Articles under category:
Lower Bounds
Lower Bounds
ToC Library Graduate Surveys 9 (2020) 100 pages
A Survey on Distribution Testing: Your Data is Big. But is it Blue?
by Clément L. Canonne
A Survey on Distribution Testing: Your Data is Big. But is it Blue?
by Clément L. Canonne
Vol 20, Article 7 (pp 1-62)
Lower Bound Techniques in the Comparison-Query Model and Applications to Inversion Minimization
by Ivan Hu, Dieter van Melkebeek, and Andrew Morgan
Lower Bound Techniques in the Comparison-Query Model and Applications to Inversion Minimization
by Ivan Hu, Dieter van Melkebeek, and Andrew Morgan
Vol 20, Article 1 (pp 1-70)
Polynomial Identity Testing via Evaluation of Rational Functions
by Ivan Hu, Dieter van Melkebeek, and Andrew Morgan
Polynomial Identity Testing via Evaluation of Rational Functions
by Ivan Hu, Dieter van Melkebeek, and Andrew Morgan
Vol 19, Article 11 (pp 1-14)
A Strong XOR Lemma for Randomized Query Complexity
by Joshua Brody, Jae Tak Kim, Peem Lerdputtipongporn, and Hariharan Srinivasulu
A Strong XOR Lemma for Randomized Query Complexity
by Joshua Brody, Jae Tak Kim, Peem Lerdputtipongporn, and Hariharan Srinivasulu
Vol 19, Article 10 (pp 1-44)
Separating $k$-Player from $t$-Player One-Way Communication, with Applications to Data Streams
by Elbert Du, Michael Mitzenmacher, David Woodruff, and Guang Yang
Separating $k$-Player from $t$-Player One-Way Communication, with Applications to Data Streams
by Elbert Du, Michael Mitzenmacher, David Woodruff, and Guang Yang
Vol 19, Article 9 (pp 1-35)
Optimal Composition Theorem for Randomized Query Complexity
by Dmytro Gavinsky, Troy Lee, Miklos Santha, and Swagato Sanyal
Optimal Composition Theorem for Randomized Query Complexity
by Dmytro Gavinsky, Troy Lee, Miklos Santha, and Swagato Sanyal
Vol 19, Article 7 (pp 1-51)
Shrinkage under Random Projections, and Cubic Formula Lower Bounds for $\mathsf{AC}^0$
by Yuval Filmus, Or Meir, and Avishay Tal
Shrinkage under Random Projections, and Cubic Formula Lower Bounds for $\mathsf{AC}^0$
by Yuval Filmus, Or Meir, and Avishay Tal
Vol 18, Article 10 (pp 1-12)
Pseudorandom Bits and Lower Bounds for Randomized Turing Machines
by Emanuele Viola
Pseudorandom Bits and Lower Bounds for Randomized Turing Machines
by Emanuele Viola
Vol 17, Article 11 (pp 1-38)
[CCC19 Spec Issue]
Hardness Magnification Near State-of-the-Art Lower Bounds
by Igor C. Oliveira, Ján Pich, and Rahul Santhanam
Hardness Magnification Near State-of-the-Art Lower Bounds
by Igor C. Oliveira, Ján Pich, and Rahul Santhanam
Vol 17, Article 10 (pp 1-88)
[CCC16 Spec Issue]
Proof Complexity Lower Bounds from Algebraic Circuit Complexity
by Michael A. Forbes, Amir Shpilka, Iddo Tzameret, and Avi Wigderson
Proof Complexity Lower Bounds from Algebraic Circuit Complexity
by Michael A. Forbes, Amir Shpilka, Iddo Tzameret, and Avi Wigderson
Vol 17, Article 5 (pp 1-27)
New Algorithms and Lower Bounds for All-Pairs Max-Flow in Undirected Graphs
by Amir Abboud, Robert Krauthgamer, and Ohad Trabelsi
New Algorithms and Lower Bounds for All-Pairs Max-Flow in Undirected Graphs
by Amir Abboud, Robert Krauthgamer, and Ohad Trabelsi
Vol 17, Article 2 (pp 1-32)
[CCC19 Spec Issue]
Barriers for Fast Matrix Multiplication from Irreversibility
by Matthias Christandl, Péter Vrana, and Jeroen Zuiddam
Barriers for Fast Matrix Multiplication from Irreversibility
by Matthias Christandl, Péter Vrana, and Jeroen Zuiddam
Vol 17, Article 1 (pp 1-30)
[CCC19 Spec Issue]
Limits on the Universal Method for Matrix Multiplication
by Josh Alman
Limits on the Universal Method for Matrix Multiplication
by Josh Alman
Vol 16, Article 14 (pp 1-8)
[NOTE]
On the Hardness of Approximating the $k$-Way Hypergraph Cut problem
by Chandra Chekuri and Shi Li
On the Hardness of Approximating the $k$-Way Hypergraph Cut problem
by Chandra Chekuri and Shi Li
Vol 16, Article 9 (pp 1-12)
On the Complexity of Computing a Random Boolean Function Over the Reals
by Pavel Hrubeš
On the Complexity of Computing a Random Boolean Function Over the Reals
by Pavel Hrubeš
Vol 16, Article 4 (pp 1-50)
[CCC18 Spec Issue]
On The Hardness of Approximate and Exact (Bichromatic) Maximum Inner Product
by Lijie Chen
On The Hardness of Approximate and Exact (Bichromatic) Maximum Inner Product
by Lijie Chen
Vol 16, Article 3 (pp 1-36)
Optimal Unateness Testers for Real-Valued Functions: Adaptivity Helps
by Roksana Baleshzar, Deeparnab Chakrabarty, Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, and C. Seshadhri
Optimal Unateness Testers for Real-Valued Functions: Adaptivity Helps
by Roksana Baleshzar, Deeparnab Chakrabarty, Ramesh Krishnan S. Pallavoor, Sofya Raskhodnikova, and C. Seshadhri
Vol 15, Article 19 (pp 1-25)
The Threshold for Subgroup Profiles to Agree is Logarithmic
by James B. Wilson
The Threshold for Subgroup Profiles to Agree is Logarithmic
by James B. Wilson
Vol 15, Article 18 (pp 1-9)
Lower Bounds for Data Structures with Space Close to Maximum Imply Circuit Lower Bounds
by Emanuele Viola
Lower Bounds for Data Structures with Space Close to Maximum Imply Circuit Lower Bounds
by Emanuele Viola
Vol 15, Article 17 (pp 1-20)
Separation of AC$^0[\oplus]$ Formulas and Circuits
by Ben Rossman and Srikanth Srinivasan
Separation of AC$^0[\oplus]$ Formulas and Circuits
by Ben Rossman and Srikanth Srinivasan
Vol 15, Article 13 (pp 1-34)
Closure Results for Polynomial Factorization
by Chi-Ning Chou, Mrinal Kumar, and Noam Solomon
Closure Results for Polynomial Factorization
by Chi-Ning Chou, Mrinal Kumar, and Noam Solomon
Vol 15, Article 8 (pp 1-7)
[NOTE]
Matrix Rigidity and the Croot-Lev-Pach Lemma
by Zeev Dvir and Benjamin L. Edelman
Matrix Rigidity and the Croot-Lev-Pach Lemma
by Zeev Dvir and Benjamin L. Edelman
Vol 15, Article 2 (pp 1-31)
Time Bounds for Streaming Problems
by Raphaël Clifford, Markus Jalsenius, and Benjamin Sach
Time Bounds for Streaming Problems
by Raphaël Clifford, Markus Jalsenius, and Benjamin Sach
Vol 14, Article 22 (pp 1-17)
On Multiparty Communication with Large versus Unbounded Error
by Alexander A. Sherstov
On Multiparty Communication with Large versus Unbounded Error
by Alexander A. Sherstov
Vol 14, Article 21 (pp 1-23)
Separation of Unbounded-Error Models in Multi-Party Communication Complexity
by Arkadev Chattopadhyay and Nikhil S. Mande
Separation of Unbounded-Error Models in Multi-Party Communication Complexity
by Arkadev Chattopadhyay and Nikhil S. Mande
Vol 14, Article 20 (pp 1-29)
Simplified Separation of Information and Communication
by Anup Rao and Makrand Sinha
Simplified Separation of Information and Communication
by Anup Rao and Makrand Sinha
Vol 14, Article 19 (pp 1-46)
A Chasm Between Identity and Equivalence Testing with Conditional Queries
by Jayadev Acharya, Clément L. Canonne, and Gautam Kamath
A Chasm Between Identity and Equivalence Testing with Conditional Queries
by Jayadev Acharya, Clément L. Canonne, and Gautam Kamath
Vol 14, Article 18 (pp 1-45)
Succinct Hitting Sets and Barriers to Proving Lower Bounds for Algebraic Circuits
by Michael A. Forbes, Amir Shpilka, and Ben Lee Volk
Succinct Hitting Sets and Barriers to Proving Lower Bounds for Algebraic Circuits
by Michael A. Forbes, Amir Shpilka, and Ben Lee Volk
Vol 14, Article 17 (pp 1-25)
New Algorithms and Lower Bounds for Circuits With Linear Threshold Gates
by R. Ryan Williams
New Algorithms and Lower Bounds for Circuits With Linear Threshold Gates
by R. Ryan Williams
Vol 14, Article 16 (pp 1-46)
On the Size of Homogeneous and of Depth-Four Formulas with Low Individual Degree
by Neeraj Kayal, Chandan Saha, and Sébastien Tavenas
On the Size of Homogeneous and of Depth-Four Formulas with Low Individual Degree
by Neeraj Kayal, Chandan Saha, and Sébastien Tavenas
Vol 14, Article 12 (pp 1-24)
Certifying Polynomials for $\mathrm{AC}^0[\oplus]$ Circuits, with Applications to Lower Bounds and Circuit Compression
by Swastik Kopparty and Srikanth Srinivasan
Certifying Polynomials for $\mathrm{AC}^0[\oplus]$ Circuits, with Applications to Lower Bounds and Circuit Compression
by Swastik Kopparty and Srikanth Srinivasan
Vol 14, Article 9 (pp 1-55)
[CCC16 Spec Issue]
Average-Case Lower Bounds and Satisfiability Algorithms for Small Threshold Circuits
by Ruiwen Chen, Rahul Santhanam, and Srikanth Srinivasan
Average-Case Lower Bounds and Satisfiability Algorithms for Small Threshold Circuits
by Ruiwen Chen, Rahul Santhanam, and Srikanth Srinivasan
Vol 14, Article 5 (pp 1-27)
Randomized Query Complexity of Sabotaged and Composed Functions
by Shalev Ben-David and Robin Kothari
Randomized Query Complexity of Sabotaged and Composed Functions
by Shalev Ben-David and Robin Kothari
Vol 13, Article 19 (pp 1-51)
[APRX-RND15 Spec Issue]
Improved NP-Inapproximability for 2ドル$-Variable Linear Equations
by Johan Håstad, Sangxia Huang, Rajsekar Manokaran, Ryan O'Donnell, and John Wright
Improved NP-Inapproximability for 2ドル$-Variable Linear Equations
by Johan Håstad, Sangxia Huang, Rajsekar Manokaran, Ryan O'Donnell, and John Wright
Vol 13, Article 18 (pp 1-15)
Monotone Projection Lower Bounds from Extended Formulation Lower Bounds
by Joshua A. Grochow
Monotone Projection Lower Bounds from Extended Formulation Lower Bounds
by Joshua A. Grochow
Vol 13, Article 11 (pp 1-36)
Superquadratic Lower Bound for 3-Query Locally Correctable Codes over the Reals
by Zeev Dvir, Shubhangi Saraf, and Avi Wigderson
Superquadratic Lower Bound for 3-Query Locally Correctable Codes over the Reals
by Zeev Dvir, Shubhangi Saraf, and Avi Wigderson
Vol 13, Article 6 (pp 1-33)
[CCC16 Spec Issue]
Arithmetic Circuits with Locally Low Algebraic Rank
by Mrinal Kumar and Shubhangi Saraf
Arithmetic Circuits with Locally Low Algebraic Rank
by Mrinal Kumar and Shubhangi Saraf
Vol 13, Article 4 (pp 1-22)
On the (Non) NP-Hardness of Computing Circuit Complexity
by Cody D. Murray and R. Ryan Williams
On the (Non) NP-Hardness of Computing Circuit Complexity
by Cody D. Murray and R. Ryan Williams
Vol 12, Article 12 (pp 1-38)
Lower Bounds for Non-Commutative Skew Circuits
by Nutan Limaye, Guillaume Malod, and Srikanth Srinivasan
Lower Bounds for Non-Commutative Skew Circuits
by Nutan Limaye, Guillaume Malod, and Srikanth Srinivasan
Vol 12, Article 10 (pp 1-35)
Robust Lower Bounds for Communication and Stream Computation
by Amit Chakrabarti, Graham Cormode, and Andrew McGregor
Robust Lower Bounds for Communication and Stream Computation
by Amit Chakrabarti, Graham Cormode, and Andrew McGregor
Vol 11, Article 19 (pp 471-489)
Adapt or Die: Polynomial Lower Bounds for Non-Adaptive Dynamic Data Structures
by Joshua Brody and Kasper Green Larsen
Adapt or Die: Polynomial Lower Bounds for Non-Adaptive Dynamic Data Structures
by Joshua Brody and Kasper Green Larsen
Vol 11, Article 15 (pp 395-401)
[NOTE]
Groups with Identical $k$-Profiles
by George Glauberman and Łukasz Grabowski
Groups with Identical $k$-Profiles
by George Glauberman and Łukasz Grabowski
Vol 11, Article 14 (pp 357-393)
Non-Commutative Arithmetic Circuits with Division
by Pavel Hrubeš and Avi Wigderson
Non-Commutative Arithmetic Circuits with Division
by Pavel Hrubeš and Avi Wigderson
Vol 11, Article 11 (pp 285-298)
New Lower Bounds for the Border Rank of Matrix Multiplication
by Joseph M. Landsberg and Giorgio Ottaviani
New Lower Bounds for the Border Rank of Matrix Multiplication
by Joseph M. Landsberg and Giorgio Ottaviani
Vol 10, Article 17 (pp 453-464)
An Optimal Lower Bound for Monotonicity Testing over Hypergrids
by Deeparnab Chakrabarty and C. Seshadhri
An Optimal Lower Bound for Monotonicity Testing over Hypergrids
by Deeparnab Chakrabarty and C. Seshadhri
Vol 10, Article 15 (pp 389-419)
[Boolean Spec Issue]
Tight Bounds for Monotone Switching Networks via Fourier Analysis
by Siu Man Chan and Aaron Potechin
Tight Bounds for Monotone Switching Networks via Fourier Analysis
by Siu Man Chan and Aaron Potechin
Vol 10, Article 10 (pp 237-256)
Lower Bounds for the Average and Smoothed Number of Pareto-Optima
by Tobias Brunsch, Navin Goyal, Luis Rademacher, and Heiko Röglin
Lower Bounds for the Average and Smoothed Number of Pareto-Optima
by Tobias Brunsch, Navin Goyal, Luis Rademacher, and Heiko Röglin
Vol 9, Article 22 (pp 685-702)
Hamming Approximation of NP Witnesses
by Daniel Sheldon and Neal E. Young
Hamming Approximation of NP Witnesses
by Daniel Sheldon and Neal E. Young
Vol 9, Article 14 (pp 471-557)
Towards an Optimal Separation of Space and Length in Resolution
by Jakob Nordström and Johan Håstad
Towards an Optimal Separation of Space and Length in Resolution
by Jakob Nordström and Johan Håstad
Vol 9, Article 10 (pp 403-411)
On the Real $\tau$-Conjecture and the Distribution of Complex Roots
by Pavel Hrubeš
On the Real $\tau$-Conjecture and the Distribution of Complex Roots
by Pavel Hrubeš
Vol 9, Article 9 (pp 349-401)
Quantum Money from Hidden Subspaces
by Scott Aaronson and Paul Christiano
Quantum Money from Hidden Subspaces
by Scott Aaronson and Paul Christiano
Vol 8, Article 12 (pp 269-289)
SDP Gaps from Pairwise Independence
by Siavosh Benabbas, Konstantinos Georgiou, Avner Magen, and Madhur Tulsiani
SDP Gaps from Pairwise Independence
by Siavosh Benabbas, Konstantinos Georgiou, Avner Magen, and Madhur Tulsiani
Vol 8, Article 11 (pp 239-267)
Tight Bounds on the Approximability of Almost-Satisfiable Horn SAT and Exact Hitting Set
by Venkatesan Guruswami and Yuan Zhou
Tight Bounds on the Approximability of Almost-Satisfiable Horn SAT and Exact Hitting Set
by Venkatesan Guruswami and Yuan Zhou
Vol 8, Article 8 (pp 197-208)
The Communication Complexity of Gap Hamming Distance
by Alexander A. Sherstov
The Communication Complexity of Gap Hamming Distance
by Alexander A. Sherstov
■
Vol 8, Article 1 (pp 1-51)
Time-Space Efficient Simulations of Quantum Computations
by Dieter van Melkebeek and Thomas Watson
Time-Space Efficient Simulations of Quantum Computations
by Dieter van Melkebeek and Thomas Watson
Vol 7, Article 12 (pp 177-184)
[NOTE]
On Circuit Lower Bounds from Derandomization
by Scott Aaronson and Dieter van Melkebeek
On Circuit Lower Bounds from Derandomization
by Scott Aaronson and Dieter van Melkebeek
Vol 7, Article 10 (pp 147-153)
[NOTE]
The Influence Lower Bound Via Query Elimination
by Rahul Jain and Shengyu Zhang
The Influence Lower Bound Via Query Elimination
by Rahul Jain and Shengyu Zhang
Vol 6, Article 10 (pp 227-245)
A Separation of NP and coNP in Multiparty Communication Complexity
by Dmitry Gavinsky and Alexander A. Sherstov
A Separation of NP and coNP in Multiparty Communication Complexity
by Dmitry Gavinsky and Alexander A. Sherstov
Vol 6, Article 9 (pp 201-225)
Separating Deterministic from Randomized Multiparty Communication Complexity
by Paul Beame, Matei David, Toniann Pitassi, and Philipp Woelfel
Separating Deterministic from Randomized Multiparty Communication Complexity
by Paul Beame, Matei David, Toniann Pitassi, and Philipp Woelfel
Vol 6, Article 6 (pp 113-134)
Rounds vs. Queries Tradeoff in Noisy Computation
by Navin Goyal and Michael Saks
Rounds vs. Queries Tradeoff in Noisy Computation
by Navin Goyal and Michael Saks
Vol 6, Article 1 (pp 1-25)
A New Quantum Lower Bound Method, with an Application to a Strong Direct Product Theorem for Quantum Search
by Andris Ambainis
A New Quantum Lower Bound Method, with an Application to a Strong Direct Product Theorem for Quantum Search
by Andris Ambainis
Vol 5, Article 13 (pp 257-282)
Optimal Cryptographic Hardness of Learning Monotone Functions
by Dana Dachman-Soled, Homin K. Lee, Tal Malkin, Rocco A. Servedio, Andrew Wan, and Hoeteck Wee
Optimal Cryptographic Hardness of Learning Monotone Functions
by Dana Dachman-Soled, Homin K. Lee, Tal Malkin, Rocco A. Servedio, Andrew Wan, and Hoeteck Wee
Vol 5, Article 6 (pp 125-134)
Hard Metrics from Cayley Graphs of Abelian Groups
by Ilan Newman and Yuri Rabinovich
Hard Metrics from Cayley Graphs of Abelian Groups
by Ilan Newman and Yuri Rabinovich
Vol 5, Article 4 (pp 83-117)
SDP Gaps and UGC-hardness for Max-Cut-Gain
by Subhash Khot and Ryan O'Donnell
SDP Gaps and UGC-hardness for Max-Cut-Gain
by Subhash Khot and Ryan O'Donnell
Vol 4, Article 7 (pp 137-168)
Norms, XOR Lemmas, and Lower Bounds for Polynomials and Protocols
by Emanuele Viola and Avi Wigderson
Norms, XOR Lemmas, and Lower Bounds for Polynomials and Protocols
by Emanuele Viola and Avi Wigderson
Vol 4, Article 6 (pp 129-135)
The One-Way Communication Complexity of Hamming Distance
by T. S. Jayram, Ravi Kumar, and D. Sivakumar
The One-Way Communication Complexity of Hamming Distance
by T. S. Jayram, Ravi Kumar, and D. Sivakumar
Vol 4, Article 2 (pp 21-51)
Optimal lower bounds for the Korkine-Zolotareff parameters of a lattice and for Schnorr's algorithm for the shortest vector problem
by Miklós Ajtai
Optimal lower bounds for the Korkine-Zolotareff parameters of a lattice and for Schnorr's algorithm for the shortest vector problem
by Miklós Ajtai
Vol 3, Article 12 (pp 221-238)
An Ω(n1/3) Lower Bound for Bilinear Group Based Private Information Retrieval
by Alexander Razborov and Sergey Yekhanin
An Ω(n1/3) Lower Bound for Bilinear Group Based Private Information Retrieval
by Alexander Razborov and Sergey Yekhanin
Vol 3, Article 8 (pp 159-177)
Removing Degeneracy May Require a Large Dimension Increase
by Jiří Matoušek and Petr Škovroň
Removing Degeneracy May Require a Large Dimension Increase
by Jiří Matoušek and Petr Škovroň
Vol 3, Article 7 (pp 129-157)
Quantum Versus Classical Proofs and Advice
by Scott Aaronson and Greg Kuperberg
Quantum Versus Classical Proofs and Advice
by Scott Aaronson and Greg Kuperberg
Vol 3, Article 5 (pp 81-102)
An Exponential Separation between Regular and General Resolution
by Michael Alekhnovich, Jan Johannsen, Toniann Pitassi, and Alasdair Urquhart
An Exponential Separation between Regular and General Resolution
by Michael Alekhnovich, Jan Johannsen, Toniann Pitassi, and Alasdair Urquhart
Vol 2, Article 9 (pp 173-183)
Tolerant Versus Intolerant Testing for Boolean Properties
by Eldar Fischer and Lance Fortnow
Tolerant Versus Intolerant Testing for Boolean Properties
by Eldar Fischer and Lance Fortnow
Vol 2, Article 4 (pp 65-90)
Rank Bounds and Integrality Gaps for Cutting Planes Procedures
by Joshua Buresh-Oppenheim, Nicola Galesi, Shlomo Hoory, Avner Magen, and Toniann Pitassi
Rank Bounds and Integrality Gaps for Cutting Planes Procedures
by Joshua Buresh-Oppenheim, Nicola Galesi, Shlomo Hoory, Avner Magen, and Toniann Pitassi
Vol 2, Article 2 (pp 19-51)
Proving Integrality Gaps without Knowing the Linear Program
by Sanjeev Arora, Béla Bollobás, László Lovász, and Iannis Tourlakis
Proving Integrality Gaps without Knowing the Linear Program
by Sanjeev Arora, Béla Bollobás, László Lovász, and Iannis Tourlakis
Vol 2, Article 1 (pp 1-18)
All Quantum Adversary Methods are Equivalent
by Robert Špalek and Mario Szegedy
All Quantum Adversary Methods are Equivalent
by Robert Špalek and Mario Szegedy
Vol 1, Article 9 (pp 177-216)
Linear Equations, Arithmetic Progressions and Hypergraph Property Testing
by Noga Alon and Asaf Shapira
Linear Equations, Arithmetic Progressions and Hypergraph Property Testing
by Noga Alon and Asaf Shapira
Vol 1, Article 8 (pp 149-176)
A Non-linear Time Lower Bound for Boolean Branching Programs
by Miklós Ajtai
A Non-linear Time Lower Bound for Boolean Branching Programs
by Miklós Ajtai
Vol 1, Article 3 (pp 37-46)
Polynomial Degree and Lower Bounds in Quantum Complexity: Collision and Element Distinctness with Small Range
by Andris Ambainis
Polynomial Degree and Lower Bounds in Quantum Complexity: Collision and Element Distinctness with Small Range
by Andris Ambainis
Vol 1, Article 2 (pp 29-36)
Quantum Lower Bound for the Collision Problem with Small Range
by Samuel Kutin
Quantum Lower Bound for the Collision Problem with Small Range
by Samuel Kutin