The weighted \(k\)-server is a variant of the \(k\)-server problem, where the cost of moving a server is the server’s weight times the distance through which it moves. The problem is famous for its intriguing properties and for evading standard techniques for designing and analyzing online algorithms. Even on uniform metric spaces with sufficiently many points, the deterministic competitive ratio of weighted \(k\)-server is known to increase doubly exponentially with respect to \(k\), while the behavior of its randomized competitive ratio is not fully understood. Specifically, no upper bound better than doubly exponential is known, while the best known lower bound is singly exponential in \(k\). In this paper, we close the exponential gap between these bounds by giving an \(\exp(\mathcal O(k^2))\)-competitive randomized online algorithm for the weighted \(k\)-server problem on uniform metrics, thus breaking the doubly exponential barrier for deterministic algorithms for the first time. This is achieved by a recursively defined notion of a phase which, on the one hand, forces a lower bound on the cost of any offline solution, while, on the other hand, also admits a randomized online algorithm with bounded expected cost. The algorithm is also recursive; it involves running several algorithms virtually and in parallel and following the decisions of one of them in a random order. We also show that our techniques can be lifted to construct an \(\exp(\mathcal O(k^2))\)-competitive randomized online algorithm for the generalized \(k\)-server problem on weighted uniform metrics.

A stark disparity exists in the energy consumption for performing transmissions and the tasks of sensing and processing in wireless embedded systems. We present our early work to design a novel transmitter that enables transmissions at a similar energy consumption as other tasks in wireless embedded systems. In particular, the proposed transmitter does not require a carrier emitting device, which is essential to support backscatter transmitters, but has also limited their widespread deployment. The proposed transmitter exploits the capability of tunnel diode oscillators to function as a low-power, self-oscillating mixer. This property enables us to mix a weak baseband signal with a locally generated carrier signal at a peak power consumption below 100 microwatts. Nevertheless, the tunnel diode oscillator trades off the stability for low energy consumption leading to poor link reliability. In this study, we investigate error correction codes to increase link reliability. Our experiments demonstrate the potential of the transmitter to support short-range transmissions with a low energy consumption and enhanced link reliability.