152 research outputs found
The Dispersive Art Gallery Problem
We introduce a new variant of the art gallery problem that comes from safety issues. In this variant we are not interested in guard sets of smallest cardinality, but in guard sets with largest possible distances between these guards. To the best of our knowledge, this variant has not been considered before. We call it the Dispersive Art Gallery Problem. In particular, in the dispersive art gallery problem we are given a polygon ? and a real number ?, and want to decide whether ? has a guard set such that every pair of guards in this set is at least a distance of ? apart.
In this paper, we study the vertex guard variant of this problem for the class of polyominoes. We consider rectangular visibility and distances as geodesics in the L?-metric. Our results are as follows. We give a (simple) thin polyomino such that every guard set has minimum pairwise distances of at most 3. On the positive side, we describe an algorithm that computes guard sets for simple polyominoes that match this upper bound, i.e., the algorithm constructs worst-case optimal solutions. We also study the computational complexity of computing guard sets that maximize the smallest distance between all pairs of guards within the guard sets. We prove that deciding whether there exists a guard set realizing a minimum pairwise distance for all pairs of guards of at least 5 in a given polyomino is NP-complete.
We were also able to find an optimal dynamic programming approach that computes a guard set that maximizes the minimum pairwise distance between guards in tree-shaped polyominoes, i.e., computes optimal solutions; due to space constraints, details can be found in the full version of our paper [Christian Rieck and Christian Scheffer, 2022]. Because the shapes constructed in the NP-hardness reduction are thin as well (but have holes), this result completes the case for thin polyominoes
Efficiently Reconfiguring a Connected Swarm of Labeled Robots
When considering motion planning for a swarm of n labeled robots, we need to rearrange a given start configuration into a desired target configuration via a sequence of parallel, continuous, collision-free robot motions. The objective is to reach the new configuration in a minimum amount of time; an important constraint is to keep the swarm connected at all times. Problems of this type have been considered before, with recent notable results achieving constant stretch for not necessarily connected reconfiguration: If mapping the start configuration to the target configuration requires a maximum Manhattan distance of d, the total duration of an overall schedule can be bounded to ?(d), which is optimal up to constant factors. However, constant stretch could only be achieved if disconnected reconfiguration is allowed, or for scaled configurations (which arise by increasing all dimensions of a given object by the same multiplicative factor) of unlabeled robots.
We resolve these major open problems by (1) establishing a lower bound of ?(?n) for connected, labeled reconfiguration and, most importantly, by (2) proving that for scaled arrangements, constant stretch for connected reconfiguration can be achieved. In addition, we show that (3) it is NP-hard to decide whether a makespan of 2 can be achieved, while it is possible to check in polynomial time whether a makespan of 1 can be achieved
Posibles consecuencias del cambio climático global en bosques de Lago Puelo
p.79-87Se caracteriza topoclimáticamente los habitats del bosque mixto de coihue (Nothofagus dom beyi) y ciprés (Austrocedrus chilensis), del mixto con especies valdivianas y del de lenga (Nothofagus pumilio) en el Parque Nacional y Reserva Estricta Lago Puelo. Se analiza la posible consecuencia del cambio climático en la distribución y composición de dichos bosques. De mantenerse las tendencias que en la actualidad se observan para la temperatura y la precipitación, el clima en el año 2030 serÃa más húmedo, más frÃo en el invierno y más caluroso en el verano. La vegetación deberÃa sufrir cambios para alcanzar un nuevo equilibrio, el cual tentativamente favorecerÃa a la lenga y a especies higrófilas como Pilgerodendron uviferum, Fitzroya cupressoides, Lama apiculata y Myrceugenia exsucca
Connected Coordinated Motion Planning with Bounded Stretch
We consider the problem of coordinated motion planning for a swarm of simple, identical robots: From a given start grid configuration of robots, we need to reach a desired target configuration via a sequence of parallel, continuous, collision-free robot motions, such that the set of robots induces a connected grid graph at all integer times. The objective is to minimize the makespan of the motion schedule, i.e., to reach the new configuration in a minimum amount of time. We show that this problem is NP-hard, even for deciding whether a makespan of 2 can be achieved, while it is possible to check in polynomial time whether a makespan of 1 can be achieved.
On the algorithmic side, we establish simultaneous constant-factor approximation for two fundamental parameters, by achieving constant stretch for constant scale. Scaled shapes (which arise by increasing all dimensions of a given object by the same multiplicative factor) have been considered in previous seminal work on self-assembly, often with unbounded or logarithmic scale factors; we provide methods for a generalized scale factor, bounded by a constant. Moreover, our algorithm achieves a constant stretch factor: If mapping the start configuration to the target configuration requires a maximum Manhattan distance of d, then the total duration of our overall schedule is ?(d), which is optimal up to constant factors
Messung individueller Risikoeinstellungen
Es werden verschiedene Methoden zur Messung der Risikoeinstellung einzelner Individuen vorgestellt und kritisch diskutiert. Berücksichtigt werden unter anderem Selbsteinschätzungen und experimentell orientierte Verfahren. Die Zusammenstellung wendet sich insbesondere an Wissenschaftler und Praktiker, die nach anwendbaren Verfahren zur Risikoeinstellungsmessung suchen
Connected Coordinated Motion Planning with Bounded Stretch
We consider the problem of connected coordinated motion planning for a large
collective of simple, identical robots: From a given start grid configuration
of robots, we need to reach a desired target configuration via a sequence of
parallel, collision-free robot motions, such that the set of robots induces a
connected grid graph at all integer times. The objective is to minimize the
makespan of the motion schedule, i.e., to reach the new configuration in a
minimum amount of time. We show that this problem is NP-complete, even for
deciding whether a makespan of 2 can be achieved, while it is possible to check
in polynomial time whether a makespan of 1 can be achieved. On the algorithmic
side, we establish simultaneous constant-factor approximation for two
fundamental parameters, by achieving constant stretch for constant scale.
Scaled shapes (which arise by increasing all dimensions of a given object by
the same multiplicative factor) have been considered in previous seminal work
on self-assembly, often with unbounded or logarithmic scale factors; we provide
methods for a generalized scale factor, bounded by a constant. Moreover, our
algorithm achieves a constant stretch factor: If mapping the start
configuration to the target configuration requires a maximum Manhattan distance
of , then the total duration of our overall schedule is ,
which is optimal up to constant factors.Comment: 28 pages, 18 figures, full version of an extended abstract that
appeared in the proceedings of the 32nd International Symposium on Algorithms
and Computation (ISAAC 2021); revised version (more details added, and typing
errors corrected
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