Srikanth Srinivasan

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All published works
Action Title Year Authors
+ PDF Chat Low Degree Local Correction Over the Boolean Cube 2025 Prashanth Amireddy
Amik Raj Behera
Manaswi Paraashar
Srikanth Srinivasan
Madhu Sudan
+ PDF Chat Low Degree Local Correction Over the Boolean Cube 2024 Prashanth Amireddy
Amik Raj Behera
Manaswi Paraashar
Srikanth Srinivasan
Madhu Sudan
+ Local Correction of Linear Functions over the Boolean Cube 2024 Prashanth Amireddy
Amik Raj Behera
Manaswi Paraashar
Srikanth Srinivasan
Madhu Sudan
+ PDF Chat Local Correction of Linear Functions over the Boolean Cube 2024 Prashanth Amireddy
Amik Raj Behera
Manaswi Paraashar
Srikanth Srinivasan
Madhu Sudan
+ Optimal Explicit Small-Depth Formulas for the Coin Problem 2023 Srikanth Srinivasan
Utkarsh Tripathi
+ Schur Polynomials Do Not Have Small Formulas If the Determinant does not 2023 Prasad Chaugule
Mrinal Kumar
Nutan Limaye
Chandra Kanta Mohapatra
Adrian She
Srikanth Srinivasan
+ PDF Chat A Robust Version of Heged\H{u}s's Lemma, with Applications 2023 Srikanth Srinivasan
+ Towards Optimal Depth-Reductions for Algebraic Formulas 2023 Hervé Fournier
Nutan Limaye
Guillaume Malod
Srikanth Srinivasan
Sébastien Tavenas
+ Low-Degree Testing Over Grids 2023 Prashanth Amireddy
Srikanth Srinivasan
Madhu Sudan
+ PDF Chat On the Partial Derivative Method Applied to Lopsided Set-Multilinear Polynomials 2022 Nutan Limaye
Srikanth Srinivasan
Sébastien Tavenas
+ PDF Chat Vanishing Spaces of Random Sets and Applications to Reed-Muller Codes 2022 Siddharth Bhandari
Prahladh Harsha
Ramprasad Saptharishi
Srikanth Srinivasan
+ PDF Chat A #SAT Algorithm for Small Constant-Depth Circuits with PTF gates 2022 Swapnam Bajpai
Vaibhav Krishan
Deepanshu Kush
Nutan Limaye
Srikanth Srinivasan
+ A Robust Version of Hegedűs's Lemma, with Applications 2022 Srikanth Srinivasan
+ Vanishing Spaces of Random Sets and Applications to Reed-Muller Codes 2022 Siddharth Bhandari
Prahladh Harsha
Ramprasad Saptharishi
Srikanth Srinivasan
+ On Vanishing Properties of Polynomials on Symmetric Sets of the Boolean Cube, in Positive Characteristic. 2021 Srikanth Srinivasan
S. Venkitesh
+ On the Probabilistic Degree of an $n$-variate Boolean Function 2021 Srikanth Srinivasan
S. Venkitesh
+ PDF Chat On the probabilistic degree of OR over the reals 2021 Siddharth Bhandari
Prahladh Harsha
Tulasimohan Molli
Srikanth Srinivasan
+ PDF Chat On the Probabilistic Degrees of Symmetric Boolean Functions 2021 Srikanth Srinivasan
Utkarsh Tripathi
S. Venkitesh
+ On the Probabilistic Degree of an n-Variate Boolean Function. 2021 Srikanth Srinivasan
S. Venkitesh
+ A Fixed-Depth Size-Hierarchy Theorem for $\mathrm{AC}^0[\oplus]$ via the Coin Problem 2021 Nutan Limaye
Karteek Sreenivasaiah
Srikanth Srinivasan
Utkarsh Tripathi
S. Venkitesh
+ On the Probabilistic Degree of an $n$-variate Boolean Function 2021 Srikanth Srinivasan
S. Venkitesh
+ On Vanishing Properties of Polynomials on Symmetric Sets of the Boolean Cube, in Positive Characteristic 2021 Srikanth Srinivasan
S. Venkitesh
+ PDF Chat Strongly Exponential Separation between Monotone VP and Monotone VNP 2020 Srikanth Srinivasan
+ Schur polynomials do not have small formulas if the determinant doesn't 2020 Prasad Chaugule
Mrinal Kumar
Nutan Limaye
Chandra Kanta Mohapatra
Adrian She
Srikanth Srinivasan
+ PDF Chat Local decoding and testing of polynomials over grids 2020 Mitali Bafna
Srikanth Srinivasan
Madhu Sudan
+ A robust version of Hegedus’s lemma, with applications 2020 Srikanth Srinivasan
+ A Robust Version of Hegedűs's Lemma, with Applications. 2020 Srikanth Srinivasan
+ High-fidelity superconducting quantum processors via laser-annealing of transmon qubits 2020 Eric Zhang
Srikanth Srinivasan
Neereja Sundaresan
Daniela F. Bogorin
Yves Martin
Jared Hertzberg
John Timmerwilke
Emily Pritchett
Jeng-Bang Yau
Cindy Wang
+ Demonstration of quantum volume 64 on a superconducting quantum computing system 2020 Petar Jurcevic
Ali Javadi-Abhari
Lev S. Bishop
Isaac Lauer
Daniela F. Bogorin
Markus Brink
Lauren Capelluto
Oktay Günlük
Toshinari Itoko
Naoki Kanazawa
+ Schur Polynomials do not have small formulas if the Determinant doesn't! 2019 Prasad Chaugule
Mrinal Kumar
Nutan Limaye
Chandra Kanta Mohapatra
Adrian She
Srikanth Srinivasan
+ On the Probabilistic Degrees of Symmetric Boolean functions 2019 Srikanth Srinivasan
Utkarsh Tripathi
S. Venkitesh
+ Decoding Downset codes over a finite grid 2019 Srikanth Srinivasan
Utkarsh Tripathi
S. Venkitesh
+ Strongly Exponential Separation Between Monotone VP and Monotone VNP. 2019 Srikanth Srinivasan
+ PDF Chat None 2019 Ben Rossman
Srikanth Srinivasan
+ PDF Chat Small-Depth Multilinear Formula Lower Bounds for Iterated Matrix Multiplication with Applications 2019 Suryajith Chillara
Nutan Limaye
Srikanth Srinivasan
+ Decoding Downset codes over a finite grid 2019 Srikanth Srinivasan
Utkarsh Tripathi
S. Venkitesh
+ On the Probabilistic Degrees of Symmetric Boolean functions 2019 Srikanth Srinivasan
Utkarsh Tripathi
S. Venkitesh
+ Schur Polynomials do not have small formulas if the Determinant doesn't! 2019 Prasad Chaugule
Mrinal Kumar
Nutan Limaye
Chandra Kanta Mohapatra
Adrian She
Srikanth Srinivasan
+ On the Probabilistic Degrees of Symmetric Boolean Functions. 2019 Srikanth Srinivasan
Utkarsh Tripathi
S. Venkitesh
+ Schur Polynomials do not have small formulas if the Determinant doesn't! 2019 Prasad Chaugule
Mrinal Kumar
Nutan Limaye
Chandra Kanta Mohapatra
Adrian She
Srikanth Srinivasan
+ Strongly Exponential Separation Between Monotone VP and Monotone VNP 2019 Srikanth Srinivasan
+ On the Probabilistic Degree of OR over the Reals 2018 Siddharth Bhandari
Prahladh Harsha
Tulasimohan Molli
Srikanth Srinivasan
+ PDF Chat On the Probabilistic Degree of OR over the Reals 2018 Siddharth Bhandari
Prahladh Harsha
Tulasimohan Molli
Srikanth Srinivasan
+ PDF Chat A Near-Optimal Depth-Hierarchy Theorem for Small-Depth Multilinear Circuits 2018 Suryajith Chillara
Christian Engels
Nutan Limaye
Srikanth Srinivasan
+ The Coin Problem in Constant Depth: Sample Complexity and Parity Gates. 2018 Nutan Limaye
Karteek Sreenivasaiah
Srikanth Srinivasan
Utkarsh Tripathi
S. Venkitesh
+ PDF Chat Robust Multiplication-Based Tests for Reed–Muller Codes 2018 Prahladh Harsha
Srikanth Srinivasan
+ PDF Chat On polynomial approximations to AC 2018 Prahladh Harsha
Srikanth Srinivasan
+ A Near-Optimal Depth-Hierarchy Theorem for Small-Depth Multilinear Circuits 2018 Suryajith Chillara
Christian Engels
Nutan Limaye
Srikanth Srinivasan
+ Deterministically Counting Satisfying Assignments for Constant-Depth Circuits with Parity Gates, with Implications for Lower Bounds 2018 Ninad Rajgopal
Rahul Santhanam
Srikanth Srinivasan
+ The Coin Problem in Constant Depth: Sample Complexity and Parity Gates. 2018 Nutan Limaye
Karteek Sreenivasaiah
Srikanth Srinivasan
Utkarsh Tripathi
S. Venkitesh
+ A Fixed-Depth Size-Hierarchy Theorem for AC$^0[\oplus]$ via the Coin Problem 2018 Nutan Limaye
Karteek Sreenivasaiah
Srikanth Srinivasan
Utkarsh Tripathi
S. Venkitesh
+ PDF Chat Average-Case Lower Bounds and Satisfiability Algorithms for Small Threshold Circuits 2018 Ruiwen Chen
Rahul Santhanam
Srikanth Srinivasan
+ On the Probabilistic Degree of OR over the Reals 2018 Siddharth Bhandari
Prahladh Harsha
Tulasimohan Molli
Srikanth Srinivasan
+ A #SAT Algorithm for Small Constant-Depth Circuits with PTF gates 2018 Swapnam Bajpai
Vaibhav Krishan
Deepanshu Kush
Nutan Limaye
Srikanth Srinivasan
+ A Near-Optimal Depth-Hierarchy Theorem for Small-Depth Multilinear Circuits 2018 Suryajith Chillara
Christian Engels
Nutan Limaye
Srikanth Srinivasan
+ Small-depth Multilinear Formula Lower Bounds for Iterated Matrix Multiplication, with Applications 2017 Suryajith Chillara
Nutan Limaye
Srikanth Srinivasan
+ Local decoding and testing of polynomials over grids 2017 Srikanth Srinivasan
Madhu Sudan
+ Separation of AC$^0[\oplus]$ Formulas and Circuits 2017 Benjamin Rossman
Srikanth Srinivasan
+ On polynomial approximations over $\mathbb{Z}/2^k\mathbb{Z}$ 2017 Abhishek Bhrushundi
Prahladh Harsha
Srikanth Srinivasan
+ PDF Chat Super-Polylogarithmic Hypergraph Coloring Hardness via Low-Degree Long Codes 2017 Venkatesan Guruswami
Prahladh Harsha
Johan Håstad
Srikanth Srinivasan
Girish Varma
+ On polynomial approximations over ℤ/2 k ℤ. 2017 Abhishek Bhrushundi
Prahladh Harsha
Srikanth Srinivasan
+ Small-depth Multilinear Formula Lower Bounds for Iterated Matrix Multiplication, with Applications. 2017 Suryajith Chillara
Nutan Limaye
Srikanth Srinivasan
+ PDF Chat None 2017 Hervé Fournier
Nutan Limaye
Meena Mahajan
Srikanth Srinivasan
+ Separation of AC$^0[\oplus]$ Formulas and Circuits 2017 Benjamin Rossman
Srikanth Srinivasan
+ Local decoding and testing of polynomials over grids 2017 Mitali Bafna
Srikanth Srinivasan
Madhu Sudan
+ Small-depth Multilinear Formula Lower Bounds for Iterated Matrix Multiplication, with Applications 2017 Suryajith Chillara
Nutan Limaye
Srikanth Srinivasan
+ PDF Chat On the hardness of the noncommutative determinant 2016 V. Arvind
Srikanth Srinivasan
+ PDF Chat Composition limits and separating examples for some boolean function complexity measures 2016 Justin Gilmer
Michael Saks
Srikanth Srinivasan
+ PDF Chat None 2016 Nutan Limaye
Guillaume Malod
Srikanth Srinivasan
+ Robust Multiplication-Based Tests for Reed-Muller Codes. 2016 Prahladh Harsha
Srikanth Srinivasan
+ Lower bounds for non-commutative skew circuits. 2015 Nutan Limaye
Guillaume Malod
Srikanth Srinivasan
+ Derandomized Graph Product Results Using the Low Degree Long Code 2015 Irit Dinur
Prahladh Harsha
Srikanth Srinivasan
Girish Varma
+ Derandomized Graph Product Results using the Low Degree Long Code 2014 Irit Dinur
Prahladh Harsha
Srikanth Srinivasan
Girish Varma
+ An Exponential Lower Bound for Homogeneous Depth Four Arithmetic Formulas 2014 Neeraj Kayal
Nutan Limaye
Chandan Saha
Srikanth Srinivasan
+ PDF Chat Super-polylogarithmic hypergraph coloring hardness via low-degree long codes 2014 Venkatesan Guruswami
Prahladh Harsha
Johan Håstad
Srikanth Srinivasan
Girish Varma
+ PDF Chat A tail bound for read‐<i>k</i> families of functions 2014 Dmitry Gavinsky
Shachar Lovett
Michael Saks
Srikanth Srinivasan
+ An Exponential Lower Bound for Homogeneous Depth Four Arithmetic Formulas. 2014 Neeraj Kayal
Nutan Limaye
Chandan Saha
Srikanth Srinivasan
+ Derandomized Graph Product Results using the Low Degree Long Code 2014 Irit Dinur
Prahladh Harsha
Srikanth Srinivasan
Girish Varma
+ Composition limits and separating examples for some Boolean function complexity measures 2013 Justin Gilmer
Michael Saks
Srikanth Srinivasan
+ PDF Chat Composition Limits and Separating Examples for Some Boolean Function Complexity Measures 2013 Justin Gilmer
Michael Saks
Srikanth Srinivasan
+ Spectral analysis and generation of certain highly oscillatory curves related to chaos, part 2: Calculation aspects 2013 Goong Chen
Tingwen Huang
Maria Christina Mariani
Roza Espandeary
Rym Kanes
M. Ziyan Sheriff
Srikanth Srinivasan
+ PDF Chat None 2013 Aditya Bhaskara
Devendra Desai
Srikanth Srinivasan
+ Super-polylogarithmic hypergraph coloring hardness via low-degree long codes. 2013 Venkatesan Guruswami
Prahladh Harsha
Johan Håstad
Srikanth Srinivasan
Girish Varma
+ Composition limits and separating examples for some Boolean function complexity measures 2013 Justin Gilmer
Michael J. Saks
Srikanth Srinivasan
+ Optimal Hitting Sets for Combinatorial Shapes 2012 Aditya Bhaskara
Devendra Desai
Srikanth Srinivasan
+ Streaming algorithms for recognizing nearly well-parenthesized expressions 2012 Andreas Krebs
Nutan Limaye
Srikanth Srinivasan
+ A Tail Bound for Read-k Families of Functions 2012 Dmitry Gavinsky
Shachar Lovett
Michael Saks
Srikanth Srinivasan
+ A Tail Bound for Read-k Families of Functions. 2012 Dmitry Gavinsky
Shachar Lovett
Michael Saks
Srikanth Srinivasan
+ PDF Chat Optimal Hitting Sets for Combinatorial Shapes 2012 Aditya Bhaskara
Devendra Desai
Srikanth Srinivasan
+ A Tail Bound for Read-k Families of Functions 2012 Dmytro Gavinsky
Shachar Lovett
Michael J. Saks
Srikanth Srinivasan
+ Streaming algorithms for recognizing nearly well-parenthesized expressions 2012 Andreas Krebs
Nutan Limaye
Srikanth Srinivasan
+ Optimal Hitting Sets for Combinatorial Shapes 2012 Aditya Bhaskara
Devendra Desai
Srikanth Srinivasan
+ PDF Chat Almost settling the hardness of noncommutative determinant 2011 Steve Chien
Prahladh Harsha
Alistair Sinclair
Srikanth Srinivasan
+ PDF Chat Streaming Algorithms for Recognizing Nearly Well-Parenthesized Expressions 2011 Andreas Krebs
Nutan Limaye
Srikanth Srinivasan
+ PDF Chat New Results on Noncommutative and Commutative Polynomial Identity Testing 2010 V. Arvind
Partha Mukhopadhyay
Srikanth Srinivasan
+ PDF Chat On the hardness of the noncommutative determinant 2010 V. Arvind
Srikanth Srinivasan
+ Circuit Lower Bounds, Help Functions, and the Remote Point Problem 2010 V. Arvind
Srikanth Srinivasan
+ The Remote Point Problem, Small Bias Space, and Expanding Generator Sets 2009 V. Arvind
Srikanth Srinivasan
+ On Lower Bounds for Constant Width Arithmetic Circuits 2009 V. Arvind
Pushkar S. Joglekar
Srikanth Srinivasan
+ Arithmetic Circuits and the Hadamard Product of Polynomials 2009 V. Arvind
Pushkar S. Joglekar
Srikanth Srinivasan
+ Circuit Lower Bounds, Help Functions, and the Remote Point Problem 2009 V. Arvind
Srikanth Srinivasan
+ PDF Chat On Lower Bounds for Constant Width Arithmetic Circuits 2009 V. Arvind
Pushkar S. Joglekar
Srikanth Srinivasan
+ On the Hardness of the Noncommutative Determinant. 2009 V. Arvind
Srikanth Srinivasan
+ On Lower Bounds for Constant Width Arithmetic Circuits 2009 V. Arvind
Pushkar S. Joglekar
Srikanth Srinivasan
+ On the hardness of the noncommutative determinant 2009 V. Arvind
Srikanth Srinivasan
+ The Remote Point Problem, Small Bias Space, and Expanding Generator Sets 2009 V. Arvind
Srikanth Srinivasan
+ PDF Chat New Results on Noncommutative and Commutative Polynomial Identity Testing 2008 V. Arvind
Partha Mukhopadhyay
Srikanth Srinivasan
+ New results on Noncommutative and Commutative Polynomial Identity Testing 2008 V. Arvind
Partha Mukhopadhyay
Srikanth Srinivasan
+ New results on Noncommutative and Commutative Polynomial Identity Testing 2008 V. Arvind
Partha Mukhopadhyay
Srikanth Srinivasan
Common Coauthors
Commonly Cited References
Action Title Year Authors # of times referenced
+ PDF Chat Polylogarithmic independence fools <i>AC</i> <sup>0</sup> circuits 2008 Mark Braverman
8
+ PDF Chat Optimal Testing of Reed-Muller Codes 2010 Arnab Bhattacharyya
Swastik Kopparty
Grant Schoenebeck
Madhu Sudan
David Zuckerman
7
+ PDF Chat None 2016 Raghu Meka
Hoi H. Nguyen
Van Khu Vu
7
+ PDF Chat Analysis of Boolean Functions 2014 Ryan O’Donnell
6
+ PDF Chat Homogeneous Formulas and Symmetric Polynomials 2011 Pavel Hrubeš
Amir Yehudayoff
5
+ Making the Long Code Shorter 2012 Boaz Barak
Parikshit Gopalan
Johan Håstad
Raghu Meka
Prasad Raghavendra
David Steurer
5
+ Analysis of Boolean Functions 2014 Ryan O’Donnell
5
+ PDF Chat An Average-Case Depth Hierarchy Theorem for Boolean Circuits 2017 Johan Håstad
Benjamin Rossman
Rocco A. Servedio
Li-Yang Tan
4
+ Arithmetic circuits: The chasm at depth four gets wider 2012 Pascal Koiran
4
+ PDF Chat New algorithms and lower bounds for circuits with linear threshold gates 2014 Ryan Williams
4
+ An exact characterization of symmetric functions in qAC0[2] 2001 Chi-Jen Lu
4
+ Clifford algebras and approximating the permanent 2003 Steve Chien
Lars Eilstrup Rasmussen
Alistair Sinclair
4
+ PDF Chat On polynomial approximations to AC 2018 Prahladh Harsha
Srikanth Srinivasan
4
+ PDF Chat Optimal Testing of Multivariate Polynomials over Small Prime Fields 2013 Elad Haramaty
Amir Shpilka
Madhu Sudan
4
+ New algorithms and lower bounds for circuits with linear threshold gates 2014 Ryan Williams
4
+ Short monotone formulae for the majority function 1984 Leslie G. Valiant
4
+ Completeness classes in algebra 1979 Leslie G. Valiant
4
+ PDF Chat Set Systems with Restricted Cross-Intersections and the Minimum Rank ofInclusion Matrices 2005 Peter Keevash
Benny Sudakov
4
+ The complexity of computing the permanent 1979 Leslie G. Valiant
4
+ On representations by low-degree polynomials 2002 Roman Smolensky
4
+ Probabilistic algorithms for sparse polynomials 1979 Richard Zippel
4
+ Quaternionic determinants 1996 Helmer Aslaksen
3
+ Multi-linear formulas for permanent and determinant are of super-polynomial size 2009 Ran Raz
3
+ Hilbert functions and the finite degree Zariski closure in finite field combinatorial geometry 2015 Zipei Nie
Anthony Y. Wang
3
+ Lower Bounds on Balancing Sets and Depth-2 Threshold Circuits 2019 Pavel Hrubeš
Sivaramakrishnan Natarajan Ramamoorthy
Anup Rao
Amir Yehudayoff
3
+ PDF Chat Super-polylogarithmic hypergraph coloring hardness via low-degree long codes 2014 Venkatesan Guruswami
Prahladh Harsha
Johan Håstad
Srikanth Srinivasan
Girish Varma
3
+ PDF Chat On a lemma of Littlewood and Offord 1945 P. Erdős
3
+ A fast and simple randomized parallel algorithm for the maximal independent set problem 1986 Noga Alon
László Babai
Alon Itai
3
+ Balancing sets of vectors 2009 Gábor Hegedüs
3
+ PDF Chat On the Probabilistic Degree of OR over the Reals 2018 Siddharth Bhandari
Prahladh Harsha
Tulasimohan Molli
Srikanth Srinivasan
3
+ PDF Chat Faster All-Pairs Shortest Paths via Circuit Complexity 2018 Ryan Williams
3
+ PDF Chat Pseudorandom Generators for Polynomial Threshold Functions 2013 Raghu Meka
David Zuckerman
3
+ PDF Chat Super-Polylogarithmic Hypergraph Coloring Hardness via Low-Degree Long Codes 2017 Venkatesan Guruswami
Prahladh Harsha
Johan Håstad
Srikanth Srinivasan
Girish Varma
3
+ Separation Between Read-once Oblivious Algebraic Branching Programs (ROABPs) and Multilinear Depth Three Circuits 2016 Neeraj Kayal
Vineet Nair
Chandan Saha
3
+ Finite Rings With Identity 1974 Bernard R. McDonald
3
+ Making the long code shorter, with applications to the Unique Games Conjecture 2011 Boaz Barak
Parikshit Gopalan
Johan Håstad
Raghu Meka
Prasad Raghavendra
David Steurer
3
+ PDF Chat Derandomized graph products 1995 Noga Alon
Uriel Feige
Avi Wigderson
David Zuckerman
3
+ Algebras with Polynomial Identities and Computing the Determinant 2007 Steve Chien
Alistair Sinclair
3
+ PDF Chat Entropy Waves, the Zig-Zag Graph Product, and New Constant-Degree Expanders 2002 Omer Reingold
Salil Vadhan
Avi Wigderson
3
+ PDF Chat Conditional Hardness for Approximate Coloring 2009 Irit Dinur
Elchanan Mossel
Oded Regev
3
+ On the Number of Real Roots of a Random Algebraic Equation 1938 J. E. Littlewood
A. C. Offord
3
+ New Permanent Estimators via Non-Commutative Determinants 2000 Alexander Barvinok
3
+ A Monte-Carlo Algorithm for Estimating the Permanent 1993 Narendra Karmarkar
Richard M. Karp
Richard Lipton
László Lovász
Michael Luby
3
+ PDF Chat Probabilistic Polynomials and Hamming Nearest Neighbors 2015 Josh Alman
Ryan Williams
3
+ Clifford algebras and approximating the permanent 2002 Steve Chien
Lars Eilstrup Rasmussen
Alistair Sinclair
3
+ Pseudorandom generators for combinatorial shapes 2011 Parikshit Gopalan
Raghu Meka
Omer Reingold
David Zuckerman
3
+ Counting Classes are at Least as Hard as the Polynomial-Time Hierarchy 1992 Seinosuke Toda
Mitsunori Ogiwara
3
+ On the power of homogeneous depth 4 arithmetic circuits 2014 Mrinal Kumar
Shubhangi Saraf
3
+ PDF Chat Improved Bounds for Reduction to Depth 4 and Depth 3 2013 Sébastien Tavenas
3
+ PDF Chat The communication complexity of the Hamming distance problem 2006 Wei Huang
Yaoyun Shi
Shengyu Zhang
Yufan Zhu
2