Amit Kumar

EAAI Journal 2026 Journal Article

A note on “Optimizing the selection of the secret parameters for public key cryptosystems by using interval linear programming and fully fuzzy linear programming”

• Raina Ahuja
• Parul Tomar
• Amit Kumar
• S.S. Appadoo

Bas (Eng. Appl. Artif. Intell. (2025) 144 (110168)) claimed that, to the best of their knowledge, no mathematical programming-based method has been proposed in the literature to determine optimal secret parameters of public key cryptosystems in an interval or fuzzy environment. To fill this gap, Bas proposed an interval mathematical programming problem (IMPP) and a fuzzy mathematical programming problem (FMPP) for the Rivest, Shamir, Adleman (RSA) public key cryptosystem. Bas also proposed a method to solve IMPP as well as a method to solve FMPP. In these methods, firstly, IMPP and FMPP are transformed into crisp mathematical programming problem (CMPP). Then, using an optimal solution of the transformed CMPP, an optimal solution of original IMPP and FMPP is obtained. In this note, it is pointed out that the subtraction operation of triangular fuzzy numbers (TFNs), used in the method to transform FMPP into CMPP, is not valid. Due to which the transformed CMPP is not equivalent to the original FMPP. Hence, Bas's method to solve FMPP is not valid in its present form. Keeping the same in mind, Bas's method is modified by replacing the invalid subtraction operation of TFNs with the valid subtraction operation. Furthermore, using the modified method, correct results for the RSA public key cryptosystem corresponding to existing data, considered by Bas to illustrate their proposed method, are obtained. It is pertinent to mention that the subtraction operation of intervals, used in Bas's method to transform IMPP into CMPP, is valid.

SODA Conference 2025 Conference Paper

Breaking the Two Approximation Barrier for Various Consensus Clustering Problems

• Debarati Das 0001
• Amit Kumar

NeurIPS Conference 2025 Conference Paper

Learning-Augmented Algorithms for $k$-median via Online Learning

• Anish Hebbar
• Rong Ge
• Amit Kumar
• Debmalya Panigrahi

The field of learning-augmented algorithms seeks to use ML techniques on past instances of a problem to inform an algorithm designed for a future instance. In this paper, we introduce a novel model for learning-augmented algorithms inspired by online learning. In this model, we are given a sequence of instances of a problem and the goal of the learning-augmented algorithm is to use prior instances to propose a solution to a future instance of the problem. The performance of the algorithm is measured by its average performance across all the instances, where the performance on a single instance is the ratio between the cost of the algorithm's solution and that of an optimal solution for that instance. We apply this framework to the classic $k$-median clustering problem, and give an efficient learning algorithm that can approximately match the average performance of the best fixed $k$-median solution in hindsight across all the instances. We also experimentally evaluate our algorithm and show that its empirical performance is close to optimal, and also that it automatically adapts the solution to a dynamically changing sequence.

NeurIPS Conference 2025 Conference Paper

Matchings Under Biased and Correlated Evaluations

• Amit Kumar
• Nisheeth K. Vishnoi

We study a two-institution stable matching model in which candidates from two distinct groups are evaluated using partially correlated signals that are group-biased. This extends prior work (which assumes institutions evaluate candidates in an identical manner) to a more realistic setting in which institutions rely on overlapping, but independently processed, criteria. These evaluations could consist of a variety of informative tools such as standardized tests, shared recommendation systems, or AI-based assessments with local noise. Two key parameters govern evaluations: the bias parameter $\beta \in (0, 1]$, which models systematic disadvantage faced by one group, and the correlation parameter $\gamma \in [0, 1]$, which captures the alignment between institutional rankings. We study the representation ratio $\mathcal{R}(\beta, \gamma)$, i. e. , the ratio of disadvantaged to advantaged candidates selected by the matching process in this setting. Focusing on a regime in which all candidates prefer the same institution, we characterize the large-market equilibrium and derive a closed-form expression for the resulting representation ratio. Prior work shows that when $\gamma = 1$, this ratio scales linearly with $\beta$. In contrast, we show that $\mathcal{R}(\beta, \gamma)$ increases nonlinearly with $\gamma$ and even modest losses in correlation can cause sharp drops in the representation ratio. Our analysis identifies critical $\gamma$-thresholds where institutional selection behavior undergoes discrete transitions, and reveals structural conditions under which evaluator alignment or bias mitigation are most effective. Finally, we show how this framework and results enable interventions for fairness-aware design in decentralized selection systems.

AAAI Conference 2024 Conference Paper

Towards Fairness in Online Service with K Servers and Its Application on Fair Food Delivery

• Daman Deep Singh
• Amit Kumar
• Abhijnan Chakraborty

The k-SERVER problem is one of the most prominent problems in online algorithms with several variants and extensions. However, simplifying assumptions like instantaneous server movements and zero service time has hitherto limited its applicability to real-world problems. In this paper, we introduce a realistic generalization of k-SERVER without such assumptions – the k-FOOD problem, where requests with source-destination locations and an associated pickup time window arrive in an online fashion, and each has to be served by exactly one of the available k servers. The k-FOOD problem offers the versatility to model a variety of real-world use cases such as food delivery, ride sharing, and quick commerce. Moreover, motivated by the need for fairness in online platforms, we introduce the FAIR k-FOOD problem with the max-min objective. We establish that both k-FOOD and FAIR k-FOOD problems are strongly NP-hard and develop an optimal offline algorithm that arises naturally from a time-expanded flow network. Subsequently, we propose an online algorithm DOC4FOOD involving virtual movements of servers to the nearest request location. Experiments on a real-world food-delivery dataset, alongside synthetic datasets, establish the efficacy of the proposed algorithm against state-of-the-art fair food delivery algorithms.

AAAI Conference 2024 Conference Paper

Universal Weak Coreset

• Ragesh Jaiswal
• Amit Kumar

Coresets for k-means and k-median problems yield a small summary of the data, which preserves the clustering cost with respect to any set of k centers. Recently coresets have also been constructed for constrained k-means and k-median problems. However, the notion of coresets has the drawback that (i) they can only be applied in settings where the input points are allowed to have weights, and (ii) in general metric spaces, the size of the coresets can depend logarithmically on the number of points. The notion of weak coresets, which has less stringent requirements than coresets, has been studied in the context of classical k-means and k-median problems. A weak coreset is a pair (J,S) of subsets of points, where S acts as a summary of the point set and J as a set of potential centers. This pair satisfies the properties that (i) S is a good summary of the data as long as the k centers are chosen from J only, and (ii) there is a good choice of k centers in J with a cost close to the optimal cost. We develop this framework, which we call universal weak coresets, for constrained clustering settings. In conjunction with recent coreset constructions for constrained settings, our designs give greater data compression, are conceptually simpler, and apply to a wide range of constrained k-median and k-means problems.

NeurIPS Conference 2023 Conference Paper

Bias in Evaluation Processes: An Optimization-Based Model

• L. Elisa Celis
• Amit Kumar
• Anay Mehrotra
• Nisheeth K. Vishnoi

Biases with respect to socially-salient attributes of individuals have been well documented in evaluation processes used in settings such as admissions and hiring. We view such an evaluation process as a transformation of a distribution of the true utility of an individual for a task to an observed distribution and model it as a solution to a loss minimization problem subject to an information constraint. Our model has two parameters that have been identified as factors leading to biases: the resource-information trade-off parameter in the information constraint and the risk-averseness parameter in the loss function. We characterize the distributions that arise from our model and study the effect of the parameters on the observed distribution. The outputs of our model enrich the class of distributions that can be used to capture variation across groups in the observed evaluations. We empirically validate our model by fitting real-world datasets and use it to study the effect of interventions in a downstream selection task. These results contribute to an understanding of the emergence of bias in evaluation processes and provide tools to guide the deployment of interventions to mitigate biases.

EAAI Journal 2023 Journal Article

Design of a novel mixed interval type-2 fuzzy logic controller for 2-DOF robot manipulator with payload

• Anupam Kumar
• Ritu Raj
• Amit Kumar
• Bharat Verma

This paper investigates a novel coupling-based mixed interval type-2 fuzzy logic controller (MIT2FLC) for trajectory tracking problems of highly nonlinear and complex robot manipulator plants. The major impediment for these types of plants is coupling between the robotic links at the time of operation. In addition, the performances of these plants are adversely affected by parameter uncertainties, random noise and external disturbances. Therefore, the MIT2FLC approach with an additional degree of freedom in the membership functions is proposed to efficiently deal with the problem of uncertainty and provide robust performance. The Grey wolf optimization (GWO) is implemented to calculate the optimal parameters of the proposed controller. For checking the performance, the MIT2FLC approach is compared with its type-1 fuzzy counterparts, namely mixed type-1 fuzzy logic controller (MT1FLC), type-1 fuzzy logic controller (T1FLC) and PID controllers. Robustness analysis of the proposed controller is investigated for external disturbances, varying system parameters, and random noise.

JBHI Journal 2021 Journal Article

A New Force Myography-Based Approach for Continuous Estimation of Knee Joint Angle in Lower Limb Amputees and Able-Bodied Subjects

• Amit Kumar
• Anoop Kant Godiyal
• Pradeep Joshi
• Deepak Joshi

In this paper, we present a new method for estimating knee joint angle using force myography. The technique utilized force myogram signals from thigh muscles while subjects walked on a treadmill at different speeds, i. e. , slow, medium, fast, and run. An eight-channel in-house force myography (FMG) data acquisition system was developed to collect the data wirelessly from seven healthy subjects and a transfemoral amputee. An artificial neural network was employed to estimate the knee joint angle from force myogram signals. The root-mean-square error across the healthy subjects was 6. 9±1. 5° at slow (1. 5 km/hr), 6. 5±1. 3° at medium (4 km/hr), 7. 4±2. 2° at fast (6 km/hr) speeds, and 8. 1±2. 2° while running (8 km/hr). The root-mean-square error, across the trials, for the transfemoral amputee was 4. 0±1. 2° at slow (1 km/hr), 3. 2±0. 6° at medium (2 km/hr) and 3. 8±0. 9° at fast (3 km/hr) speeds. The proposed approach is useful in real-time gait analysis. The system is easily wearable, convenient in out-door use, portable, and commercially viable.

NeurIPS Conference 2021 Conference Paper

A Regression Approach to Learning-Augmented Online Algorithms

• Keerti Anand
• Rong Ge
• Amit Kumar
• Debmalya Panigrahi

The emerging field of learning-augmented online algorithms uses ML techniques to predict future input parameters and thereby improve the performance of online algorithms. Since these parameters are, in general, real-valued functions, a natural approach is to use regression techniques to make these predictions. We introduce this approach in this paper, and explore it in the context of a general online search framework that captures classic problems like (generalized) ski rental, bin packing, minimum makespan scheduling, etc. We show nearly tight bounds on the sample complexity of this regression problem, and extend our results to the agnostic setting. From a technical standpoint, we show that the key is to incorporate online optimization benchmarks in the design of the loss function for the regression problem, thereby diverging from the use of off-the-shelf regression tools with standard bounds on statistical error.

EAAI Journal 2020 Journal Article

A note on “Novel scaled prioritized intuitionistic fuzzy soft interaction averaging aggregation operators and their application to multi criteria decision making”

• Akansha Mishra
• Amit Kumar
• S.S. Appadoo

Garg and Arora (2018) pointed out that it is not appropriate to use the existing intuitionistic fuzzy soft (IFS) aggregations operators (Arora and Garg, 2018a, b), proposed by themselves, as these aggregation operators gives undesirable results under some circumstances. To resolve the flaws of these aggregation operators, Garg and Arora (2018) proposed the improved operational laws of IFS numbers and hence, proposed a new IFS aggregation operator (named as Scaled prioritized intuitionistic fuzzy soft interaction (SPIFSI) aggregation operator). Garg and Arora (2018) also proposed a SPIFSI aggregation operator based intuitionistic fuzzy soft multi criteria decision making (IFSMCDM) approach for solving IFSMCDM problems (Multi criteria decision making problems in which the rating value of each alternative over each criterion is represented by an IFS set). Although, Garg and Arora (2018) have claimed that their proposed SPIFSI aggregation operator is valid as it satisfies the idempotency, boundedness and monotonicity properties. But, in actual case, for the SPIFSI aggregation operator, proposed by Garg and Kumar (2018), the monotonicity property is not satisfying. Therefore, the SPIFSI aggregation operator, proposed by Garg and Arora (2018), and hence, the SPIFSI aggregation operator based IFSMCDM approach, are not valid. Since, in future, other researchers may use the SPIFSI aggregation operator in their research work. Also, the researchers may use the SPIFSI aggregation operator based IFSMCDM approach for solving real life IFSMCDM problems. Therefore, the aim of this note is to make the researchers aware about the discrepancies of the SPIFSI aggregation operator as well as the SPIFSI aggregation operator based IFMCDM approach. Furthermore, to make the researchers aware that improved operational laws of IFS numbers, proposed by Garg and Arora (2018), are also not valid.

EAAI Journal 2017 Journal Article

A note on “A new fuzzy regression model based on absolute deviation”

• Abdullah Al-Qudaimi
• Amit Kumar

Li et al. (2016) proposed a least absolute deviation method to find such fuzzy regression models whose all the parameters are trapezoidal fuzzy numbers. Since, the method, proposed by Li et al. , is published in Engineering Applications of Artificial Intelligence (a very reputed International Journal) as well as it is easy to apply Li et al. method in real life problems. So, other researchers may be attracted to apply the method, proposed by Li et al. , to find the solution of real life problems. However, after a deep study of the work done by Li et al. , it is noticed that the multiplication of two trapezoidal fuzzy numbers, proposed by Li et al. as well as used in this method, is not valid. Hence, the aim of this note is to make the researchers aware about the valid multiplication of trapezoidal fuzzy numbers that should be used in Li et al. method.

TCS Journal 2016 Journal Article

Minimizing average flow-time under knapsack constraint

• Suman K. Bera
• Syamantak Das
• Amit Kumar

We give the first logarithmic approximation for minimizing average flow-time of jobs in the subset parallel machine setting (also called the restricted assignment setting) under a single knapsack constraint. In a knapsack constraint setting, each job has a profit, and the set of jobs which get scheduled must have a total profit of at least a quantity Π. Our result extends the work of Gupta et al. (2009) [8] who considered the special case where the profit of each job is unity. Our algorithm is based on rounding a natural LP relaxation for this problem. In fact, we show that one can use techniques based on iterative rounding.

EAAI Journal 2014 Journal Article

A novel general approach to evaluating the reliability of gas turbine system

• Manjit Verma
• Amit Kumar

In this paper, a new methodology named as vague lambda–tau, is proposed for reliability analysis of the repairable systems based on a trapezoidal vague set with different left and right heights. In this methodology, the trapezoidal vague set with different left and right heights is coupled with the conventional lambda–tau method to evaluate the vague expressions for OR-transition of the Petri Nets model. The qualitative and quantitative analysis of gas turbine system has been discussed in this work. In qualitative analysis, the Petri Net model is obtained from its equivalent Fault Tree and in quantitative analysis, the reliability parameters are evaluated using the vague lambda–tau methodology. The system reliability can be analyzed in a more flexible and intelligent manner by using the proposed approach.

TCS Journal 2014 Journal Article

Approximation algorithms for the partition vertex cover problem

• Suman K. Bera
• Shalmoli Gupta
• Amit Kumar
• Sambuddha Roy

We consider a natural generalization of the Partial Vertex Cover problem. Here an instance consists of a graph G = ( V, E ), a cost function c: V → Z +, a partition P 1, …, P r of the edge set E, and a parameter k i for each partition P i. The objective is to find a minimum cost set of vertices which cover at least k i edges from the partition P i. We call this the Partition-VC problem. In this paper, we give matching upper and lower bound on the approximability of this problem. Our algorithm is based on a novel LP relaxation for this problem. This LP relaxation is obtained by adding knapsack cover inequalities to a natural LP relaxation of the problem. We show that this LP has integrality gap of O ( log ⁡ r ), where r is the number of sets in the partition of the edge set. We also extend our result to more general settings. For example we consider a problem where additionally edges have profits, and we would like to pick a minimum cost set of vertices which cover edges of total profit at least Π i for each partition P i. We call this the Knapsack Partition Vertex Cover problem. We give an O ( log ⁡ r ) approximation algorithm for this problem as well.

ICRA Conference 2005 Conference Paper

Towards Decentralization of Multi-robot Navigation Functions

• Herbert G. Tanner
• Amit Kumar

We present a navigation function through which a group of mobile agents can be coordinated to achieve a particular formation, both in terms of shape and orientation, while avoiding collisions between themselves and with obstacles in the environment. Convergence is global and complete, subject to the constraints of the navigation function methodology. Algebraic graph theoretic properties associated with the interconnection graph are shown to affect the shape of the navigation function. The approach is centralized but the potential function is constructed in a way that facilitates complete decentralization. The strategy presented will also serve as a point of reference and comparison in quantifying the cost of decentralization in terms of performance.

ICRA Conference 2002 Conference Paper

Distributed Relational Decision Framework for Scalable Enterprise Systems

• Amit Kumar
• Arthur C. Sanderson
• Robert J. Graves
• Raj Subbu

Describes a framework to support enterprise-level decision-making in network-based scalable systems. The fundamental principle of this approach asserts that decision tasks over a set of multiple, distributed, logically interrelated databases may be cast in the semantics of the underlying distributed database management system (DBMS). In this form, the augmented relational decision framework takes advantage of the principles of normalization and decomposition that are inherent to the relational DBMS model. The decision process is viewed as an instantiation of the relational schema, and the resulting representation of normal form hierarchies and data dependencies structures the process. Definition of a value function (or rule set) over the augmented relational decision space guides the search for desirable instances of the decision relations that constitute the suggested outcomes.