We consider the problem of constructing a communication infrastructure from scratch, for a collection of identical wireless nodes. Combinatorially, this means a) finding a set of links that form a strongly connected spanning graph on a set of @math points in the plane, and b) scheduling it efficiently in the SINR model of interference. The nodes must converge on a solution in a distributed manner, having no means of communication beyond the sole wireless channel. We give distributed connectivity algorithms that run in time @math , where @math is the ratio between the longest and shortest distances among nodes. Given that algorithm without prior knowledge of the instance are essentially limited to using uniform power, this is close to best possible. Our primary aim, however, is to find efficient structures, measured in the number of slots used in the final schedule of the links. Our main result is algorithms that match the efficiency of centralized solutions. Specifically, the networks can be scheduled in @math slots using (arbitrary) power control, and in @math slots using a simple oblivious power scheme. Additionally, the networks have the desirable properties that the latency of a converge-cast and of any node-to-node communication is optimal @math time.
The Minimum-Latency Aggregation Scheduling problem is closely related to connectivity, where the latency for transmitting messages to a sink is to be minimized. A large literature is known, but the first worst-case analysis in the SINR model was given in @cite_3 , with a @math bound on the schedule length by a centralized algorithm and @math by a distributed algorithm. The centralized bound was improved to optimal @math in @cite_4 .
@cite_4 @cite_3
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Given @math wireless transceivers located in a plane, a fundamental problem in wireless communications is to construct a strongly connected digraph on them such that the constituent links can be scheduled in fewest possible time slots, assuming the SINR model of interference. In this paper, we provide an algorithm that connects an arbitrary point set in @math slots, improving on the previous best bound of @math due to Moscibroda. This is complemented with a super-constant lower bound on our approach to connectivity. An important feature is that the algorithms allow for bi-directional (half-duplex) communication. One implication of this result is an improved bound of @math on the worst-case capacity of wireless networks, matching the best bound known for the extensively studied average-case. We explore the utility of oblivious power assignments, and show that essentially all such assignments result in a worst case bound of @math slots for connectivity. This rules out a recent claim of a @math bound using oblivious power. On the other hand, using our result we show that @math slots suffice, where @math is the ratio between the largest and the smallest links in a minimum spanning tree of the points. Our results extend to the related problem of minimum latency aggregation scheduling, where we show that aggregation scheduling with @math latency is possible, improving upon the previous best known latency of @math . We also initiate the study of network design problems in the SINR model beyond strong connectivity, obtaining similar bounds for biconnected and @math -edge connected structures. Minimum-Latency Aggregation Scheduling (MLAS) is a problem of fundamental importance in wireless sensor networks. There however has been very little effort spent on designing algorithms to achieve sufficiently fast data aggregation under the physical interference model which is a more realistic model than traditional protocol interference model. In particular, a distributed solution to the problem under the physical interference model is challenging because of the need for global-scale information to compute the cumulative interference at any individual node. In this paper, we propose a distributed algorithm that solves the MLAS problem under the physical interference model in networks of arbitrary topology in O(K) time slots, where K is the logarithm of the ratio between the lengths of the longest and shortest links in the network. We also give a centralized algorithm to serve as a benchmark for comparison purposes, which aggregates data from all sources in O(log3n) time slots (where n is the total number of nodes). This is the current best algorithm for the problem in the literature. The distributed algorithm partitions the network into cells according to the value K, thus obviating the need for global information. The centralized algorithm strategically combines our aggregation tree construction algorithm with the non-linear power assignment strategy in [9]. We prove the correctness and efficiency of our algorithms, and conduct empirical studies under realistic settings to validate our analytical results.