Computing a Minimum-Cost kk-hop Steiner Tree in Tree-Like Metrics

We consider the problem of computing a Steiner tree of minimum cost under a $k$-hop constraint which requires the depth of the tree to be at most $k$. Our main result is an exact algorithm for metrics induced by graphs of bounded treewidth that runs in time $n^{O(k)}$. For the special case of a path, we give a simple algorithm that solves the problem in polynomial time, even if $k$ is part of the input. The main result can be used to obtain, in quasi-polynomial time, a near-optimal solution that violates the $k$-hop constraint by at most one hop for more general metrics induced by graphs of bounded highway dimension

Speed-Robust Scheduling

The speed-robust scheduling problem is a two-stage problem where given $m$ machines, jobs must be grouped into at most $m$ bags while the processing speeds of the given $m$ machines are unknown. After the speeds are revealed, the grouped jobs must be assigned to the machines without being separated. To evaluate the performance of algorithms, we determine upper bounds on the worst-case ratio of the algorithm's makespan and the optimal makespan given full information. We refer to this ratio as the robustness factor. We give an algorithm with a robustness factor $2-1/m$ for the most general setting and improve this to $1.8$ for equal-size jobs. For the special case of infinitesimal jobs, we give an algorithm with an optimal robustness factor equal to $e/(e-1) \approx 1.58$. The particular machine environment in which all machines have either speed $0$ or $1$ was studied before by Stein and Zhong (SODA 2019). For this setting, we provide an algorithm for scheduling infinitesimal jobs with an optimal robustness factor of $(1+\sqrt{2})/2 \approx 1.207$. It lays the foundation for an algorithm matching the lower bound of $4/3$ for equal-size jobs

Skilog: A Smart Sensor System for Performance Analysis and Biofeedback in Ski Jumping

In ski jumping, low repetition rates of jumps limit the effectiveness of training. Thus, increasing learning rate within every single jump is key to success. A critical element of athlete training is motor learning, which has been shown to be accelerated by feedback methods. In particular, a fine-grained control of the center of gravity in the in-run is essential. This is because the actual takeoff occurs within a blink of an eye ($\sim$300ms), thus any unbalanced body posture during the in-run will affect flight. This paper presents a smart, compact, and energy-efficient wireless sensor system for real-time performance analysis and biofeedback during ski jumping. The system operates by gauging foot pressures at three distinct points on the insoles of the ski boot at 100Hz. Foot pressure data can either be directly sent to coaches to improve their feedback, or fed into a ML model to give athletes instantaneous in-action feedback using a vibration motor in the ski boot. In the biofeedback scenario, foot pressures act as input variables for an optimized XGBoost model. We achieve a high predictive accuracy of 92.7% for center of mass predictions (dorsal shift, neutral stand, ventral shift). Subsequently, we parallelized and fine-tuned our XGBoost model for a RISC-V based low power parallel processor (GAP9), based on the PULP architecture. We demonstrate real-time detection and feedback (0.0109ms/inference) using our on-chip deployment. The proposed smart system is unobtrusive with a slim form factor (13mm baseboard, 3.2mm antenna) and a lightweight build (26g). Power consumption analysis reveals that the system's energy-efficient design enables sustained operation over multiple days (up to 300 hours) without requiring recharge.Comment: 5 pages, 2 tables, 4 figure, Accepted at IEEE BioCAS 202