New geometric representations and domination problems on tolerance and multitolerance graphs

Tolerance graphs model interval relations in such a way that intervals can tolerate a certain amount of overlap without being in conflict. In one of the most natural generalizations of tolerance graphs with direct applications in the comparison of DNA sequences from different organisms, namely multitolerance graphs, two tolerances are allowed for each interval – one from the left and one from the right side. Several efficient algorithms for optimization problems that are NPhard in general graphs have been designed for tolerance and multitolerance graphs. In spite of this progress, the complexity status of some fundamental algorithmic problems on tolerance and multitolerance graphs, such as the dominating set problem, remained unresolved until now, three decades after the introduction of tolerance graphs. In this article we introduce two new geometric representations for tolerance and multitolerance graphs, given by points and line segments in the plane. Apart from being important on their own, these new representations prove to be a powerful tool for deriving both hardness results and polynomial time algorithms. Using them, we surprisingly prove that the dominating set problem can be solved in polynomial time on tolerance graphs and that it is APX-hard on multitolerance graphs, solving thus a longstanding open problem. This problem is the first one that has been discovered with a different complexity status in these two graph classes. Furthermore we present an algorithm that solves the independent dominating set problem on multitolerance graphs in polynomial time, thus demonstrating the potential of this new representation for further exploitation via sweep line algorithms

Self-Stabilizing Byzantine-Resilient Communication in Dynamic Networks

We consider the problem of communicating reliably in a dynamic network in the presence of up to k Byzantine failures. It was shown that this problem can be solved if and only if the dynamic graph satisfies a certain condition, that we call "RDC condition". In this paper, we present the first self-stabilizing algorithm for reliable communication in this setting - that is: in addition to permanent Byzantine failures, there can also be an arbitrary number of transient failures. We prove the correctness of this algorithm, provided that the RDC condition is "always eventually satisfied"

SensorCloud: Towards the Interdisciplinary Development of a Trustworthy Platform for Globally Interconnected Sensors and Actuators

Although Cloud Computing promises to lower IT costs and increase users' productivity in everyday life, the unattractive aspect of this new technology is that the user no longer owns all the devices which process personal data. To lower scepticism, the project SensorCloud investigates techniques to understand and compensate these adoption barriers in a scenario consisting of cloud applications that utilize sensors and actuators placed in private places. This work provides an interdisciplinary overview of the social and technical core research challenges for the trustworthy integration of sensor and actuator devices with the Cloud Computing paradigm. Most importantly, these challenges include i) ease of development, ii) security and privacy, and iii) social dimensions of a cloud-based system which integrates into private life. When these challenges are tackled in the development of future cloud systems, the attractiveness of new use cases in a sensor-enabled world will considerably be increased for users who currently do not trust the Cloud.Comment: 14 pages, 3 figures, published as technical report of the Department of Computer Science of RWTH Aachen Universit