Dr. Srikrishnan Divakaran is a Theoretical Computer Scientist with over 25 years of experience in education and research, as well as over 5 years of industry experience in computing and finance with leading international companies. In 2002, Dr. Divakaran received his PhD from Rutgers University in New Brunswick, New Jersey. He then worked as an Assistant Professor in the Computer Science department at Hofstra University on Long Island, NY, from 2002 to 2008, and as an Associate Professor at DAIICT from 2009 to 2016, before becoming an Associate Professor at Ahmedabad University's School of Engineering and Applied Sciences.

Dr. Divakaran has taught a variety of courses in Computer Science and related disciplines such as Applied Mathematics, Computational Biology/Bioinformatics and Data Sciences. Dr. Divakaran’s research focuses on the design and analysis of algorithms for problems with applications in Computational Biology/Bioinformatics, Combinatorial Optimization and Data Science.  Dr. Divakaran’s current research focus is mostly on the design and analysis of algorithms and heuristics for problems with applications in Data Science.  Dr. Divakaran has also played a key role in designing (i) the Bioinformatics specialization as a part of Hofstra’s Master’s degree in Computer Science, (ii) the B.Tech (ICT) program with a specialization in Computational Sciences at DAIICT, and (iii) the B.S. Computer Science (Honors) program at Ahmedabad University. He has also (i) guided many undergraduate students in gaining a better understanding of research through summer internships and summer research projects; and (ii) mentored many groups of students for ACM programming competitions.

Research Summary of Srikrishnan Divakaran

I am a Theoretical Computer Scientist with research interests in the design and analysis of algorithms for problems with applications in Computational Biology, Combinatorial Optimization and Data Science. My current research focus is mostly on problems with applications in Data Science.

Data Science Research

In Data Science, I'm interested in the design and analysis of (i) Decision Tree (DT) based methods for problems in Sports Data Analytics (SDA); (ii) Image Registration (IR) algorithms in medical imaging; (iii) Machine Learning (ML) and Deep Neural Network (DNN) based models for Atmospheric Correction (AC); and (iv) Image Fusion Tools in the context of Digital Agriculture.

DT based methods for problems in Sports Data Analytics (SDA): This study entails using DT-based methodologies to assist coaches in developing better athletic training and game-winning strategies. This initiative is part of a SDA study led by Professors Mehul Raval and Kaya Tolga, as well as a PhD student named Srishti Sharma. In this research, we constructed DT based models for analyzing the sleep and recovery data, training statistics and cognitive state of basketball players to predict their game scores. We leverage the high interpretability aspect of DT to developing a hybrid approach that employs classification/regression trees and random forests in conjunction with factor analysis (for computational efficiency - quadratic speedup) for predicting the weighted game score.

Image Registration (IR) algorithms in medical imaging:  IR involves integrating the features from multiple images by merging these images into a single image by relating them through a common coordinate system. Some applications of IR include (i) correction of MRI images for small amount of subject motion during    imaging; (ii) spatial normalization - integrate several     images of a subject into a single image.  In this research, I use combinatorial and information theoretic strategies to (i) uncover point features/structures (i.e., features that serve as the foundation for lines, surfaces, and bodies); (ii) align these features; and (iii) verify their accuracy.

Machine Learning (ML) and Deep Neural Network (DNN) based models for Atmospheric Correction (AC): AC is the process of retrieving correct surface reflectance (SR) values from the top of the atmosphere (TOA) radiance values by removing the effect of the atmosphere from the electromagnetic radiation reflected from the earth. Traditionally, AC has been done using physics-based methods. These methods are computationally demanding and rely on pre-computed lookup tables based on approximations of the true correlations between these variables. The goal of this project is to develop effective and efficient AC solutions using machine learning and deep neural networks. This work is done in collaboration with Professor Mehul Raval and a PhD scholar, Mr. Maitrik Shah.

Image Fusion Tools in the context of Digital Agriculture: My study in this project is focused on the characterization of higher-dimensional maps for integrating satellite, unmanned aerial vehicle (UAV), and multi-sensor farm data. Satellites provide time series data in the form of multispectral images depicting land surface characteristics over several square kilometers, UAVs provide multispectral farm data with very high resolution over a few hundred square meters, and low-cost sensors and IOT devices provide accurate spatial and time series data of land and soil characteristics over a few meters. The goal of this project is to use the synergies between the three data sources to create a high-dimensional farm map. This work entails (i) characterizing higher dimensional maps in terms of attributes obtained from these three data sources; (ii) developing ML based models and algorithms to construct these higher dimensional maps from these three data sources.

Our Results: For the sports analytics problem, we used a hybrid strategy that used factor analysis to compactly characterize the athlete's data in terms of seven latent components, and then used these factors to build a collection of decision trees for predicting and interpreting game scores. Our forecasts have an MSE of 0.013 and an R2 of 0.971, which is superior to traditional multi-linear regression (MSE 0.053, R2 0.689) and DT (MSE 0.036, R2 0.798) techniques. When applied to our suggested model, interpretability techniques can aid coaches in understanding model outcomes and assisting them in squad selection.

For the IR challenge, I created novel IR algorithms that create templates based on consensus reached by aligning features/structures of related images, and then utilize this template to devise various techniques for different types of image registrations in different imaging contexts.

Our DNN emulator's predictions for the AC problem were comparable to the 6S physics-based atmospheric correction model in most contexts (coefficients of correlation between the model predicted surface reflectance and the 6S physics-based model were 0.9777, 0.9770, 0.9781, and 0.9788 for the Blue, Green, Red, and NIR bands, respectively), while requiring significantly less computational resources.

Computational Biology Research

My research in Computational Biology focused on the development and analysis of approximation algorithms and heuristics for the following problems: (1) Constrained Generalized Tree Alignment and (2) Fast Heuristics for Exact String Matching.

Constrained Generalized Tree Alignment: For a given set S of related biological sequences, the generalized tree alignment problem is the problem of constructing an evolutionary tree for S of minimum cost, where the cost of the tree is the sum of its edge costs and the cost of an edge represents either the mutational distance or the similarity of the biological sequences associated with the ends of the edge. This problem involves simultaneously constructing a phylogenetic tree and a minimum cost evolutionary tree for S. This problem is known to be MAX-SNP Hard and is one of the widely studied problems in Computational Biology.

In many instances of the generalized tree alignment problem, a partial phylogenetic tree is known either based on known biological relationships between sequences or based on clustering information. In these situations there are no incentives for algorithms to exploit the knowledge of partial phylogenetic tree to construct evolutionary trees. However, if constraints are placed on the evolutionary tree topology, then there is incentive for algorithms to use the partial phylogenetic tree to restrict the number of tree topologies it considers and construct biologically relevant minimum cost evolutionary tree for S. So, I proposed the following natural generalization of the generalized tree alignment problem:

Given a set of k related biological sequences and a phylogenetic forest comprising of node disjoint phylogenetic trees that specifies the topological constraints that any evolutionary tree needs to satisfy, construct a minimum cost evolutionary tree for S.

Fast Heuristics for Exact String Matching: The online exact string matching problem consists of finding all occurrences of a given pattern P of length n in a text T of length m. It is a problem in computer science that has been studied widely since the 70’s and has applications in bio-informatics, computational biology, image processing, data compression and many other areas.

Our Results: Constant approximation techniques have been devised for the constrained generalized tree alignment problem. These algorithms are computationally quick and provide a guaranteed error bound of 2-2/k for the special situation of generalized tree alignment.

I proposed a fast heuristic for the precise string matching problem that has a worst-case time complexity of O((m+n)/∆), where ∆ is the alphabet size, and in practice is O(log(m)) time. . This method starts by finding sub-patterns in P using O(∆³) time preprocessing,  of P and then using a slightly modified Boyer-Moore algorithm to find P in T in O((m+n)/∆) time.

Combinatorial Optimization Research

My research in Combinatorial Optimization focused on the construction and analysis of approximation algorithms for problems such as (i) Scheduling with set-ups, (ii) List Update Problem and (iii) Bin Packing.  

Scheduling with set-ups: In this problem, my research was on the design of online and offline approximation algorithms for problems of scheduling with set-ups (problems where jobs are classified into types and jobs of a given type can be served only by a machine set-up for that type).  These problems are of significant interest in attempting to exploit batching to reduce set-up time.

List Update Problem: In this problem, my research interests was on the design and analysis of online and approximation algorithms for the following variant of the List Update Problem:

Static List Update Problem: Given an ordered list ρ (an ordering among the items in L) and a request sequence σ, we need to determine how to reorganize L while serving σ so as to minimize the total servicing (access and list reorganization) cost. 

This is a very hard problem that has been widely studied by theoretical computer scientists since 1980’s and has widespread applications in distributed systems in the context of designing paging and resource allocation algorithms.

Bin Packing: In this problem, my research was on the design of fast heuristics and approximation schemes for classical bin packing and its variants. The classical bin packing problem can be defined as follows:

Given an infinite supply of bins with capacity C and a list L = (a₁, a₂, …, a_n) of items, where for i in [1..n] 0 <= s_i <= C denotes the size of item a_i, we need to pack the items into a minimum number of bins under the constraint that the sum of the sizes of the items in each bin is no greater than C. 

This problem has a wide variety of applications including cutting stock applications, packing problems in supply chain management, and resource allocation problems in distributed systems. 

Our Results: As part of my PhD research, I began working on a project on scheduling with set-ups with Prof. Michael Saks. For the weighted completion time and maximum lateness criterion, we were able to get new approximation algorithms for the offline problem of scheduling a succession of jobs on a single machine with sequence independent set-up times. For this problem, our methods were the first known polynomial time constant approximation algorithms. With the goal of lowering the maximum flow time, we proposed an O(1)-competitive online algorithm for a problem with sequence independent set-ups and arbitrary job release times for the online problem. We also show how to prove that the associated offline problem is NP-complete.

For the static list update problem, I was able to characterize the list reorganizations in an optimal offline solution in terms of an initial list permutation followed by a sequence of m element transfers, where an element transfer is a type of list reorganization in which only the requested item can be moved. Then I used this characterization to create an offline method that is an O(l²(l − 1)!m) time optimal offline algorithm.

For the bin packing problem, I devised a fast scalable heuristic that divides the given problem into similar sub-problems of constant size and solves these constant size sub-problems by evaluating just a fixed number of bin configurations with bounded unused space. My empirical investigation demonstrates the scalability of our heuristic as well as its tighter empirical analysis for difficult cases due to a better lower constraint on the required wastage in an optimal solution. I also published a n^O(k2) time approach for solving the 1-dimensional cutting stock problem, which is a constrained counterpart of the bin packing problem.

Articles in Books and Journals

S. Divakaran. Explainable Algorithms for Image Registration with Applications in Medical Imaging, Explainable AI in Healthcare (xAI 2022) (under review), CRC Press, 2022.

S. Divakaran, Data Science: Principles and Concepts in Modeling Decision Trees, Data Science in Agriculture and Natural Resource Management, 55-74, Studies in Big Data, Springer, 2022.

S. Divakaran and M. Saks, An Online Algorithm for a Problem in Scheduling with Set-ups and Release Times, Algorithmica 60(2): 301-315, 2011.

S. Divakaran, Approximation algorithms for constrained generalized tree alignment problem, Discrete Applied Mathematics 157(7): 1407-1422, 2009.

S. Divakaran and M. Saks, Approximation Algorithms for problems in Scheduling with set-ups, Discrete Applied Mathematics, Volume 156(5), 719-729, 2008.

S. Divakaran, Approximation Algorithms for problems in Scheduling with Set-ups, Graduate Dissertations, Rutgers, The State University of New Jersey, 2001, ISBN: 0-493-47085-9.

S. Divakaran and M. Saks, An Online Scheduling Problem with Job Set-ups, Center for Discrete Mathematics & Theoretical Computer Science, 2000-34.

Conference and Workshop Articles

Srishti Sharma, Srikrishnan Divakaran, Tolga Kaya and Mehul Raval. A Hybrid Approach for Interpretable Game Performance Prediction in Basketball, International Joint Conference on Neural Networks (IJCNN 2022), Padua, Italy, July 18-23, 2022.

M. Shah, M. Raval and S. Divakaran. A Deep Learning Perspective to Atmospheric Correction of Satellite Images, IEEEiGARSS 2022, Kuala Lumpur, Malaysia, July 17-22, 2022.

M. Shah, M. Raval and S. Divakaran. Deep Learning Based Emulator for 6S Atmospheric Correction Model, IEEE InGARSS 2021 (Virtual Symposium), December 6-10, 2021.

S. Divakaran. Introduction to Spatial and Temporal Data Analysis with R, Workshop on Data Science and Natural Resource Management (DSANRM2021), December 15, 2021.

S. Divakaran. Statistics of Sequence Analysis Using BLAST, Workshop on Application of Biostatistics in Biotechnology and Pharmaceutical Sciences, L.M. College of Pharmacy, October 21-23, 2021.

S. Divakaran, Data Clustering with Applications in Computational Biology, Big Data: Algorithms, Frameworks and Machine Learning Techniques for Problems in Evolving Networks and Computer Vision, Big Data Analytics 2019, December 17-20, 2019.

S. Divakaran, Algorithms for Exact String Matching, Learning in Data Science: Models, Algorithms and Tools, Summer School, July 17-22, 2017.

S.Divakaran, Fast Algorithms for Exact String Matching. Winter School of Combinatorics, Charles University, (Filed as  CoRR abs/1509.09228), 2016.

S. Divakaran, An Approximation Algorithm for a Multi-dimensional Resource Allocation Problem, Proceedings of the 13^th International Conference on Combinatorial Optimization, CO2004, Lancaster, UK, pp 15, March 28-31, 2004.

S. Divakaran, A framework for Request Scheduling in Web Servers, Special Focus on Next Generation Networks Technologies and Applications, DIMACS, Piscataway, New Jersey,  December, 2002.

S. Divakaran and M. Saks, Online Scheduling with release time and set-ups, Proceedings of the 12^th International Conference on Combinatorial Optimization, CO2002, CNAM Paris, pp 43, April 8-10, 2002.

S. Divakaran and M. Saks, Approximation Algorithms for Offline Scheduling with set-ups, Proceedings of the 12^th International Conference on Combinatorial Optimization, CO2002, CNAM Paris, pp 44, April 8-10, 2002.

M. Rangarajan, S. Divakaran, T. Nguyen and L. Iftode, Multi-threaded HLRC DSM, 1^st Workshop on Software Distributed Shared Memory, Rhodes, Greece, June 25, 1999.

Technical Reports

S. Divakaran, An Optimal Algorithm for 1-D Cutting Stock Problem, CoRR abs/2001.01531 (2020)

S. Divakaran, A Fast Scalable Heuristic for Bin Packing. CoRR abs/1904.12467, DOI: 10.13140/RG.2.2.12887.52643 (2019)

S. Divakaran, Fast Approximation Schemes for Bin Packing. CoRR abs/1902.03422, DOI: 10.13140/RG.2.2.28815.64165 (2019)

S.Divakaran, A Fast Heuristic for Exact String Matching. CoRR abs/1512.03512 (2015)

S.Divakaran, Fast Algorithms for Exact String Matching. CoRR abs/1509.09228 (2015)

S. Divakaran, An Optimal Offline Algorithm for List Update. CoRR abs/1404.7638 (2014)

S. Divakaran, A Fast Template Based Heuristic For Global Multiple Sequence Alignment. CoRR abs/1302.6030 (2013)

S. Divakaran, Approximation Algorithms for Constrained Generalized Tree Alignment Problem, DIMACS Technical Report 2007-21.

S. Divakaran, Approximation Algorithms for a Multi-dimensional Resource Allocation Problem, DIMACS Technical Report 2006-24.

S. Divakaran and M. Saks, Online Scheduling with release time and set-ups, DIMACS Technical Report 2001-50.

S. Divakaran and M. Saks, Approximation Algorithms for Offline Scheduling with set-ups, DIMACS Technical Report 2001-49.

Teaching Statement of Srikrishnan Divakaran

I am a Theoretical Computer Scientist with over 25 years of experience teaching a wide variety of courses in Computer Science and related disciplines like Combinatorial Optimization, Computational Biology and Data Science. In addition, I have (i) supervised many undergraduate/graduate capstone research projects and (ii) mentored several students in fine tuning their preparation for ACM/IEEE/Google coding and summer of code challenges.

Teaching has provided me enormous joy and a sense of satisfaction in helping shape the thinking of many young students. In addition, I have gained better insights and deeper understanding of many elementary concepts. I also believe my teaching has had a good impact on student learning as evidenced by (i) acceptance of my students in institutes of higher learning and Industry, (ii) student feedback, and (iii) unsolicited compliments from students and alumni. 

My goals in teaching are to help students develop the ability to solve problems, equip them with a good conceptual understanding along with practical problem solving skills. I address these goals by focusing on the following:

Motivation: I introduce a concept by motivating its usefulness by describing the key idea, its application context, and its strengths in comparison with other approaches.

First Principles:  I have observed that many concepts in computing are simple at their core and can be extended in simple ways to yield powerful but simple ways for solving problems. So, I believe in explaining key concepts by first explaining the relevant first principles and then highlight some of the subtleties and challenges in putting them together. This helps in developing their intuition without getting bogged down by the technicalities.

Illustration of Concepts: I illustrate a concept by employing problems that range from direct applications to problems that involve subtle twists. I illustrate the use of techniques by first solving some simple instances of a problem. Then, I illustrate the power of a technique by comparing it with other alternate ways of solving problems. This helps the student to the computational complexity and challenges/limitations of the various ideas/techniques in different contexts

Critical Thinking: I believe that developing critical thinking is an essential part of learning.  I believe that students should be taught to think through ideas and understand what the strengths and limitations of new ideas are, and how these ideas can be applied and extended? I attempt to provide this experience through carefully designed tutorials/ group projects that complement their lectures.  In these tutorials, I assign some extensions of simple instances to small groups and initiate the discussion by giving hints, suggestions and raising questions. The objective of the group activities is to help them collaborate with one another and also critique each other’s ideas. This experience, although slow and frustrating has helped many of my students develop deeper intuition and greater rigor in writing their proofs.

List of Courses Taught in the past 10 years

Theory: Discrete Mathematics, Probability and Statistics,   Advanced Statistics, Design and Analysis of Algorithms, Data Structures and Algorithms, Advanced Data Structures and Algorithms, Approximation Algorithms, Online Computation, and Combinatorial Optimization.

Bioinformatics/Computational Biology: Algorithms for Computational Biology, Statistical Methods for Bioinformatics.

Data Science: Foundations of Data Science, Elements of Statistical Learning.

Others: Operating Systems, Distributed Systems