Mobile Sensor Networks: Bounds on Capacity and Complexity of Realizability
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We study the models, proposed by Chen Gu et al. in 2018, of mobile sensor networks where the sensors receive information continuously and can store an infinite amount of information. Their paper proposed two models—the combinatorial mobile sensor network (CMSN) where each time exactly two sensors communicate, and the geometric mobile sensor network (GMSN) where the sensors move in constant velocities on a line—and a way to measure the capacity of a network to diffuse information. We found the maximum and minimum capacities of GMSNs, a restricted form of CMSN (RCMSN) where every two sensors communicate exactly once, and restricted GMSNs (RGMSNs) where there is only a limited number of distinct speeds of sensors. We also found the expected capacity of GMSNs and RGMSNs with no more than three different velocities. Finally, we found that the problem of determining if an RCMSN is equivalent to a GMSN is NP-Hard, but whether a CMSN is equivalent to an RGMSN with a given number of distinct velocities can be determined in polynomial time.
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