Abhishek Sahu

Abhishek Sahu

The \emph{Separation Lemma} is a simple yet powerful tool, akin to the well-known \emph{Isolation Lemma}, that guarantees the uniqueness of certain set sums. Bandopadhyay et al.\ introduced this lemma to establish lower bounds for the \ALP problem with respect to certain structural parameters, relying on random weight assignments in the process. The lemma's applicability extends well beyond that specific work, especially in proving hardness results. However, while effective, these hardness results inherently rely on probabilistic assumptions. In this work, we give a fully \emph{deterministic} construction for the weight assignment required by the Separation Lemma. We provide formal proofs of correctness, explicit examples, and show how deterministic weights can replace randomized ones, thereby derandomizing existing hardness results for path-packing problems. Our exposition highlights a clear progression from the original randomized foundations to deterministic constructions and their practical implications.

Aritra Banik, Sujoy Bhore, Palash Dey et al.

The kidney exchange mechanism allows many patient-donor pairs who are otherwise incompatible with each other to come together and exchange kidneys along a cycle. However, due to infrastructure and legal constraints, kidney exchange can only be performed in small cycles in practice. In reality, there are also some altruistic donors who do not have any paired patients. This allows us to also perform kidney exchange along paths that start from some altruistic donor. Unfortunately, the computational task is NP-complete. To overcome this computational barrier, an important line of research focuses on designing faster algorithms, both exact and using the framework of parameterized complexity. The standard parameter for the kidney exchange problem is the number $t$ of patients that receive a healthy kidney. The current fastest known deterministic FPT algorithm for this problem, parameterized by $t$, is $O^\star\left(14^t\right)$. In this work, we improve this by presenting a deterministic FPT algorithm that runs in time $O^\star\left((4e)^t\right)\approx O^\star\left(10.88^t\right)$. This problem is also known to be W[1]-hard parameterized by the treewidth of the underlying undirected graph. A natural question here is whether the kidney exchange problem admits an FPT algorithm parameterized by the pathwidth of the underlying undirected graph. We answer this negatively in this paper by proving that this problem is W[1]-hard parameterized by the pathwidth of the underlying undirected graph. We also present some parameterized intractability results improving the current understanding of the problem under the framework of parameterized complexity.

Abhishek Sahu, Peter H. Aaen, Praveen Damacharla

In this paper, we present a machine learning based architecture for microwave characterization of inkjet printed components on flexible substrates. Our proposed architecture uses several machine learning algorithms and automatically selects the best algorithm to extract the material parameters (ink conductivity and dielectric properties) from on-wafer measurements. Initially, the mutual dependence between material parameters of the inkjet printed coplanar waveguides (CPWs) and EM-simulated propagation constants is utilized to train the machine learning models. Next, these machine learning models along with measured propagation constants are used to extract the ink conductivity and dielectric properties of the test prototypes. To demonstrate the applicability of our proposed approach, we compare and contrast four heuristic based machine learning models. It is shown that eXtreme Gradient Boosted Trees Regressor (XGB) and Light Gradient Boosting (LGB) algorithms perform best for the characterization problem under study.