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.
Protocols and applications that rely on unicast and multicast communication are well accepted and still gain more and more popularity. However, these communication paradigms are not optimal for a class of wireless applications where communication partners neither establish specific relationships nor need roles like client and server between each other before data exchange. Applications we have in mind deal with up to several thousands of peers as autonomous wireless network nodes. Nodes communicate events like traffic accidents in a local region or information of common interest to a larger group of network nodes. Intermediate nodes forward or rather "gossip" information like in a social communication model, comparable to the news of the big fire of Rome in neronian times travelling through Europe and finally reaching villages in rural areas. The challenge of such a concept is to find efficient local rules, which balance communication with respect to bandwidth usage, latency of data, and data delivery ratio. We introduce the promising application AutoNomos -a decentralized traffic information system -which is well suited for the evaluation of such a data dissemination protocol. Next, we present our new approach called AutoCast that is well optimized and self-adaptable towards various dynamic topologies. We compare AutoCast against the theoretical optimum and existing data dissemination protocols. Finally, simulations will demonstrate the efficiency of the approach.
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