Near-optimal multicriteria spanner constructions in wireless ad hoc networks
IEEE/ACM Transactions on Networking (TON)
Gabriel Graphs in Arbitrary Metric Space and their Cellular Automaton for Many Grids
ACM Transactions on Autonomous and Adaptive Systems (TAAS)
Improved local algorithms for spanner construction
Theoretical Computer Science
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We present a local distributed algorithm that, given a wireless ad hoc network modeled as a unit disk graph U in the plane, constructs a planar power spanner of U whose degree is bounded by k and whose stretch factor is bounded by 1 + (2\sin{\frac{\pi}{k}})^{p}, where k \geq 10 is an integer parameter and p \in [2, 5] is the power exponent constant. For the same degree bound k, the stretch factor of our algorithm significantly improves the previous best bounds by Song et al. We show that this bound is near-optimal by proving that the slightly smaller stretch factor of 1 + (2\sin{\frac{\pi}{k + 1}})^{p} is unattainable for the same degree bound k. In contrast to previous algorithms for the problem, the presented algorithm is local. As a consequence, the algorithm is highly scalable and robust. Finally, while the algorithm is efficient and easy to implement in practice, it relies on deep insights on the geometry of unit disk graphs and novel techniques that are of independent interest.