Physical intuition is pivotal for intelligent agents to perform complex tasks. In this paper we investigate the passive acquisition of an intuitive understanding of physical principles as well as the active utilisation of this intuition in the context of generalised object stacking. To this end, we provide ShapeStacks 1 : a simulation-based dataset featuring 20,000 stack configurations composed of a variety of elementary geometric primitives richly annotated regarding semantics and structural stability. We train visual classifiers for binary stability prediction on the ShapeStacks data and scrutinise their learned physical intuition. Due to the richness of the training data our approach also generalises favourably to real-world scenarios achieving state-of-the-art stability prediction on a publicly available benchmark of block towers. We then leverage the physical intuition learned by our model to actively construct stable stacks and observe the emergence of an intuitive notion of stackability -an inherent object affordance -induced by the active stacking task. Our approach performs well even in challenging conditions where it considerably exceeds the stack height observed during training or in cases where initially unstable structures must be stabilised via counterbalancing.

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In wireless ad hoc or sensor networks, distributed node coloring is a fundamental problem closely related to establishing efficient communication through TDMA schedules. For networks with maximum degree ∆, a ∆ + 1 coloring is the ultimate goal in the distributed setting as this is always possible. In this work we propose ∆ + 1 coloring algorithms for the synchronous and asynchronous setting. All algorithms have a runtime of O(∆ log n) time slots. This improves on the previous algorithms for the SINR model either in terms of the number of required colors or the runtime and matches the runtime of local broadcasting in the SINR model (which can be seen as a lower bound).

We consider the distributed construction of a deterministic local broadcasting schedule in the SINR model of interference. During the execution of such a schedule each node should be able to transmit one message to its neighbors. Our construction requires only O(∆ log n) time slots, where ∆ is the maximum node degree in the network and n the number of nodes. We prove that the length of the constructed schedule is asymptotically optimal, i.e. of length O(∆). Considering the simulation of CON GEST algorithms in the SINR model, our deterministic schedule achieves a runtime of O(τ ∆ 2 + ∆ log n) time slots, where τ is the original runtime in the CON GEST model. We show that there is a lower bound of Ω(∆ 2) for the simulation of each one of the τ rounds, hence our simulation is optimal apart from the logarithmic factor. If we restrict the knowledge of the nodes and let the maximum node degree ∆ be unknown, we can prove that at least Ω(D +τ ∆ 2) time slots are required to simulate synchronized CON GEST algorithms in the SINR model of interference, where D is the diameter of the network. For our algorithms we assume location information to be given. Regarding the case without location information we argue that a deterministic algorithm to compute local broadcasting schedules by Derbel and Talbi [ICDCS'10], which requires transmission power adaption, needs messages of size O(log n) to simulate CON GEST algorithms. This is a logarithmic factor less than stated by the authors.

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