distance at least
\r{ho} from the other agent, for some real \r{ho} > 1 unknown to them. Such
distance estimation mechanism can be implemented, e.g., using chemical sensors.
Each agent emits some chemical substance (scent), and the sensor of the other
agent detects it, i.e., sniffs. The intensity of the scent decreases with the
distance.Comment: A preliminary version of this paper appeared in the Proc. 23rd
International Colloquium on Structural Information and Communication
Complexity (SIROCCO 2016), LNCS 998
Optimal online and offline algorithms for robot-assisted restoration of barrier coverage
Cooperation between mobile robots and wireless sensor networks is a line of
research that is currently attracting a lot of attention. In this context, we
study the following problem of barrier coverage by stationary wireless sensors
that are assisted by a mobile robot with the capacity to move sensors. Assume
that sensors are initially arbitrarily distributed on a line segment
barrier. Each sensor is said to cover the portion of the barrier that
intersects with its sensing area. Owing to incorrect initial position, or the
death of some of the sensors, the barrier is not completely covered by the
sensors. We employ a mobile robot to move the sensors to final positions on the
barrier such that barrier coverage is guaranteed. We seek algorithms that
minimize the length of the robot's trajectory, since this allows the
restoration of barrier coverage as soon as possible. We give an optimal
linear-time offline algorithm that gives a minimum-length trajectory for a
robot that starts at one end of the barrier and achieves the restoration of
barrier coverage. We also study two different online models: one in which the
online robot does not know the length of the barrier in advance, and the other
in which the online robot knows the length of the barrier. For the case when
the online robot does not know the length of the barrier, we prove a tight
bound of on the competitive ratio, and we give a tight lower bound of
on the competitive ratio in the other case. Thus for each case we give an
optimal online algorithm.Comment: 20 page
Locally constrained homomorphisms on graphs of bounded treewidth and bounded degree.
A homomorphism from a graph G to a graph H is locally bijective, surjective, or injective if its restriction to the neighborhood of every vertex of G is bijective, surjective, or injective, respectively. We prove that the problems of testing whether a given graph G allows a homomorphism to a given graph H that is locally bijective, surjective, or injective, respectively, are NP-complete, even when G has pathwidth at most 5, 4 or 2, respectively, or when both G and H have maximum degree 3. We complement these hardness results by showing that the three problems are polynomial-time solvable if G has bounded treewidth and in addition G or H has bounded maximum degree
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