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We present a new Min-Max theorem for an optimization problem closely connected to matchings and vertex covers in balanced hypergraphs. The result generalizes Kőnig’s Theorem (Berge and Las Vergnas in Ann N Y Acad Sci 175:32–40, 1970; Fulkerson et al. in Math Progr Study 1:120–132, 1974) and Hall’s Theorem (Conforti et al. in Combinatorica 16:325–329, 1996) for balanced hypergraphs.
The integration of sensors is one of the major tasks in embedded, control and “internet of things” (IoT) applications. For the integration mainly digital interfaces are used, starting from rather simple pulse-width modulation (PWM) interface to more complex interfaces like CAN (Controller Area Network). Even though these interfaces are tethered by definition, a wireless realization is highly welcome in many applications to reduce cable and connector cost, increase the flexibility and realize new emerging applications like wireless control systems. Currently used wireless solutions like Bluetooth, WirelessHART or IO-Link Wireless use dedicated communication standards and corresponding higher protocol layers to realize the wireless communication. Due to the complexity of the communication and the protocol handling, additional latency and jitter are introduced to the data communication that can meet the requirements for many applications. Even though tunnelling of other bus data like CAN data is generally also possible the latency and jitter prevent the tunnelling from being transparent for the bus system. Therefore a new basic technology based on dual-mode radio is used to realize a wireless communication on the physical layer only, enabling a reliable and real-time data transfer. As this system operates on the physical layer it is independent of any higher layers of the OSI (open systems interconnection) model. Hence it can be used for several different communication systems to replace the tethered physical layer. A prototype is developed and tested for real-time wireless PWM, SENT (single-edge nibble transmission) and CAN data transfer with very low latency and jitter.