HQuad: Statistics of Hamiltonian Cycles in Wireless Rechargeable Sensor Networks

The rise of wireless rechargeable sensor networks calls for an analytical study of planned charging trips of wireless charging vehicles (WCVs). Often times, the WCV receives a number of charging requests and form a Hamiltonian cycle and visit these nodes one-by-one. Therefore, it is important to learn the statistics of such cycles. In this work, we use a heuristic algorithm, which we term HQuad, that takes O(N) to generate a Hamiltonian cycle in a 2-D network plane before we analyze its statistics. HQuad is based on a recursive approximation of dividing the region into four quadrants and the non-empty quadrants will be visited one-by-one. Our analysis is based on Poisson point distribution of nodes and models such Hamiltonian cycles surprisingly well in both expected values and the distribution functions of lengths as a function of different network parameters. Numerical results of our analysis model are compared with simulations and demonstrated to be accurate.