Pankaj Kumar

Pankaj Kumar, Haiko Müller, Sebastian Ordyniak et al.

In the Min-Sum-Radii (MSR) clustering problem, we are given a finite set X of n points in a metric space. The objective is to find at most k clusters centered at a subset of these points such that every point of X is assigned to one of the clusters, minimizing the sum of the radii of the clusters. The problem is known to be NP-hard even on metrics induced by weighted planar graphs and metrics with constant doubling dimension, as shown by Gibson et al. (SWAT 2008). In this work, we investigate the parameterized complexity of MSR on metrics induced by undirected graphs. We distinguish between weighted graph metrics (with positive edge weights) and unweighted graph metrics (where all edges have unit weight). Weighted Graph Metrics: We show that MSR is W[1]-hard on metrics induced by weighted bipartite graphs, when parameterized by the combined parameter k (the number of clusters) and Delta (the cost of the clustering). We then investigate the structural parameterized complexity of the problem. Drexler et al. (arXiv:2310.02130) showed that the MSR problem admits an XP algorithm on metrics induced by weighted graphs when parameterized by treewidth, and asked whether this can be improved to fixed-parameter tractability. We first answer their question in the negative, and more strongly show that MSR stays W[1]-hard on metrics induced by undirected weighted bipartite graphs when parameterized by the vertex cover number plus k. We then turn our attention to parameters for dense graphs and show that MSR remains W[1]-hard when parameterized by k+Delta even on cliques and complete bipartite graphs. On the positive side, we employ the known XP algorithm parameterized by treewidth, to show that the MSR problem is FPT when parameterized by the parameter treewidth plus Delta.

Pankaj Kumar, Pranamesh Chakraborty, Subrahmanya Swamy Peruru

Automated Vehicle (AV) control in mixed traffic, where AVs coexist with human-driven vehicles, poses significant challenges in balancing safety, efficiency, comfort, fuel efficiency, and compliance with traffic rules while capturing heterogeneous driver behavior. Traditional car-following models, such as the Intelligent Driver Model (IDM), often struggle to generalize across diverse traffic scenarios and typically do not account for fuel efficiency, motivating the use of learning-based approaches. Although Deep Reinforcement Learning (DRL) has shown strong microscopic performance in car-following conditions, its macroscopic traffic flow characteristics remain underexplored. This study focuses on analyzing the macroscopic traffic flow characteristics and fuel efficiency of DRL-based models in mixed traffic. A Twin Delayed Deep Deterministic Policy Gradient (TD3) algorithm is implemented for AVs' control and trained using the NGSIM highway dataset, enabling realistic interaction with human-driven vehicles. Traffic performance is evaluated using the Fundamental Diagram (FD) under varying driver heterogeneity, heterogeneous time-gap penetration levels, and different shares of RL-controlled vehicles. A macroscopic level comparison of fuel efficiency between the RL-based AV model and the IDM is also conducted. Results show that traffic performance is sensitive to the distribution of safe time gaps and the proportion of RL vehicles. Transitioning from fully human-driven to fully RL-controlled traffic can increase road capacity by approximately 7.52%. Further, RL-based AVs also improve average fuel efficiency by about 28.98% at higher speeds (above 50 km/h), and by 1.86% at lower speeds (below 50 km/h) compared to the IDM. Overall, the DRL framework enhances traffic capacity and fuel efficiency without compromising safety.

Nishi Doshi, Urvi Oza, Pankaj Kumar

Diabetic Retinopathy (DR) is an art and science of recording and classifying the retinal images of a diabetic patient. DR classification deals with classifying retinal fundus image into five stages on the basis of severity of diabetes. One of the major issue faced while dealing with DR classification problem is the large and varying size of images. In this paper we propose and explore the use of several downscaling algorithms before feeding the image data to a Deep Learning Network for classification. For improving training and testing; we amalgamate two datasets: Kaggle and Indian Diabetic Retinopathy Image Dataset. Our experiments have been performed on a novel Multi Channel Inception V3 architecture with a unique self crafted preprocessing phase. We report results of proposed approach using accuracy, specificity and sensitivity, which outperform the previous state of the art methods. Index Terms: Diabetic Retinopathy, Downscaling Algorithms, Multichannel CNN Architecture, Deep Learning

Pankaj Kumar, Subhankar Mishra

Large Language Models (LLMs) have emerged as a promising cornerstone for the development of natural language processing (NLP) and artificial intelligence (AI). However, ensuring the robustness of LLMs remains a critical challenge. To address these challenges and advance the field, this survey provides a comprehensive overview of current studies in this area. First, we systematically examine the nature of robustness in LLMs, including its conceptual foundations, the importance of consistent performance across diverse inputs, and the implications of failure modes in real-world applications. Next, we analyze the sources of non-robustness, categorizing intrinsic model limitations, data-driven vulnerabilities, and external adversarial factors that compromise reliability. Following this, we review state-of-the-art mitigation strategies, and then we discuss widely adopted benchmarks, emerging metrics, and persistent gaps in assessing real-world reliability. Finally, we synthesize findings from existing surveys and interdisciplinary studies to highlight trends, unresolved issues, and pathways for future research.

Pankaj Kumar, Aditya Mishra, Pranamesh Chakraborty et al.

Developing an autonomous vehicle control strategy for signalised intersections (SI) is one of the challenging tasks due to its inherently complex decision-making process. This study proposes a Deep Reinforcement Learning (DRL) based longitudinal vehicle control strategy at SI. A comprehensive reward function has been formulated with a particular focus on (i) distance headway-based efficiency reward, (ii) decision-making criteria during amber light, and (iii) asymmetric acceleration/ deceleration response, along with the traditional safety and comfort criteria. This reward function has been incorporated with two popular DRL algorithms, Deep Deterministic Policy Gradient (DDPG) and Soft-Actor Critic (SAC), which can handle the continuous action space of acceleration/deceleration. The proposed models have been trained on the combination of real-world leader vehicle (LV) trajectories and simulated trajectories generated using the Ornstein-Uhlenbeck (OU) process. The overall performance of the proposed models has been tested using Cumulative Distribution Function (CDF) plots and compared with the real-world trajectory data. The results show that the RL models successfully maintain lower distance headway (i.e., higher efficiency) and jerk compared to human-driven vehicles without compromising safety. Further, to assess the robustness of the proposed models, we evaluated the model performance on diverse safety-critical scenarios, in terms of car-following and traffic signal compliance. Both DDPG and SAC models successfully handled the critical scenarios, while the DDPG model showed smoother action profiles compared to the SAC model. Overall, the results confirm that DRL-based longitudinal vehicle control strategy at SI can help to improve traffic safety, efficiency, and comfort.