We present randomized distributed algorithms for connectivity and aggregation in multi-hop wireless networks under the SINR model. The connectivity problem asks for a set of links that strongly connect a given set of wireless nodes, along with an efficient schedule. Aggregation asks for a spanning in-arborescence (converge-cast tree), along with a schedule that additionally obeys the partial order defined by the tree. Here we treat the multi-hop case, where nodes have limited power that restricts the links they can potentially form. We show that connectivity is possible for any set of n nodes in O(log n) slots, which matches the best centralized bound known, and that aggregation is possible in O(D + log n) time (D being the maximum hop-distance), which is optimal.

Efficient spectrum use in wireless sensor networks through spatial reuse requires effective models of packet reception at the physical layer in the presence of interference. Despite recent progress in analytic and simulations research into worst-case behavior from interference effects, these efforts generally assume geometric path loss and isotropic transmission, assumptions which have not been borne out in experiments.Our paper aims to provide a methodology for grounding theoretical results into wireless interference in experimental reality. We develop a new framework for wireless algorithms in which distancebased path loss is replaced by an arbitrary gain matrix, typically obtained by measurements of received signal strength (RSS). We experimentally evaluate the framework in two indoors testbeds with 20 and 60 motes, and confirm superior predictive performance in packet reception rate for a gain matrix model over a geometric distance-based model.At the heart of our approach is a new parameter ζ called metricity which indicates how close the gain matrix is to a distance metric, effectively measuring the complexity of the environment. A powerful theoretical feature of this parameter is that all known SINR scheduling algorithms that work in general metric spaces carry over to arbitrary gain matrices and achieve equivalent performance guarantees in terms of ζ as previously obtained in terms of the path loss constant. Our experiments confirm the sensitivity of ζ to the nature of the environment. Finally, we show analytically and empirically how multiple channels can be leveraged to improve metricity and thereby performance. We believe our contributions will facilitate experimental validation for recent advances in algorithms for physical wireless interference models.

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