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 experimental results for an assortment of polygons, including nonorthogonal polygons with holes.
Abstract.One unfortunate consequence of the success story of wireless sensor networks (WSNs) in separate research communities is an evergrowing gap between theory and practice. Even though there is a increasing number of algorithmic methods for WSNs, the vast majority has never been tried in practice; conversely, many practical challenges are still awaiting efficient algorithmic solutions. The main cause for this discrepancy is the fact that programming sensor nodes still happens at a very technical level. We remedy the situation by introducing Wiselib, our algorithm library that allows for simple implementations of algorithms onto a large variety of hardware and software. This is achieved by employing advanced C++ techniques such as templates and inline functions, allowing to write generic code that is resolved and bound at compile time, resulting in virtually no memory or computation overhead at run time.The Wiselib runs on different host operating systems, such as Contiki, iSense OS, and ScatterWeb. Furthermore, it runs on virtual nodes simulated by Shawn. For any algorithm, the Wiselib provides data structures that suit the specific properties of the target platform. Algorithm code does not contain any platform-specific specializations, allowing a single implementation to run natively on heterogeneous networks.In this paper, we describe the building blocks of the Wiselib, and analyze the overhead. We demonstrate the effectiveness of our approach by showing how routing algorithms can be implemented. We also report on results from experiments with real sensor-node hardware.
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