Abhishek Mishra

The Special Integrals author web page link:

https://www.amishra.in/integrals

1 Research Interests

Analysis of Algorithms and Problem Complexity (MSC Code: 68Q25)
Computational Difficulty of Problems (Lower Bounds, Completeness, Difficulty of Approximation, etc., MSC Code: 68Q17)

2 Education

Doctor of Philosophy in Computer Science & Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi, 2011, CGPA: 9.69.
Title of Thesis: Observations on Task Scheduling Algorithms for Multi Core Systems.
Thesis Advisor: Prof. Anil Kumar Tripathi.
Bachelor of Technology in Computer Science & Engineering, Institute of Technology, Banaras Hindu University, Varanasi, 2003, DGPA: 8.77.
All India Senior School Certificate Examination, Central Board of Secondary Education, 1999, 77.4%.
All India Secondary School Examination, Central Board of Secondary Education, 1997, 66.4%.

3 Appointments

Department of Computer Science & Information Systems, Birla Institute of Technology & Science, Pilani — Assistant Professor Grade-I (2018/05/07 – Continuing).
Department of Computer Science & Information Systems, Birla Institute of Technology & Science, Pilani — Assistant Professor on temporary against regular position (equivalent to Grade-II) (2015/05/07 – 2018/05/06).
Department of Computer Science & Engineering, Jaypee University of Information Technology — Assistant Professor (Senior Grade) (2015/03/04 – 2015/05/04}.
Department of Computer Science & Engineering, Indian Institute of Technology Jodhpur — Assistant Professor (on Contract) (equivalent to Grade-II) (2012/09/17 – 2014/12/30).
Department of Computer Science & Engineering, Institute of Technology, Banaras Hindu University — Research Scholar (2008/07/15 – 2011/09/15}.
Rajiv Gandhi South Campus (Barkachha), Mirjapur, Banaras Hindu University — Lecturer on Contract (Computer Science) (2007/09/25 – 2008/05/31).
Department of Computer Science, School of Management Sciences, Varanasi — Lecturer (2007/08/01 – 2007/09/24).
Weapons and Electronics Systems Engineering Establishment, New Delhi — Scientist `B' of Defence Research & Development Organisation (2005/08/05 – 2007/07/31).
Institute of Armament Technology, Pune — Scientist `B' of Defence Research & Development Organisation (2005/04/14 – 2005/08/03).
Tata Elxsi Limited, Bangalore — Engineer - Networking & Communications (2003/07/02 – 2005/01/03).

4 Publications in Reverse Chronological Order

(C = Conference, J = Journal, M = Manuscript, P = Preprint, R = Research Monograph, T = Technical Report)

[27T] Tejas Nareddy and Abhishek Mishra. “Recovery reductions, conjectures, and barriers.” Electronic Colloquium on Computational Complexity, report no. 157, 2025.
DOI / Link: https://eccc.weizmann.ac.il/report/2025/157/

[26R] Abhishek Mishra. Special Integrals. University Texts in the Mathematical Sciences. Springer Nature Singapore, 2025.
DOI / Link: https://doi.org/10.1007/978-981-97-7514-9

[25P] Tejas Nareddy and Abhishek Mishra. “New techniques for constructing rare-case hard functions.” arXiv:2411.09597v2 [cs.CC], 2025.
DOI / Link: https://doi.org/10.48550/arXiv.2411.09597

[24P] Ravi Kant, Sarthak Agarwal, Aakash Gupta, and Abhishek Mishra. “Exploring the performance of genetic algorithm and variable neighborhood search for solving the single depot multiple set orienteering problem: A comparative study.” arXiv:2411.12300 [math.OC], 2024.
DOI / Link: https://doi.org/10.48550/arXiv.2411.12300

[23P] Tejas Nareddy and Abhishek Mishra. “Hardness amplification via group theory.” arXiv:2411.09619 [cs.CC], 2024.
DOI / Link: https://doi.org/10.48550/arXiv.2411.09619

[22P] Ravi Kant, Salmaan Shahid, Anuvind Bhat, and Abhishek Mishra. “Variable neighborhood search for the multi-depot multiple set orienteering problem.” arXiv:2408.08922 [math.OC], 2024.
DOI / Link: https://doi.org/10.48550/arXiv.2408.08922

[21C] Ravi Kant and Abhishek Mishra. “The multi-depot multiple set orienteering problem: An integer linear programming formulation.” In Proceedings of the 13th International Conference on Operations Research and Enterprise Systems (ICORES), pages 350–355, 2024.
DOI / Link: https://www.scitepress.org/Papers/2024/124205/124205.pdf

[20C] Ravi Kant and Abhishek Mishra. “A compact formulation for the mDmSOP: Theoretical and computational time analysis.” In Proceedings of the 11th International Conference on Frontiers of Intelligent Computing: Theory and Applications (FICTA), pages 115–124, 2023.
DOI / Link: https://link.springer.com/chapter/10.1007/978-981-99-6702-5_9

[19C] Ravi Kant, Abhishek Mishra, and Siddharth Sharma. “The single depot multiple set orienteering problem.” In Proceedings of the 12th International Conference on Operations Research and Enterprise Systems (ICORES), pages 175–179, 2023.
DOI / Link: https://www.scitepress.org/Papers/2023/116818/116818.pdf

[18C] Ravi Kant and Abhishek Mishra. “The orienteering problem: A review of variants and solution approaches.” In Proceedings of the 26th World Multi-Conference on Systemics, Cybernetics and Informatics (WMSCI), pages 41–46, 2022.
DOI / Link: https://www.iiis.org/CDs2022/CD2022Summer/papers/SA919CB.pdf

[17C] Pratik S. and Abhishek Mishra. “A simulated annealing based energy efficient task scheduling algorithm for multi-core processors.” In Proceedings of the 13th International Joint Conference on Computational Intelligence (IJCCI), pages 81–87, 2021.
DOI / Link: https://www.scitepress.org/Papers/2021/106259/106259.pdf

[16C] Abhishek Mishra, Kamal Sheel Mishra, and Pramod Kumar Mishra. “Performance evaluation of simulated annealing-based task scheduling algorithms.” In Springer Proceedings of Information Management and Machine Intelligence (ICIMMI), pages 145–152, 2021.
DOI / Link: https://link.springer.com/chapter/10.1007/978-981-15-4936-6_15

[15J] Abhishek Mishra and Prasoon Trivedi. “Benchmarking the contention aware nature inspired metaheuristic task scheduling algorithms.” Cluster Computing, 23:537–553, 2020.
DOI / Link: https://link.springer.com/article/10.1007/s10586-019-02943-z

[14J] Rohan Sharma, Bibhas Adhikari, and Abhishek Mishra. “Structural and spectral properties of corona graphs.” Discrete Applied Mathematics, 228:14–31, 2017.
DOI / Link: https://doi.org/10.1016/j.dam.2017.01.005

[13J] Abhishek Mishra and Pramod Kumar Mishra. “A randomized scheduling algorithm for multiprocessor environments using local search.” Parallel Processing Letters, 26(1):1650002, 2016.
DOI / Link: https://www.worldscientific.com/doi/abs/10.1142/S012962641650002X

[12C] Rohan Sharma, Bibhas Adhikari, and Abhishek Mishra. “On spectra of corona graphs.” In Proceedings of the Conference on Algorithms and Discrete Applied Mathematics (CALDAM), pages 126–137, 2015.
DOI / Link: https://link.springer.com/chapter/10.1007/978-3-319-14974-5_13

[11J] Abhishek Mishra and Anil Kumar Tripathi. “Complexity of a problem of energy efficient real-time task scheduling on a multicore processor.” Complexity, 21(1):259–267, 2015.
DOI / Link: https://onlinelibrary.wiley.com/doi/epdf/10.1002/cplx.21561

[10J] Abhishek Mishra and Anil Kumar Tripathi. “Energy efficient voltage scheduling for multi-core processors with software controlled dynamic voltage scaling.” Applied Mathematical Modelling, 38(14):3456–3466, 2014.
DOI / Link: https://www.sciencedirect.com/science/article/pii/S0307904X13008147

[09J] Abhishek Mishra and Anil Kumar Tripathi. “A monte carlo algorithm for real time task scheduling on multi-core processors with software controlled dynamic voltage scaling.” Applied Mathematical Modelling, 38(7-8):1929–1947, 2014.
DOI / Link: https://www.sciencedirect.com/science/article/pii/S0307904X13006355

[08J] Pramod Kumar Mishra, Abhishek Mishra, Kamal Sheel Mishra, and Anil Kumar Tripathi. “Benchmarking the clustering algorithms for multiprocessor environments using dynamic priority of modules.” Applied Mathematical Modelling, 36(12):6243–6263, 2012.
DOI / Link: https://www.sciencedirect.com/science/article/pii/S0307904X12000935

[07J] Pramod Kumar Mishra, Kamal Sheel Mishra, Abhishek Mishra, and Anil Kumar Tripathi. “A randomized scheduling algorithm for multiprocessor environments.” Parallel Processing Letters, 22(4):1250015, 2012.
DOI / Link: https://www.worldscientific.com/doi/abs/10.1142/S0129626412500156

[06J] Pramod Kumar Mishra, Kamal Sheel Mishra, and Abhishek Mishra. “A clustering algorithm for multiprocessor environments using dynamic priority of modules.” Annales mathematicae et informaticae, 38:99–110, 2011.
DOI / Link: https://ami.uni-eszterhazy.hu/uploads/papers/finalpdf/AMI_38_from99to110.pdf

[05J] Abhishek Mishra and Anil Kumar Tripathi. “An extension of edge zeroing heuristic for scheduling precedence constrained task graphs on parallel systems using cluster dependent priority scheme.” Journal of Information and Computing Science, 6(2):83–96, 2011.
DOI / Link: https://doc.global-sci.org/uploads/Issue/JICS/jicvol6no2paper01short.pdf

[04J] Abhishek Mishra and Anil Kumar Tripathi. “Energy efficient task scheduling of send-receive task graphs on distributed multi-core processors with software controlled dynamic voltage scaling.” International Journal of Computer Science & Information Technology, 3(2):204–210, 2011.
DOI / Link: https://airccse.org/journal/jcsit/0411csit15.pdf

[03J] Pramod Kumar Mishra, Kamal Sheel Mishra, and Abhishek Mishra. “A clustering heuristic for multiprocessor environments using computation and communication loads of modules.” International Journal of Computer Science & Information Technology, 2(5):170–182, 2010.
DOI / Link: https://airccse.org/journal/jcsit/1010ijcsit13.pdf

[02C] Abhishek Mishra and Anil Kumar Tripathi. “An extention of edge zeroing heuristic for scheduling precedence constrained task graphs on parallel systems using cluster dependent priority scheme.” In Proceedings of the IEEE International Conference on Computer & Communication Technology (ICCCT), pages 647–651, 2010.
DOI / Link: https://ieeexplore.ieee.org/document/5640450

[01M] Abhishek Mishra. “A 150-page list of identities and theorems.” The ‘Special Integrals’ monograph refers to this handwritten manuscript. 1997.
DOI / Link: https://drive.google.com/file/d/15Mkmny3bumOxaM-YLc2qlcSoufFekjyt/view?usp=sharing

5 Research Statement

5.1 Introduction — Research Vision

My research is centered on algorithmic and complexity-theoretic questions motivated by hardness amplification, number-theoretic constructions, and combinatorial optimization problems such as orienteering variants. I aim to bridge deep theoretical advances (hardness magnification, recovery reductions) with algorithmic design and applied optimization, training students to contribute both theory and implementable methods. The core ideas and recent work are summarized below; full details and references appear in my curriculum vitae.

5.2 Current Research

5.2.1 Special Integrals

My research monograph Special Integrals (Springer Nature, 2025) [26R] grew from my explorations of integral representations for series and special functions in 1997 [01M]. It collects novel integral identities and techniques accessible to readers with calculus and complex analysis background; several identities appear to be new. The monograph establishes analytic frameworks that I am now leveraging in algorithmic number-theoretic investigations (see below).

5.2.2 Mathematical Techniques in Computational Complexity

Recent collaborative work develops new families of reductions and constructions that strengthen our understanding of average-case and rare-case hardness.

Recovery reductions and random-noise model: In joint work (Nareddy & Mishra, 2025) [27T] we defined a random-noise model and used group-theoretic constructions (symmetric groups, permutation group algorithms) to produce robust deterministic recovery reductions for canonical NP-complete problems (SAT, k-SAT, CLIQUE). These reductions unify several hardness phenomena via a single group-theoretic black-box approach.
Rare-case hard functions via number theory: Building on distribution of primes and Chinese remainder techniques, we constructed number-theoretic polynomials that are rare-case hard under standard complexity assumptions (Nareddy & Mishra, 2025) [25P]. This line connects analytic number theory with complexity-theoretic constructions.
Hardness amplification through group theory: Our 2024 work [23P] explores group-action based amplification, resolving portions of an open question posed by Goldreich (2020) for counting modulo problems and providing limits for our techniques.

5.2.3 Multiple Set Orienteering Problem (mSOP) and Optimization

I have supervised and co-authored a string of papers developing modeling and algorithmic strategies for set-based orienteering variants and their multi-depot / multi-salesperson generalizations [24P, 22P, 21C, 20C, 19C, 18C]. The work includes integer-linear programming formulations, compact encodings, and heuristic / metaheuristic comparisons (recent ICORES and FICTA proceedings). These applied optimization projects provide fertile ground for student projects.

5.3 Future Research Plan (Five-Year Roadmap)

I plan a coordinated program along four themes that leverage existing results and expand into new directions:

5.3.1 Hardness Magnification Beyond Locality Barriers

Hardness magnification offers a pathway from modest lower bounds to dramatic complexity separations. I will seek new magnification results that bypass known locality barriers using structured reductions and combinatorial constructions, focusing on sparse instances of natural problems. Potential milestones: (i) identify candidate sparse problems amenable to magnification; (ii) design reductions preserving sparsity and structure; (iii) target a breakthrough conditional result linking modest lower bounds to circuit lower bounds.

5.3.2 Conditional Lower Bounds via Network Coding Conjecture

I will explore conditional lower bounds derived from the Network Coding Conjecture (NCC) and related communication / throughput conjectures. Applications include lower bounds for sorting, multiplication circuits, and function inversion in memory and external-storage models. This connects to data-structure lower bounds and practical implications for parallel / distributed systems.

5.3.3 Quantum Number-Theoretic Algorithms

Leveraging my mathematical background, I plan to investigate quantum algorithms for number-theoretic tasks (e.g., Gauss sum estimation, exponential congruences) and to adapt classical analytic techniques to hybrid classical–quantum algorithm design.

5.3.4 Additive Combinatorics and Average-Case Hardness

I will apply additive combinatorics and probabilistic constructions to push average-case hardness results, aiming to produce explicit worst-case to average-case reductions for families of algebraic problems. This theme complements the number-theoretic constructions and the hardness magnification agenda.

5.4 Conclusion

My research aims to integrate mathematical depth with algorithmic applicability — advancing complexity theory while producing methods that can be implemented and taught. Full references and an extended list of publications appear in my curriculum vitae.

6 Graduated PhD Advisees

Ravi Kant

Current Position: Assistant Professor (Contractual - II)

Current Affiliation: Department of Computer Science and Engineering, Thapar Institute of Engineering & Technology

Supervised individually

Title of Thesis: The Set Orienteering Problem: A Review of Variants and Solution Approaches

Graduated from: BITS Pilani, 2024
Rohan Sharma

Current Position: Assistant Professor - I

Current Affiliation: Department of Computer Science and Engineering, Thapar Institute of Engineering & Technology

Partially co-supervised with: Dr. Bibhas Adhikari

Area of Thesis: Complex Networks

Graduated from: IIT Jodhpur, 2018

7 Teaching Experience

In the current semester, I am teaching Advanced Algorithms and Complexity (sole instructor) and Theory of Computation tutorial (shared with two instructors). I have taught forty-five complete iterations of fourteen different courses (except the tutorials). The details are as follows:

Design and Analysis of Algorithms (Undergraduate, ten iterations), shared with one instructor in 2017, 2020, 2021, 2022, 2023, 2024, and 2025; sole instructor in 2018 (twice) and 2019 at BITS Pilani.
Advanced Algorithms and Complexity (Graduate, ten iterations), shared with one instructor in 2015 and 2016; sole instructor in 2018, 2019, 2020 (twice), 2021, 2022, 2023, and 2024 at BITS Pilani.
Cryptography (Undergraduate, ten iterations), sole instructor in 2016, 2017, 2018, 2019, 2020, 2022, 2024, and 2025; shared with one instructor in 2021 and 2023 at BITS Pilani.
Data Structures and Algorithms (Undergraduate, one iteration), shared with one instructor in 2016 at BITS Pilani.
Theory of Computation (tutorial) (Undergraduate, four iterations), shared with one instructor in 2016, 2017, and 2024; and shared with two instructors in 2023 at BITS Pilani.
Advanced Compilation Techniques (Graduate, two iterations), sole instructor in 2015 and 2017 at BITS Pilani.
Discrete Structures for Computer Science (Undergraduate, one iteration), shared with one instructor in 2019 at BITS Pilani.
Discrete Structures for Computer Science (tutorial) (Undergraduate, three iterations), shared with two instructors in 2019, 2020, and 2022 at BITS Pilani.
Design and Analysis of Algorithms (tutorial) (Undergraduate, three iterations), shared with one instructor in 2017 and 2020; shared with two instructors in 2021 at BITS Pilani.
Computational Complexity (new course designed by me), Undergraduate, one iteration), sole instructor in 2014 at IIT Jodhpur.
Operating Systems (Undergraduate, one iteration), sole instructor in 2014 at IIT Jodhpur.
Data Structures and Algorithms (tutorial) (Undergraduate, one iteration), shared with two instructors in 2014 at IIT Jodhpur.
Theory of Computation (Undergraduate, two iterations), sole instructor in 2013 and 2014 at IIT Jodhpur.
Algorithms-II (Undergraduate, two iterations), shared with one instructor in 2013; sole instructor in 2014 at IIT Jodhpur.
Compiler Design (Undergraduate, two iterations), the first time as a sole instructor and the second time shared with one instructor in 2013 at IIT Jodhpur.
Advanced Course in Operating Systems (Graduate, one iteration), sole instructor in 2008 at BHU.
Operating System (Graduate, one iteration), sole instructor in 2008 at BHU.
Discrete Mathematical Structures (Graduate, one iteration), sole instructor in 2007 at BHU.

8 Teaching Statement

8.1 Introduction

My teaching focuses on making rigorous theoretical material accessible and useful for both undergraduate and graduate students. I balance precise, board-centered explanations with carefully selected slides and examples, and I emphasize problem-solving, algorithmic thinking, and connections to current research. This statement summarizes my teaching experience, philosophy, course design work, and future plans.

8.2 Teaching Experience

I have taught forty-five complete iterations of fourteen different courses across undergraduate and graduate programs. Major courses I have taught (selected):

Design and Analysis of Algorithms (Undergraduate; 10 iterations)
Advanced Algorithms and Complexity (Graduate; 10 iterations)
Cryptography (Undergraduate; 10 iterations)
Theory of Computation (Undergraduate; tutorials and full courses)
Advanced Compilation Techniques, Operating Systems, Discrete Mathematical Structures, and several programming and algorithms labs.

I teach both large lectures and small tutorials, and I have experience with in-person and online instruction, including creating and using recorded lecture videos for online teaching.

8.3 Teaching Philosophy

My core pedagogical goals are clarity, accessibility, and active engagement:

Start from first principles. I do not assume prior mastery; I explain definitions and the intuition behind them before formal proofs.
Board-first exposition. Students tell me they learn best when concepts are worked out on the board step-by-step. I use slides selectively for overviews, diagrams, or material that benefits from prepared visualizations.
Active problem-solving. I integrate short in-class problems, tutorial sheets, and take-home exercises that reinforce lecture concepts and develop technical maturity.
Frequent feedback. I solicit and act on student feedback. In online teaching, I respond promptly to chat and forum questions to maintain interaction.
Research-informed teaching. Where appropriate, I present recent research results and open problems to graduate classes to motivate advanced coursework and student projects.

8.4 Course Design and Innovation

I have designed and taught a new undergraduate course titled Computational Complexity (IIT Jodhpur, 2014). The course syllabus included:

Turing machines and uncomputability;
Time and space complexity classes (P, NP, PSPACE, etc.);
Polynomial hierarchy and nonuniform classes (P/poly);
Randomized complexity (BPP, RP, ZPP);
Interactive proofs and PCP; and
Applications to cryptography and quantum complexity.

I structure new courses with clear learning objectives, a sequence of scaffolded problem sets, and project options that let motivated students explore research directions.

8.5 Assessment and Student Projects

My assessment strategy combines homework, quizzes, projects, and exams to evaluate both understanding and creative application:

Homeworks: Regular problem sets that mix routine exercises with one or two open-ended questions.
Quizzes: Short in-course quizzes to encourage continuous learning.
Projects: Semester-long projects for advanced students (theoretical experiments or implementations), often resulting in undergraduate research reports or small publications.
Office hours and mentoring: I hold regular office hours and actively mentor students for thesis and research internships.

8.6 Lecture Media and Resources

During the COVID-19 period I produced a set of lecture videos for Advanced Algorithms and Complexity and related topics. These videos cover core topics such as P vs NP intuition, reductions and NP-completeness, randomized algorithms, interactive proofs, and approximation techniques. (Links and detailed listings of these lecture videos are available on request.)

8.7 Future Teaching Plan

In the future, I will be interested in teaching the following courses:

Fine-Grained Complexity and Algorithms
Classical and Quantum Number Theoretic Algorithms

8.8 Conclusion

Teaching is central to my work as a scholar and mentor. I aim to create an inclusive classroom where students with different backgrounds gain confidence and technical skill, and where motivated students can transition smoothly into research.

9 Academic Achievements

Graduate Aptitude Test in Engineering - 2008 in Computer Science & Engineering: All India Rank 21, Percentile Score 99.88, GATE Score 749.
Indian Institute of Technology Joint Entrance Examination - 1999: All India Rank 496.
National Standard Examination in Physics 1999: Placed in National Top 1%.
Indian National Mathematical Olympiad 1998: All India Rank 11.
Regional Mathematical Olympiad 1997, Uttar Pradesh: Rank 4.
XI National Level Science Talent Search Examination 1996: All India Rank 83 in Class 9.
X National Level Science Talent Search Examination 1995: All India Rank 2 in Class 8.

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Abhishek Mishra

The Special Integrals author web page link:

https://www.amishra.in/integrals

1 Research Interests

Analysis of Algorithms and Problem Complexity (MSC Code: 68Q25)

Computational Difficulty of Problems (Lower Bounds, Completeness, Difficulty of Approximation, etc., MSC Code: 68Q17)

2 Education

Doctor of Philosophy in Computer Science & Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi, 2011, CGPA: 9.69.Title of Thesis: Observations on Task Scheduling Algorithms for Multi Core Systems.Thesis Advisor: Prof. Anil Kumar Tripathi.

Bachelor of Technology in Computer Science & Engineering, Institute of Technology, Banaras Hindu University, Varanasi, 2003, DGPA: 8.77.

All India Senior School Certificate Examination, Central Board of Secondary Education, 1999, 77.4%.

All India Secondary School Examination, Central Board of Secondary Education, 1997, 66.4%.

3 Appointments

Department of Computer Science & Information Systems, Birla Institute of Technology & Science, Pilani — Assistant Professor Grade-I (2018/05/07 – Continuing).

Department of Computer Science & Information Systems, Birla Institute of Technology & Science, Pilani — Assistant Professor on temporary against regular position (equivalent to Grade-II) (2015/05/07 – 2018/05/06).

Department of Computer Science & Engineering, Jaypee University of Information Technology — Assistant Professor (Senior Grade) (2015/03/04 – 2015/05/04}.

Department of Computer Science & Engineering, Indian Institute of Technology Jodhpur — Assistant Professor (on Contract) (equivalent to Grade-II) (2012/09/17 – 2014/12/30).

Department of Computer Science & Engineering, Institute of Technology, Banaras Hindu University — Research Scholar (2008/07/15 – 2011/09/15}.

Rajiv Gandhi South Campus (Barkachha), Mirjapur, Banaras Hindu University — Lecturer on Contract (Computer Science) (2007/09/25 – 2008/05/31).

Department of Computer Science, School of Management Sciences, Varanasi — Lecturer (2007/08/01 – 2007/09/24).

Weapons and Electronics Systems Engineering Establishment, New Delhi — Scientist `B' of Defence Research & Development Organisation (2005/08/05 – 2007/07/31).

Institute of Armament Technology, Pune — Scientist `B' of Defence Research & Development Organisation (2005/04/14 – 2005/08/03).

Tata Elxsi Limited, Bangalore — Engineer - Networking & Communications (2003/07/02 – 2005/01/03).

4 Publications in Reverse Chronological Order

(C = Conference, J = Journal, M = Manuscript, P = Preprint, R = Research Monograph, T = Technical Report)

[27T] Tejas Nareddy and Abhishek Mishra. “Recovery reductions, conjectures, and barriers.” Electronic Colloquium on Computational Complexity, report no. 157, 2025.DOI / Link: https://eccc.weizmann.ac.il/report/2025/157/

[26R] Abhishek Mishra. Special Integrals. University Texts in the Mathematical Sciences. Springer Nature Singapore, 2025.DOI / Link: https://doi.org/10.1007/978-981-97-7514-9

[25P] Tejas Nareddy and Abhishek Mishra. “New techniques for constructing rare-case hard functions.” arXiv:2411.09597v2 [cs.CC], 2025.DOI / Link: https://doi.org/10.48550/arXiv.2411.09597

[23P] Tejas Nareddy and Abhishek Mishra. “Hardness amplification via group theory.” arXiv:2411.09619 [cs.CC], 2024.DOI / Link: https://doi.org/10.48550/arXiv.2411.09619

[22P] Ravi Kant, Salmaan Shahid, Anuvind Bhat, and Abhishek Mishra. “Variable neighborhood search for the multi-depot multiple set orienteering problem.” arXiv:2408.08922 [math.OC], 2024.DOI / Link: https://doi.org/10.48550/arXiv.2408.08922

[15J] Abhishek Mishra and Prasoon Trivedi. “Benchmarking the contention aware nature inspired metaheuristic task scheduling algorithms.” Cluster Computing, 23:537–553, 2020.DOI / Link: https://link.springer.com/article/10.1007/s10586-019-02943-z

[14J] Rohan Sharma, Bibhas Adhikari, and Abhishek Mishra. “Structural and spectral properties of corona graphs.” Discrete Applied Mathematics, 228:14–31, 2017.DOI / Link: https://doi.org/10.1016/j.dam.2017.01.005

[13J] Abhishek Mishra and Pramod Kumar Mishra. “A randomized scheduling algorithm for multiprocessor environments using local search.” Parallel Processing Letters, 26(1):1650002, 2016.DOI / Link: https://www.worldscientific.com/doi/abs/10.1142/S012962641650002X

[12C] Rohan Sharma, Bibhas Adhikari, and Abhishek Mishra. “On spectra of corona graphs.” In Proceedings of the Conference on Algorithms and Discrete Applied Mathematics (CALDAM), pages 126–137, 2015.DOI / Link: https://link.springer.com/chapter/10.1007/978-3-319-14974-5_13

[11J] Abhishek Mishra and Anil Kumar Tripathi. “Complexity of a problem of energy efficient real-time task scheduling on a multicore processor.” Complexity, 21(1):259–267, 2015.DOI / Link: https://onlinelibrary.wiley.com/doi/epdf/10.1002/cplx.21561

[07J] Pramod Kumar Mishra, Kamal Sheel Mishra, Abhishek Mishra, and Anil Kumar Tripathi. “A randomized scheduling algorithm for multiprocessor environments.” Parallel Processing Letters, 22(4):1250015, 2012.DOI / Link: https://www.worldscientific.com/doi/abs/10.1142/S0129626412500156

[01M] Abhishek Mishra. “A 150-page list of identities and theorems.” The ‘Special Integrals’ monograph refers to this handwritten manuscript. 1997.DOI / Link: https://drive.google.com/file/d/15Mkmny3bumOxaM-YLc2qlcSoufFekjyt/view?usp=sharing

5 Research Statement

5.1 Introduction — Research Vision

5.2 Current Research

5.2.1 Special Integrals

5.2.2 Mathematical Techniques in Computational Complexity

Recent collaborative work develops new families of reductions and constructions that strengthen our understanding of average-case and rare-case hardness.

Hardness amplification through group theory: Our 2024 work [23P] explores group-action based amplification, resolving portions of an open question posed by Goldreich (2020) for counting modulo problems and providing limits for our techniques.

5.2.3 Multiple Set Orienteering Problem (mSOP) and Optimization

5.3 Future Research Plan (Five-Year Roadmap)

I plan a coordinated program along four themes that leverage existing results and expand into new directions:

5.3.1 Hardness Magnification Beyond Locality Barriers

5.3.2 Conditional Lower Bounds via Network Coding Conjecture

5.3.3 Quantum Number-Theoretic Algorithms

Leveraging my mathematical background, I plan to investigate quantum algorithms for number-theoretic tasks (e.g., Gauss sum estimation, exponential congruences) and to adapt classical analytic techniques to hybrid classical–quantum algorithm design.

5.3.4 Additive Combinatorics and Average-Case Hardness

5.4 Conclusion

My research aims to integrate mathematical depth with algorithmic applicability — advancing complexity theory while producing methods that can be implemented and taught. Full references and an extended list of publications appear in my curriculum vitae.

6 Graduated PhD Advisees

Ravi Kant

Current Position: Assistant Professor (Contractual - II)

Current Affiliation: Department of Computer Science and Engineering, Thapar Institute of Engineering & Technology

Supervised individually

Title of Thesis: The Set Orienteering Problem: A Review of Variants and Solution Approaches

Graduated from: BITS Pilani, 2024

Rohan Sharma

Current Position: Assistant Professor - I

Current Affiliation: Department of Computer Science and Engineering, Thapar Institute of Engineering & Technology

Partially co-supervised with: Dr. Bibhas Adhikari

Area of Thesis: Complex Networks

Graduated from: IIT Jodhpur, 2018

7 Teaching Experience

Doctor of Philosophy in Computer Science & Engineering, Indian Institute of Technology (Banaras Hindu University), Varanasi, 2011, CGPA: 9.69.
Title of Thesis: Observations on Task Scheduling Algorithms for Multi Core Systems.
Thesis Advisor: Prof. Anil Kumar Tripathi.

[27T] Tejas Nareddy and Abhishek Mishra. “Recovery reductions, conjectures, and barriers.” Electronic Colloquium on Computational Complexity, report no. 157, 2025.
DOI / Link: https://eccc.weizmann.ac.il/report/2025/157/

[26R] Abhishek Mishra. Special Integrals. University Texts in the Mathematical Sciences. Springer Nature Singapore, 2025.
DOI / Link: https://doi.org/10.1007/978-981-97-7514-9

[25P] Tejas Nareddy and Abhishek Mishra. “New techniques for constructing rare-case hard functions.” arXiv:2411.09597v2 [cs.CC], 2025.
DOI / Link: https://doi.org/10.48550/arXiv.2411.09597

[23P] Tejas Nareddy and Abhishek Mishra. “Hardness amplification via group theory.” arXiv:2411.09619 [cs.CC], 2024.
DOI / Link: https://doi.org/10.48550/arXiv.2411.09619

[22P] Ravi Kant, Salmaan Shahid, Anuvind Bhat, and Abhishek Mishra. “Variable neighborhood search for the multi-depot multiple set orienteering problem.” arXiv:2408.08922 [math.OC], 2024.
DOI / Link: https://doi.org/10.48550/arXiv.2408.08922

[15J] Abhishek Mishra and Prasoon Trivedi. “Benchmarking the contention aware nature inspired metaheuristic task scheduling algorithms.” Cluster Computing, 23:537–553, 2020.
DOI / Link: https://link.springer.com/article/10.1007/s10586-019-02943-z

[14J] Rohan Sharma, Bibhas Adhikari, and Abhishek Mishra. “Structural and spectral properties of corona graphs.” Discrete Applied Mathematics, 228:14–31, 2017.
DOI / Link: https://doi.org/10.1016/j.dam.2017.01.005

[13J] Abhishek Mishra and Pramod Kumar Mishra. “A randomized scheduling algorithm for multiprocessor environments using local search.” Parallel Processing Letters, 26(1):1650002, 2016.
DOI / Link: https://www.worldscientific.com/doi/abs/10.1142/S012962641650002X

[12C] Rohan Sharma, Bibhas Adhikari, and Abhishek Mishra. “On spectra of corona graphs.” In Proceedings of the Conference on Algorithms and Discrete Applied Mathematics (CALDAM), pages 126–137, 2015.
DOI / Link: https://link.springer.com/chapter/10.1007/978-3-319-14974-5_13

[11J] Abhishek Mishra and Anil Kumar Tripathi. “Complexity of a problem of energy efficient real-time task scheduling on a multicore processor.” Complexity, 21(1):259–267, 2015.
DOI / Link: https://onlinelibrary.wiley.com/doi/epdf/10.1002/cplx.21561

[07J] Pramod Kumar Mishra, Kamal Sheel Mishra, Abhishek Mishra, and Anil Kumar Tripathi. “A randomized scheduling algorithm for multiprocessor environments.” Parallel Processing Letters, 22(4):1250015, 2012.
DOI / Link: https://www.worldscientific.com/doi/abs/10.1142/S0129626412500156

[01M] Abhishek Mishra. “A 150-page list of identities and theorems.” The ‘Special Integrals’ monograph refers to this handwritten manuscript. 1997.
DOI / Link: https://drive.google.com/file/d/15Mkmny3bumOxaM-YLc2qlcSoufFekjyt/view?usp=sharing