With the increasing demand for accurate indoor localization in smart homes, robotics, and commercial scenarios, achieving precise location using minimal infrastructure has become essential yet challenging. Traditional RSSI-based fingerprinting methods typically require multiple APs, limiting their practicality in single-AP scenarios commonly found in real-world home environments. To overcome this limitation, we propose a single-AP localization method that employs multi-directional beamforming to generate rich RSSI fingerprints. By sweeping the AP beamforming angle, the method captures directional RSSI features, significantly improving localization accuracy. Additionally, we introduce an angular embedding mechanism, explicitly encoding beamforming direction into neural network inputs to enhance robustness, especially under limited labeled data conditions. Extensive simulation and real-world experiments demonstrate that our proposed approach significantly outperforms conventional single-AP RSSI methods, consistently achieving sub-meter accuracy with small training datasets, thereby validating its effectiveness.

We consider fairness in submodular maximization subject to a knapsack constraint, a fundamental problem with various applications in economics, machine learning, and data mining. In the model, we are given a set of ground elements, each associated with a cost and a color, and a monotone submodular function defined over them. The goal is to maximize the submodular function while guaranteeing that the total cost does not exceed a specified budget (the knapsack constraint) and that the number of elements selected for each color falls within a designated range (the fairness constraint). While there exists some recent literature on this topic, the existence of a non-trivial approximation for the problem -- without relaxing either the knapsack or fairness constraints -- remains a challenging open question. This paper makes progress in this direction. We demonstrate that when the number of colors is constant, there exists a polynomial-time algorithm that achieves a constant approximation with high probability. Additionally, we show that if either the knapsack or fairness constraint is relaxed only to require expected satisfaction, a tight approximation ratio of (1-1/e-epsilon) can be obtained in expectation for any epsilon >0.

With the increasing demand for indoor localization, received signal strength indicator (RSSI)-based fingerprint localization has gained widespread attention due to its low equipment costs. Traditional methods only use RSSI data collected from user devices to train localization models, but the coarse granularity of RSSI often limits accuracy. Additionally, changes in the environment, such as door movements or furniture rearrangements, can render these models ineffective. While resource-intensive and time-consuming, data re-collection and model retraining are essential for capturing updated signal characteristics after environment changes, ensuring the model remains accurate and effective. To enhance localization accuracy, we expand on traditional approaches by incorporating RSSI data measured between wireless routers as additional fingerprint features, achieving nearly a 20% accuracy improvement. Furthermore, we address the challenges of dynamic environments by introducing a multi-task domain-adversarial transfer learning method, which extracts consistent features before and after environment changes. Transfer learning allows us to leverage knowledge from the environment before the change, thereby reducing the need for data re-collection after the change. Experiment results from simulated, real-world, and open dataset environments confirm the effectiveness of the proposed method in dynamic indoor localization. Our approach reduced the mean error distance (MED) by 35%, 44%, and 28%, respectively, with only 16%, 20%, and 17% of the data re-collected.