45,293 research outputs found

    Optimal Paths on the Space-Time SINR Random Graph

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    We analyze a class of Signal-to-Interference-and-Noise-Ratio (SINR) random graphs. These random graphs arise in the modeling packet transmissions in wireless networks. In contrast to previous studies on the SINR graphs, we consider both a space and a time dimension. The spatial aspect originates from the random locations of the network nodes in the Euclidean plane. The time aspect stems from the random transmission policy followed by each network node and from the time variations of the wireless channel characteristics. The combination of these random space and time aspects leads to fluctuations of the SINR experienced by the wireless channels, which in turn determine the progression of packets in space and time in such a network. This paper studies optimal paths in such wireless networks in terms of first passage percolation on this random graph. We establish both "positive" and "negative" results on the associated time constant. The latter determines the asymptotics of the minimum delay required by a packet to progress from a source node to a destination node when the Euclidean distance between the two tends to infinity. The main negative result states that this time constant is infinite on the random graph associated with a Poisson point process under natural assumptions on the wireless channels. The main positive result states that when adding a periodic node infrastructure of arbitrarily small intensity to the Poisson point process, the time constant is positive and finite

    Active Markov Information-Theoretic Path Planning for Robotic Environmental Sensing

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    Recent research in multi-robot exploration and mapping has focused on sampling environmental fields, which are typically modeled using the Gaussian process (GP). Existing information-theoretic exploration strategies for learning GP-based environmental field maps adopt the non-Markovian problem structure and consequently scale poorly with the length of history of observations. Hence, it becomes computationally impractical to use these strategies for in situ, real-time active sampling. To ease this computational burden, this paper presents a Markov-based approach to efficient information-theoretic path planning for active sampling of GP-based fields. We analyze the time complexity of solving the Markov-based path planning problem, and demonstrate analytically that it scales better than that of deriving the non-Markovian strategies with increasing length of planning horizon. For a class of exploration tasks called the transect sampling task, we provide theoretical guarantees on the active sampling performance of our Markov-based policy, from which ideal environmental field conditions and sampling task settings can be established to limit its performance degradation due to violation of the Markov assumption. Empirical evaluation on real-world temperature and plankton density field data shows that our Markov-based policy can generally achieve active sampling performance comparable to that of the widely-used non-Markovian greedy policies under less favorable realistic field conditions and task settings while enjoying significant computational gain over them.Comment: 10th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2011), Extended version with proofs, 11 page
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