The art gallery problem (AGP) is one of the classical problems in computational geometry. It asks for the minimum number of guards required to achieve visibility coverage of a given polygon. The AGP is well-known to be NP-hard even in restricted cases. In this paper, we consider the AGP with fading (AGPF): A polygonal region is to be illuminated with light sources such that every point is illuminated with at least a global threshold, light intensity decreases over distance, and we seek to minimize the total energy consumption. Choosing fading exponents of zero, one, and two are equivalent to the AGP, laser scanner applications, and natural light, respectively. We present complexity results as well as a negative solvability result. Still, we propose two practical algorithms for AGPF with fixed light positions (e.g. vertex guards) independent of the fading exponent, which we demonstrate to work well in practice. One is based on a discrete approximation, the other on non-linear programming by means of simplex-partitioning strategies. The former approach yields a fully polynomial-time approximation scheme for the AGPF with fixed light positions. The latter approach obtains better results in our experimental evaluation.

We focus on the problem of computing tight deadline miss models for real-time systems, which bound the number of potential deadline misses in a given sequence of activations of a task. In practical applications, such guarantees are often sufficient because many systems are in fact not hard real-time. Our major contribution is a general formulation of that problem in the context of systems where some tasks occasionally experience sporadic overload. Based on this new formulation, we present an algorithm that can take into account fine-grained effects of overload at the input of different tasks when computing deadline miss bounds. Finally, we show in experiments with synthetic as well as industrial data that our algorithm produces bounds that are much tighter than in previous work, in sufficiently short time.

This paper presents a distributed approach for exploring and triangulating an unknown region using a multirobot system. The resulting triangulation is a physical data structure that is a: compact representation of the workspace, contains distributed knowledge of each triangle, builds the dual graph of the triangulation, and supports reads and writes of auxiliary data. Our algorithm builds a triangulation in a closed two-dimensional Euclidean environment, starting from a single location. It provides coverage with a breadth-first search pattern and completeness guarantees. We show that the computational and communication requirements to build and maintain the triangulation and its dual graph are small. We then present a physical navigation algorithm that uses the dual graph, and show that the resulting path lengths are within a constant factor of the shortest-path Euclidean distance. Finally, we validate our theoretical results with experiments on triangulating a region with a system of low-cost robots. Analysis of the resulting triangulation shows that most of the triangles are of high quality, and cover a large area. Implementation of the triangulation, dual graph, and navigation all use communication messages of fixed size, and are a practical solution for large populations of low-cost robots.

No abstract available.

In this video, we illustrate how one of the classical areas of computational geometry has gained in practical relevance, which in turn gives rise to new, fascinating geometric problems. In particular, we demonstrate how the robot platform IRMA3D can produce high-resolution, virtual 3D environments, based on a limited number of laser scans. Computing an optimal set of scans amounts to solving an instance of the Art Gallery Problem (AGP): Place a minimum number of stationary guards in a polygonal region P, such that all points in P are guarded.

The classical Art Gallery Problem asks for the minimum number of guards that achieve visibility coverage of a given polygon. This problem is known to be NP-hard, even for very restricted and discrete special cases. For the case of vertex guards and simple orthogonal polygons, Cuoto et al. have recently developed an exact method that is based on a set cover approach. For the general problem (in which both the set of possible guard positions and the point set to be guarded are uncountable), neither constant-factor approximation algorithms nor exact solution methods are known. We present a primal-dual algorithm based on linear programming that provides lower bounds on the necessary number of guards in every step and—in case of convergence and integrality—ends with an optimal solution. We describe our implementation and give results for an assortment of polygons, including non-orthogonal polygons with holes.

In this work we present a protocol for self-synchronized duty-cycling in wireless sensor networks with energy harvesting capabilities. The protocol is implemented in Wiselib, a library of generic algorithms for sensor networks. Simulations are conducted with the sensor network simulator Shawn. They are based on the specifications of real hardware known as iSense sensor nodes. The experimental results show that the proposed mechanism is able to adapt to changing energy availabilities. Moreover, it is shown that the system is very robust against packet loss.

We propose an efficient simulation technique for the CSMA medium access protocol. It is based on the well-established model of using signal to interference and noise ratio (SINR), which is very accurate and allows for highly realistic predictions of collisions. However, traditional implementations require O(n) time to compute interference values. We evaluate how to speed this up by using efficient data structures such as k-d-trees or geometric hash tables in our implementation. There are different levels of accuracy, some of which allow for O(√n + a) lookups, where a is the number of nearby senders. We demonstrate the achievable speedup and discuss accuracy tradeoffs for different settings using the Shawn simulator.

We study a problem related to computer vision: How can a field of sensors compute higher-level properties of observed objects deterministically in sublinear time, without accessing a central authority? This issue is not only important for real-time processing of images, but lies at the very heart of understanding how a brain may be able to function. In particular, we consider a quadratic field of n "smart pixels" on a video chip that observe a B/W image. Each pixel can exchange low-level information with its immediate neighbors. We show that it is possible to compute the centers of gravity along with a principal component analysis of all connected components of the black grid graph in time O(sqrt(n)), by developing appropriate distributed protocols that are modeled after sweepline methods. Our method is not only interesting from a philosophical and theoretical point of view, it is also useful for actual applications for controling a robot arm that has to seize objects on a moving belt. We describe details of an implementation on an FPGA; the code has also been turned into a hardware design for an application-specific integrated circuit (ASIC).

We present a sensor network that monitors a hallway. It consists of 180 load sensors connected to 30 wireless sensor nodes, where the setup is of extremely low cost and easily transferred to other settings. Our network serves as a testbed for in-network data processing algorithms, for which it is highly suitable due to the many correlated sensors.

No abstract available.

In this paper we present a modular and extensible visualization framework for wireless sensor networks. These networks have typically no means of visualizing their state, measurements or computational results. Visualization is therefore a key issue to develop and operate these networks. Data emitted by individual sensor nodes is collected by the visualization software and passed to a flexible multi-layer plug-in mechanism that renders the information on a canvas. Developers can easily adapt existing or develop new custom tailored plug-ins for their specific application.