arXiv subjects

Mayank Goswami

Publications and source records attributed to Mayank Goswami.

At least 19 recordsLinked to original sources

arXiv2026

Covering and Partitioning Complex Objects with Small Pieces

We study the problems of covering or partitioning a polygon $P$ (possibly with holes) using a minimum number of small pieces, where a small piece is a connected sub-polygon contained in an axis-aligned unit square. For covering, we seek to write $P$ as a union of small pieces, and in partitioning, we furthermore require the pieces to be pairwise interior-disjoint. We show that these problems are in fact equivalent: Optimum covers and partitions have the same number of pieces. For covering, a natural local search algorithm repeatedly attempts to replace $k$ pieces from a candidate cover with $k-1$ pieces. In two dimensions and for sufficiently large $k$, we show that when no such swap is possible, the cover is a $1+O(1/\sqrt k)$-approximation, hence obtaining the first PTAS for the problem. Prior to our work, the only known algorithm was a $13$-approximation that only works for polygons without holes [Abrahamsen and Rasmussen, SODA 2025]. In contrast, in the three dimensional version of the problem, for a polyhedron $P$ of complexity $n$, we show that it is NP-hard to approximate an optimal cover or partition to within a factor that is logarithmic in $n$, even if $P$ is simple, i.e., has genus $0$ and no holes.

cs.CG↗

arXiv2026

How many users have been here for a long time? Efficient solutions for counting long aggregated visits

This paper addresses the Counting Long Aggregated Visits problem, which is defined as follows. We are given $n$ users and $m$ regions, where each user spends some time visiting some regions. For a parameter $k$ and a query consisting of a subset of $r$ regions, the task is to count the number of distinct users whose aggregate time spent visiting the query regions is at least $k$. This problem is motivated by queries arising in the analysis of large-scale mobility datasets. We present several exact and approximate data structures for supporting counting long aggregated visits, as well as conditional and unconditional lower bounds. First, we describe an exact data structure that exhibits a space-time tradeoff, as well as efficient approximate solutions based on sampling and sketching techniques. We then study the problem in geometric settings where regions are points in $\mathbb{R}^d$ and queries are hyperrectangles, and derive exact data structures that achieve improved performance in these structured spaces.

cs.DS↗

arXiv2025

Psychological stress during Examination and its estimation by handwriting in answer script

This research explores the fusion of graphology and artificial intelligence to quantify psychological stress levels in students by analyzing their handwritten examination scripts. By leveraging Optical Character Recognition and transformer based sentiment analysis models, we present a data driven approach that transcends traditional grading systems, offering deeper insights into cognitive and emotional states during examinations. The system integrates high resolution image processing, TrOCR, and sentiment entropy fusion using RoBERTa based models to generate a numerical Stress Index. Our method achieves robustness through a five model voting mechanism and unsupervised anomaly detection, making it an innovative framework in academic forensics.

cs.CV↗

arXiv2025

Material combination optimization for brazed ceramic-metal composites using Artificial Intelligence

This study proposes an Artificial Intelligence (AI) driven methodology for predicting a combination of brazed ceramic-metal composite materials. Multiple machine learning (ML) algorithms are compared with the deep learning (DL) model. The developed models are tested using k-fold validation. Nine different input-output feature configurations are evaluated to assess the model performance. The input-output feature comprises material properties, namely, the coefficient of thermal expansion (CTE) and molecular mass of brazed ceramic-metal composite materials obtained from literature and the strength parameter (average Von Mises Stress (VMS)) estimated from Finite Element Method (FEM) simulation for joint assembly structure. A multi-output model, Autoencoder (AE), has also been developed and tested to predict various features. The ML model, namely the polynomial regression (PR), outperforms the other ML/DL models with a Mean square Error (MSE) of 0.01 for the test data. The autoencoder model with a 32-16-32 structure outperforms LR, PR, RF, and ANN with an MSE of 0.04% for the prediction of unseen data. The developed multi-output model accurately predicts all the features (single and multiple), while PR fails to accurately predict multi-output features of low importance. The developed AE model predicts the different material properties with an average error of ~0.16-3.78% with literature-reported values.

physics.app-ph↗

arXiv2025

Vantage Point Selection Algorithms for Bottleneck Capacity Estimation

Motivated by the problem of estimating bottleneck capacities on the Internet, we formulate and study the problem of vantage point selection. We are given a graph $G=(V, E)$ whose edges $E$ have unknown capacity values that are to be discovered. Probes from a vantage point, i.e, a vertex $v \in V$, along shortest paths from $v$ to all other vertices, reveal bottleneck edge capacities along each path. Our goal is to select $k$ vantage points from $V$ that reveal the maximum number of bottleneck edge capacities. We consider both a non-adaptive setting where all $k$ vantage points are selected before any bottleneck capacity is revealed, and an adaptive setting where each vantage point selection instantly reveals bottleneck capacities along all shortest paths starting from that point. In the non-adaptive setting, by considering a relaxed model where edge capacities are drawn from a random permutation (which still leaves the problem of maximizing the expected number of revealed edges NP-hard), we are able to give a $1-1/e$ approximate algorithm. In the adaptive setting we work with the least permissive model where edge capacities are arbitrarily fixed but unknown. We compare with the best solution for the particular input instance (i.e. by enumerating all choices of $k$ tuples), and provide both lower bounds on instance optimal approximation algorithms and upper bounds for trees and planar graphs.

cs.DS↗

arXiv2025

Computing Diverse and Nice Triangulations

We initiate the study of computing diverse triangulations to a given polygon. Given a simple $n$-gon $P$, an integer $ k \geq 2 $, a quality measure $\sigma$ on the set of triangulations of $P$ and a factor $ \alpha \geq 1 $, we formulate the Diverse and Nice Triangulations (DNT) problem that asks to compute $k$ \emph{distinct} triangulations $T_1,\dots,T_k$ of $P$ such that a) their diversity, $\sum_{i < j} d(T_i,T_j) $, is as large as possible \emph{and} b) they are nice, i.e., $\sigma(T_i) \leq \alpha \sigma^* $ for all $1\leq i \leq k$. Here, $d$ denotes the symmetric difference of edge sets of two triangulations, and $\sigma^*$ denotes the best quality of triangulations of $P$, e.g., the minimum Euclidean length. As our main result, we provide a $\mathrm{poly}(n,k)$-time approximation algorithm for the DNT problem that returns a collection of $k$ distinct triangulations whose diversity is at least $1 - \Theta(1/k)$ of the optimal, and each triangulation satisfies the quality constraint. This is accomplished by studying \emph{bi-criteria triangulations} (BCT), which are triangulations that simultaneously optimize two criteria, a topic of independent interest. We complement our approximation algorithms by showing that the DNT problem and the BCT problem are NP-hard. Finally, for the version where diversity is defined as $\min_{i < j} d(T_i,T_j) $, we show a reduction from the problem of computing optimal Hamming codes, and provide an $n^{O(k)}$-time $\tfrac12$-approximation algorithm. This improves over the naive ${C_{n-2} \choose k} \approx 2^{O(nk)}$ time bound for enumerating all $k$-tuples among the triangulations of a simple $n$-gon, where $C_n$ denotes the $n$-th Catalan number.

cs.CG↗

arXiv2025

Additive Manufacturing Processes Protocol Prediction by Artificial Intelligence using X-ray Computed Tomography data

The quality of the part fabricated from the Additive Manufacturing (AM) process depends upon the process parameters used, and therefore, optimization is required for apt quality. A methodology is proposed to set these parameters non-iteratively without human intervention. It utilizes Artificial Intelligence (AI) to fully automate the process, with the capability to self-train any apt AI model by further assimilating the training data.This study includes three commercially available 3D printers for soft material printing based on the Material Extrusion (MEX) AM process. The samples are 3D printed for six different AM process parameters obtained by varying layer height and nozzle speed. The novelty part of the methodology is incorporating an AI-based image segmentation step in the decision-making stage that uses quality inspected training data from the Non-Destructive Testing (NDT) method. The performance of the trained AI model is compared with the two software tools based on the classical thresholding method. The AI-based Artificial Neural Network (ANN) model is trained from NDT-assessed and AI-segmented data to automate the selection of optimized process parameters. The AI-based model is 99.3 % accurate, while the best available commercial classical image method is 83.44 % accurate. The best value of overall R for training ANN is 0.82. The MEX process gives a 22.06 % porosity error relative to the design. The NDT-data trained two AI models integrated into a series pipeline for optimal process parameters are proposed and verified by classical optimization and mechanical testing methods.

cs.CV↗

arXiv2025

A Framework for the Design of Efficient Diversification Algorithms to NP-Hard Problems

There has been considerable recent interest in computing a diverse collection of solutions to a given optimization problem, both in the AI and theory communities. Given a classical optimization problem $\Pi$ (e.g., spanning tree, minimum cuts, maximum matching, minimum vertex cover) with input size $n$ and an integer $k\geq 1$, the goal is to generate a collection of $k$ maximally diverse solutions to $\Pi$. This diverse-X paradigm not only allows the user to generate very different solutions, but also helps make systems more secure and robust by handling uncertainty, and achieve energy efficiency. For problems $\Pi$ in P (such as spanning tree and minimum cut), there are efficient $\text{poly}(n,k)$ approximation algorithms available for the diverse variants [Hanaka et al. AAAI 2021, 2022, 2023, Gao et al. LATIN 2022, de Berg et al. ISAAC 2023]. In contrast, only FPT algorithms are known for NP-hard problems such as vertex covers and independent sets [Baste et al. IJCAI 2020, Eiben et al. SODA 2024, Misra et al. ISAAC 2024, Austrin et al. ICALP 2025], but in the worst case, these algorithms run in time $\exp((kn)^c)$ for some $c>0$. In this work, we address this gap and give $\text{poly}(n,k)$ or $f(k)\text{poly}(n)$ time approximation algorithms for diversification variants of several NP-hard problems such as knapsack, maximum weight independent sets (MWIS) and minimum vertex covers in planar graphs, geometric (rectangle) knapsack, enclosing points by polygon, and MWIS in unit-disk-graphs of points in convex position. Our results are achieved by developing a general framework and applying it to problems with textbook dynamic-programming algorithms to find one solution.

cs.CG↗

arXiv2024

A Theoretical Study of Neural Network Expressive Power via Manifold Topology

A prevalent assumption regarding real-world data is that it lies on or close to a low-dimensional manifold. When deploying a neural network on data manifolds, the required size, i.e., the number of neurons of the network, heavily depends on the intricacy of the underlying latent manifold. While significant advancements have been made in understanding the geometric attributes of manifolds, it's essential to recognize that topology, too, is a fundamental characteristic of manifolds. In this study, we investigate network expressive power in terms of the latent data manifold. Integrating both topological and geometric facets of the data manifold, we present a size upper bound of ReLU neural networks.

cs.LG↗

arXiv2024

Pulse excitation mode selection via AI Pipeline to Fully Automate the WUCT System

The parametric optimization for the ultrasound computed tomography system is introduced. It is hypothesized that the pulse characteristic directly affects the information present in the reconstructed profile. The ultrasound excitation modes based on pulse-width modifications are studied to estimate the effect on reconstruction quality. Studies show that the pulse width affects the response of the transducer and, thus, the reconstruction. The ultrasound scanning parameters, mainly pulse width, are assessed and optimally set by an Artificial Intelligence driven process, according to the object without the requirement of a-priori information. The optimization study uses a novel intelligent object placement procedure to ensure repeatability of the same region of interest, a key requirement to minimize the error. Further, Kanpur Theorem 1 is implemented to evaluate the quality of the acquired projection data and discard inferior quality data. Scanning results corresponding to homogeneous and heterogeneous phantoms are presented. The image processing step involves deep learning model evaluating the dice coefficient for estimating the reconstruction quality if prior information about the inner profile is known or a classical error estimate otherwise. The models segmentation accuracy is 95.72 percentage and intersection over union score is 0.8842 on the validation dataset. The article also provides valuable insights about the development and low-level control of the system.

physics.med-ph↗

arXiv2024

Self-calibrating Intelligent OCT-SLO System

A unique sample independent 3D self calibration methodology is tested on a unique optical coherence tomography and multi-spectral scanning laser ophthalmoscope (OCT-SLO) hybrid system. Operators visual cognition is replaced by computer vision using the proposed novel fully automatic AI-driven system design. Sample specific automatic contrast adjustment of the beam is achieved on the pre-instructed region of interest. The AI model deduces infrared, fluorescence, and visual spectrum optical alignment by estimating pre-instructed features quantitatively. The tested approach, however, is flexible enough to utilize any apt AI model. Relative comparison with classical signal-to-noise-driven automation is shown to be 200 percent inferior and 130 percent slower than the AI-driven approach. The best spatial resolution of the system is found to be (a) 2.41 microns in glass bead eye phantom, 0.76 with STD 0.46 microns in the mouse retina in the axial direction, and (b) better than 228 line pair per millimeter (lp per mm) or 2 microns for all three spectrums, i.e., 488 nm, 840 nm, and 520 to 550 nm emission in coronal, frontal or x-y plane. Intelligent automation reduces the possibility of developing cold cataracts (especially in mouse imaging) and patient-associated discomfort due to delay during manual alignment by facilitating easy handling for swift ocular imaging and better accuracy. The automatic novel tabletop compact system provides true functional 3D images in three different spectrums for dynamic sample profiles. This is especially useful for photodynamic imaging treatment.

physics.med-ph↗

arXiv2024

Non-invasive imaging assisted CFD simulation of 4D multi-modal fluid flow using In-situ adaptor

X-ray Computed Tomography (CT) is used to recover the true surfaces of fluid channels and fed to simulation tool (ANSYS) to create accurate cyber environment. The simulation tool also receives CT-assisted multiphase fluid profiles (belonging to the instance just before the flow starts) as an initial condition. This unique methodology is made possible by using a novel in-situ compact adaptor design is used to create fluid channels that can be placed inside any industrial X-ray CT and fulfill the above objective. It is integrated with an android based App to control the flow once placed inside CT. It is portable and compact enough: (a) to be placed inside various experimental environments, and (b) modular enough to be mounted with multi-modal systems simultaneously. Two key parameters, (a) spatial distribution and (b) the air volume fraction, are measured using two different non-invasive imaging modalities: (a) Electrical Impedance Tomography (EIT) and (d) X-ray Computed Tomography (CT). Simulated outcomes are correlated with the experimental outcomes from both EIT and X-ray CT, showing an agreement of 85 to 98 percent, respectively. Time-averaged electrically conductive fluid flow profile obtained by EIT shows a match with mass mass-attenuated fluid profile obtained by X-ray CT, justifying the utility of an in-situ adaptor. CT assistance for CFD studies can be replaced by EIT assistance as former techniques: (a) scanning time may be relatively slower than the latter, (b) it does not require rotations, (c) economical, and (d) fluid channels need not be placed inside of shielded compartment thus improving practicality. The data of analysis is shared in this work. Multimodal non-invasive imaging provides multiphase flow information, it also differentiates conductive, and mass-attenuated multiphase profiles at common cross-sections.

physics.flu-dyn↗

arXiv2024

Algorithms for the Diverse-k-SAT problem: the geometry of satisfying assignments

Given a $k$-CNF formula and an integer $s$, we study algorithms that obtain $s$ solutions to the formula that are maximally dispersed. For $s=2$, the problem of computing the diameter of a $k$-CNF formula was initiated by Creszenzi and Rossi, who showed strong hardness results even for $k=2$. Assuming SETH, the current best upper bound [Angelsmark and Thapper '04] goes to $4^n$ as $k \rightarrow \infty$. As our first result, we give exact algorithms for using the Fast Fourier Transform and clique-finding that run in $O^*(2^{(s-1)n})$ and $O^*(s^2 |\Omega_{F}|^{\omega \lceil s/3 \rceil})$ respectively, where $|\Omega_{F}|$ is the size of the solution space of the formula $F$ and $\omega$ is the matrix multiplication exponent. As our main result, we re-analyze the popular PPZ (Paturi, Pudlak, Zane '97) and Sch\"{o}ning's ('02) algorithms (which find one solution in time $O^*(2^{\varepsilon_{k}n})$ for $\varepsilon_{k} \approx 1-\Theta(1/k)$), and show that in the same time, they can be used to approximate the diameter as well as the dispersion ($s>2$) problems. While we need to modify Sch\"{o}ning's original algorithm, we show that the PPZ algorithm, without any modification, samples solutions in a geometric sense. We believe that this property may be of independent interest. Finally, we present algorithms to output approximately diverse, approximately optimal solutions to NP-complete optimization problems running in time $\text{poly}(s)O^*(2^{\varepsilon n})$ with $\varepsilon<1$ for several problems such as Minimum Hitting Set and Feedback Vertex Set. For these problems, all existing exact methods for finding optimal diverse solutions have a runtime with at least an exponential dependence on the number of solutions $s$. Our methods find bi-approximations with polynomial dependence on $s$.

cs.CC↗

arXiv2024

On Instance-Optimal Algorithms for a Generalization of Nuts and Bolts and Generalized Sorting

We generalize the classical nuts and bolts problem to a setting where the input is a collection of $n$ nuts and $m$ bolts, and there is no promise of any matching pairs. It is not allowed to compare a nut directly with a nut or a bolt directly with a bolt, and the goal is to perform the fewest nut-bolt comparisons to discover the partial order between the nuts and bolts. We term this problem \emph{bipartite sorting}. We show that instances of bipartite sorting of the same size exhibit a wide range of complexity, and propose to perform a fine-grained analysis for this problem. We rule out straightforward notions of instance-optimality as being too stringent, and adopt a \emph{neighborhood-based} definition. Our definition may be of independent interest as a unifying lens for instance-optimal algorithms for other static problems existing in literature. This includes problems like sorting (Estivill-Castro and Woods, ACM Comput. Surv. 1992), convex hull (Afshani, Barbay and Chan, JACM 2017), adaptive joins (Demaine, López-Ortiz and Munro, SODA 2000), and the recent concept of universal optimality for graphs (Haeupler, Hladík, Rozhoň, Tarjan and Tětek, 2023). As our main result on bipartite sorting, we give a randomized algorithm that is within a factor of $O(\log ^3 (n+m))$ of being instance-optimal w.h.p., with respect to the neighborhood-based definition. As our second contribution, we generalize bipartite sorting to DAG sorting, when the underlying DAG is not necessarily bipartite. As an unexpected consequence of a simple algorithm for DAG sorting, we rule out a potential lower bound on the widely-studied problem of \emph{sorting with priced information}, posed by (Charikar, Fagin, Guruswami, Kleinberg, Raghavan and Sahai, STOC 2000).

cs.DS↗

arXiv2023

An Algorithm for Bichromatic Sorting with Polylog Competitive Ratio

The problem of sorting with priced information was introduced by [Charikar, Fagin, Guruswami, Kleinberg, Raghavan, Sahai (CFGKRS), STOC 2000]. In this setting, different comparisons have different (potentially infinite) costs. The goal is to find a sorting algorithm with small competitive ratio, defined as the (worst-case) ratio of the algorithm's cost to the cost of the cheapest proof of the sorted order. The simple case of bichromatic sorting posed by [CFGKRS] remains open: We are given two sets $A$ and $B$ of total size $N$, and the cost of an $A-A$ comparison or a $B-B$ comparison is higher than an $A-B$ comparison. The goal is to sort $A \cup B$. An $Ω(\log N)$ lower bound on competitive ratio follows from unit-cost sorting. Note that this is a generalization of the famous nuts and bolts problem, where $A-A$ and $B-B$ comparisons have infinite cost, and elements of $A$ and $B$ are guaranteed to alternate in the final sorted order. In this paper we give a randomized algorithm InversionSort with an almost-optimal w.h.p. competitive ratio of $O(\log^{3} N)$. This is the first algorithm for bichromatic sorting with a $o(N)$ competitive ratio.

cs.DS↗

arXiv2023

Prescanning Assembly Optimization Criteria for Computed Tomography

Computerized Tomography assembly and system configuration are optimized for enhanced invertibility in sparse data reconstruction. Assembly generating maximum principal components/condition number of weight matrix is designated as best configuration. The gamma CT system is used for testing. The unoptimized sample location placement with 7.7% variation results in a maximum 50% root mean square error, 16.5% loss of similarity index, and 40% scattering noise in the reconstructed image relative to the optimized sample location when the proposed criteria are used. The method can help to automate the CT assembly, resulting in relatively artifact-free recovery and reducing the iteration to figure out the best scanning configuration for a given sample size, thus saving time, dosage, and operational cost.

physics.ins-det↗

arXiv2023

Learning to Segment from Noisy Annotations: A Spatial Correction Approach

Noisy labels can significantly affect the performance of deep neural networks (DNNs). In medical image segmentation tasks, annotations are error-prone due to the high demand in annotation time and in the annotators' expertise. Existing methods mostly assume noisy labels in different pixels are \textit{i.i.d}. However, segmentation label noise usually has strong spatial correlation and has prominent bias in distribution. In this paper, we propose a novel Markov model for segmentation noisy annotations that encodes both spatial correlation and bias. Further, to mitigate such label noise, we propose a label correction method to recover true label progressively. We provide theoretical guarantees of the correctness of the proposed method. Experiments show that our approach outperforms current state-of-the-art methods on both synthetic and real-world noisy annotations.

eess.IV↗

arXiv2023

Characterization of Electrical Impedance Tomography System

Electrical Impedance Tomography can be cost-effective, portable, non-invasive imaging technique. It has preclinical and a few of them already proven industrial applications. This technique can only recover images of low spatial and contrast resolution, partially due to existing physical models. The capability of discriminating between Impedance profiles in recovery is around 73 percentage. However, similar to other modalities, EITs performance depends on the hardware and recovery algorithm design and operating parameters. This work presents an empirically obtained mutual relation between the hardware design related six independent variables, namely (a) molarity of the coupling media, (b) scanning duration, (c) Size of the object, and (d) parameters defining the size of the scanning assembly (No of electrodes, area of the vessel, and percentage periphery covered by the electrodes), affecting its performance. The expression predicts that the error can be kept under a 10 percentage value in a worst-case scenario if these six parameters are kept under a given range. The root mean square error between the experiment values and predicted values from the presented equation is 1.4053. It is shown that time significantly affects the recovery process compared to other optimizing parameters. It is also shown that the accepted molarity value for the presented system is 2M.

physics.ins-det↗