A Sublinear Algorithm for Path Feasibility Among Rectangular Obstacles

The problem of finding a path between two points while avoiding obstacles is critical in robotic path planning. We focus on the feasibility problem: determining whether such a path exists. We model the robot as a query-specific rectangular object capable of moving parallel to its sides. The obstacles are axis-aligned, rectangular, and may overlap. Most previous works only consider nondisjoint rectangular objects and point-sized or statically sized robots. Our approach introduces a novel technique leveraging generalized Gabriel graphs and constructs a data structure to facilitate online queries regarding path feasibility with varying robot sizes in sublinear time. To efficiently handle feasibility queries, we propose an online algorithm utilizing sweep line to construct a generalized Gabriel graph under the $L_\infty$ norm, capturing key gap constraints between obstacles. We utilize a persistent disjoint-set union data structure to efficiently determine feasibility queries in $\mathcal{O}(\log n)$ time and $\mathcal{O}(n)$ total space.

Addressing Racial Bias in Facial Emotion Recognition

Fairness in deep learning models trained with high-dimensional inputs and subjective labels remains a complex and understudied area. Facial emotion recognition, a domain where datasets are often racially imbalanced, can lead to models that yield disparate outcomes across racial groups. This study focuses on analyzing racial bias by sub-sampling training sets with varied racial distributions and assessing test performance across these simulations. Our findings indicate that smaller datasets with posed faces improve on both fairness and performance metrics as the simulations approach racial balance. Notably, the F1-score increases by $27.2\%$ points, and demographic parity increases by $15.7\%$ points on average across the simulations. However, in larger datasets with greater facial variation, fairness metrics generally remain constant, suggesting that racial balance by itself is insufficient to achieve parity in test performance across different racial groups.