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Subhash Khot

Silver Professor; Professor of Computer Science

    20002019
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    Research Output 2000 2019

    2019

    Improved 3LIN hardness via linear label cover

    Harsha, P., Khot, S., Lee, E. & Thiruvenkatachari, D., Sep 2019, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, APPROX/RANDOM 2019. Achlioptas, D. & Vegh, L. A. (eds.). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 9. (Leibniz International Proceedings in Informatics, LIPIcs; vol. 145).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Labels
    Hardness
    Polynomials

    The Andoni–Krauthgamer–Razenshteyn characterization of sketchable norms fails for sketchable metrics

    Khot, S. & Naor, A., Jan 1 2019, p. 1814-1824. 11 p.

    Research output: Contribution to conferencePaper

    Sketching
    Normed Space
    Norm
    Metric
    Metric space

    UG-hardness to NP-hardness by losing half

    Bhangale, A. & Khot, S., Jul 1 2019, 34th Computational Complexity Conference, CCC 2019. Shpilka, A. (ed.). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, (Leibniz International Proceedings in Informatics, LIPIcs; vol. 137).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Hardness
    2018

    An improved dictatorship test with perfect completeness

    Bhangale, A., Khot, S. & Thiruvenkatachari, D., Jan 1 2018, 37th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2017. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, Vol. 93. 15

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Constraint satisfaction problems
    Boolean functions
    Hardness

    Near-optimal approximation algorithm for simultaneous Max-cut

    Bhangale, A., Khot, S., Kopparty, S., Sachdeva, S. & Thiruvenkatachari, D., Jan 1 2018, 29th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2018. Association for Computing Machinery, p. 1407-1425 19 p.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Max-cut
    Optimal Approximation
    Approximation algorithms
    Optimal Algorithm
    Approximation Algorithms

    On monotonicity testing and boolean isoperimetric-type theorems

    Khot, S., Minzer, D. & Safra, M., Jan 1 2018, In : SIAM Journal on Computing. 47, 6, p. 2238-2276 39 p.

    Research output: Contribution to journalArticle

    Isoperimetric
    Monotonicity
    Testing
    Monotone Function
    Theorem

    On non-optimally expanding sets in grassmann graphs

    Dinur, I., Khot, S., Kindler, G., Minzer, D. & Safra, M., Jun 20 2018, STOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing. Association for Computing Machinery, p. 1193-1206 14 p.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Hardness
    Fourier analysis
    Labels

    Pseudorandom sets in Grassmann graph have near-perfect expansion

    Khot, S., Minzer, D. & Safra, M., Nov 30 2018, Proceedings - 59th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2018. Thorup, M. (ed.). IEEE Computer Society, Vol. 2018-October. p. 592-601 10 p. 8555140

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Towards a proof of the 2-to-1 games conjecture?

    Dinur, I., Khot, S., Kindler, G., Minzer, D. & Safra, M., Jun 20 2018, STOC 2018 - Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing. Association for Computing Machinery, p. 1297-1306 10 p.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Hardness
    Coloring
    Labels
    Polynomials
    Color
    2017

    Hardness of coloring 2-colorable 12-uniform hypergraphs with 2(log n) ω(1) colors

    Khot, S. & Saket, R., 2017, In : SIAM Journal on Computing. 46, 1, p. 235-271 37 p.

    Research output: Contribution to journalArticle

    Probabilistically Checkable Proofs
    Uniform Hypergraph
    Coloring
    Hardness
    Colouring

    On Independent Sets, 2-to-2 Games, and Grassmann Graphs

    Khot, S., Minzer, D. & Safra, M., Jun 19 2017, STOC 2017 - Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing. Association for Computing Machinery, Vol. Part F128415. p. 576-589 14 p.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Acoustic waves
    2016

    An Ō(n) queries adaptive tester for unateness

    Khot, S. & Shinkar, I., Sep 1 2016, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques - 19th International Workshop, APPROX 2016 and 20th International Workshop, RANDOM 2016. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, Vol. 60.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Boolean functions

    Candidate hard unique game

    Khot, S. & Moshkovitz, D., Jun 19 2016, STOC 2016 - Proceedings of the 48th Annual ACM SIGACT Symposium on Theory of Computing. Association for Computing Machinery, Vol. 19-21-June-2016. p. 63-76 14 p.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Linear equations

    Hardness of bipartite expansion

    Khot, S. & Saket, R., Aug 1 2016, 24th Annual European Symposium on Algorithms, ESA 2016. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, Vol. 57. 55

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Hardness
    Polynomials

    On hardness of approximating the parameterized clique problem

    Khot, S. & Shinkar, I., Jan 14 2016, ITCS 2016 - Proceedings of the 2016 ACM Conference on Innovations in Theoretical Computer Science. Association for Computing Machinery, Inc, p. 37-45 9 p.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Clique
    Hardness
    Constraint satisfaction problems
    Quadratic equation
    Tractability
    2015

    Approximating CSPs using LP relaxation

    Khot, S. & Saket, R., 2015, Automata, Languages, and Programming - 42nd International Colloquium, ICALP 2015, Proceedings. Springer Verlag, Vol. 9134. p. 822-833 12 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 9134).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    LP Relaxation
    Constraint satisfaction problems
    Labels
    Constraint Satisfaction Problem
    Game

    On Monotonicity Testing and Boolean Isoperimetric Type Theorems

    Khot, S., Minzer, D. & Safra, M., Dec 11 2015, Proceedings - 2015 IEEE 56th Annual Symposium on Foundations of Computer Science, FOCS 2015. IEEE Computer Society, Vol. 2015-December. p. 52-58 7 p. 7354387

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Testing

    The unique games conjecture, integrality gap for cut problems and embeddability of negative-type metrics into ℓ1

    Khot, S. & Vishnoi, N. K., Feb 1 2015, In : Journal of the ACM. 62, 1, p. 8 1 p.

    Research output: Contribution to journalArticle

    Hardness
    2014

    A characterization of strong approximation resistance

    Khot, S., Tulsiani, M. & Worah, P., 2014, STOC 2014 - Proceedings of the 2014 ACM Symposium on Theory of Computing. Association for Computing Machinery, p. 634-643 10 p.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Linear programming

    Almost polynomial factor hardness for closest vector problem with preprocessing

    Khot, S., Popat, P. & Vishnoi, N. K., 2014, In : SIAM Journal on Computing. 43, 3, p. 1184-1205 22 p.

    Research output: Contribution to journalArticle

    Hardness
    Preprocessing
    Polynomials
    Polynomial

    A simple deterministic reduction for the gap minimum distance of code problem

    Austrin, P. & Khot, S., Oct 1 2014, In : IEEE Transactions on Information Theory. 60, 10, p. 6636-6645 10 p., 6868217.

    Research output: Contribution to journalArticle

    Sudan
    strike
    coding
    Hardness

    Hardness of coloring 2-colorable 12-uniform hypergraphs with 2(logn}ω(1) colors

    Khot, S. & Saket, R., Dec 7 2014, Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS. IEEE Computer Society, p. 206-215 10 p. 6979005

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Coloring
    Hardness
    Color

    Hardness of finding independent sets in 2-colorable and almost 2-colorable hypergraphs

    Khot, S. & Saket, R., 2014, Proceedings of the 25th Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2014. Association for Computing Machinery, p. 1607-1625 19 p.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Independent Set
    Hypergraph
    Hardness
    Uniform Hypergraph
    Game

    The complexity of somewhat approximation resistant predicates

    Khot, S., Tulsiani, M. & Worah, P., 2014, Automata, Languages, and Programming - 41st International Colloquium, ICALP 2014, Proceedings. PART 1 ed. Springer Verlag, Vol. 8572 LNCS. p. 689-700 12 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 8572 LNCS, no. PART 1).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Predicate
    Hardness
    Hamming distance
    Hamming Distance
    Assignment
    2013

    A characterization of approximation resistance for even k-partite CSPs

    Austrin, P. & Khot, S., 2013, ITCS 2013 - Proceedings of the 2013 ACM Conference on Innovations in Theoretical Computer Science. p. 187-196 10 p.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Constraint satisfaction problems
    Approximation
    Constraint satisfaction problem
    Random assignment

    NP-Hardness of approximately solving linear equations over reals

    Khot, S. & Moshkovitz, D., 2013, In : SIAM Journal on Computing. 42, 3, p. 752-791 40 p.

    Research output: Contribution to journalArticle

    NP-hardness
    Linear equations
    Linear equation
    Assignment
    Hardness

    Sharp kernel clustering algorithms and their associated Grothendieck inequalities

    Khot, S. & Naor, A., May 2013, In : Random Structures and Algorithms. 42, 3, p. 269-300 32 p.

    Research output: Contribution to journalArticle

    Positive Semidefinite Matrix
    Clustering algorithms
    Clustering Algorithm
    Partition
    kernel

    Towards an optimal query efficient PCP?

    Khot, S., Safra, M. & Tulsiani, M., 2013, ITCS 2013 - Proceedings of the 2013 ACM Conference on Innovations in Theoretical Computer Science. p. 173-186 14 p.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Polynomials
    Query
    Hypergraph
    Linearity test
    Trade-offs
    2012

    2 log1-εn hardness for the closest vector problem with preprocessing

    Khot, S., Popat, P. & Vishnoi, N. K., 2012, STOC '12 - Proceedings of the 2012 ACM Symposium on Theory of Computing. p. 277-288 12 p.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Hardness

    Grothendieck-Type Inequalities in Combinatorial Optimization

    Khot, S. & Naor, A., Jul 2012, In : Communications on Pure and Applied Mathematics. 65, 7, p. 992-1035 44 p.

    Research output: Contribution to journalArticle

    Combinatorial optimization
    Combinatorial Optimization
    Computational complexity
    Computational Complexity

    Hardness of finding independent sets in almost q-colorable graphs

    Khot, S. & Saket, R., 2012, Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS. p. 380-389 10 p. 6375316

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Hardness
    2011

    A simple deterministic reduction for the gap minimum distance of code problem

    Austrin, P. & Khot, S., 2011, Automata, Languages and Programming - 38th International Colloquium, ICALP 2011, Proceedings. PART 1 ed. Vol. 6755 LNCS. p. 474-485 12 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 6755 LNCS, no. PART 1).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Minimum Distance
    Rate Constant
    Hardness
    Galois field
    Coding

    A two prover one round game with strong soundness

    Khot, S. & Safra, M., 2011, Proceedings - 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, FOCS 2011. p. 648-657 10 p. 6108226

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Quadratic programming
    Polynomials
    Chemical analysis

    Combinatorial theorems about embedding trees on the real line

    Chakrabarti, A. & Khot, S., Jun 2011, In : Journal of Graph Theory. 67, 2, p. 153-168 16 p.

    Research output: Contribution to journalArticle

    Real Line
    Metric
    Theorem
    Optimality
    Metric Embeddings

    Hardness of Approximating the Closest Vector Problem with Pre-Processing

    Alekhnovich, M., Khot, S. A., Kindler, G. & Vishnoi, N. K., Dec 2011, In : Computational Complexity. 20, 4, p. 741-753 13 p.

    Research output: Contribution to journalArticle

    Hardness
    Preprocessing
    Computational complexity
    Processing
    NP-complete problem

    NP-hardness of approximately solving linear equations over reals

    Khot, S. & Moshkovitz, D., 2011, STOC'11 - Proceedings of the 43rd ACM Symposium on Theory of Computing. p. 413-419 7 p.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Linear equations
    Hardness
    Testing

    On the hardness of learning intersections of two halfspaces

    Khot, S. & Saket, R., Jan 2011, In : Journal of Computer and System Sciences. 77, 1, p. 129-141 13 p.

    Research output: Contribution to journalArticle

    Half-space
    Hardness
    Intersection
    Classify
    Threshold Function
    2010

    Approximate Lasserre integrality gap for unique games

    Khot, S., Popat, P. & Saket, R., 2010, Approximation, Randomization, and Combinatorial Optimization: Algorithms and Techniques - 13th International Workshop, APPROX 2010 and 14th International Workshop, RANDOM 2010, Proceedings. Vol. 6302 LNCS. p. 298-311 14 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 6302 LNCS).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Semidefinite Programming Relaxation
    Integrality
    Semidefinite Programming
    Labels
    Game

    Hardness of finding independent sets in almost 3-colorable graphs

    Dinur, I., Khot, S., Perkins, W. & Safra, M., 2010, Proceedings - 2010 IEEE 51st Annual Symposium on Foundations of Computer Science, FOCS 2010. p. 212-221 10 p. 5670828

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Hardness

    Hardness of reconstructing multivariate polynomials over finite fields

    Gopalan, P., Khot, S. & Saket, R., 2010, In : SIAM Journal on Computing. 39, 6, p. 2598-2621 24 p.

    Research output: Contribution to journalArticle

    Multivariate Polynomials
    Hardness
    Galois field
    Polynomials
    Polynomial

    Inapproximability of hypergraph vertex cover and applications to scheduling problems

    Bansal, N. & Khot, S., 2010, Automata, Languages and Programming - 37th International Colloquium, ICALP 2010, Proceedings. PART 1 ed. Vol. 6198 LNCS. p. 250-261 12 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 6198 LNCS, no. PART 1).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Inapproximability
    Vertex Cover
    Hypergraph
    Scheduling Problem
    Hardness

    Inapproximability of NP-complete problems, discrete fourier analysis, and geometry

    Khot, S., 2010, Proceedings of the International Congress of Mathematicians 2010, ICM 2010. p. 2676-2697 22 p.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Isoperimetry
    Inapproximability
    Fourier Analysis
    Boolean Functions
    Hypercube

    Inapproximability results for computational problems on lattices

    Khot, S., 2010, Information Security and Cryptography. Springer International Publishing, Vol. 10. p. 453-473 21 p. (Information Security and Cryptography; vol. 10).

    Research output: Chapter in Book/Report/Conference proceedingChapter

    On the unique games conjecture

    Khot, S., 2010, Proceedings - 25th Annual IEEE Conference on Computational Complexity, CCC 2010. p. 99-121 23 p. 5497893

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Fourier analysis
    Fourier Analysis
    Computational complexity
    Computational Complexity
    Game

    SDP gaps for 2-to-1 and other label-cover variants

    Guruswami, V., Khot, S., O'Donnell, R., Popat, P., Tulsiani, M. & Wu, Y., 2010, Automata, Languages and Programming - 37th International Colloquium, ICALP 2010, Proceedings. PART 1 ed. Vol. 6198 LNCS. p. 617-628 12 p. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); vol. 6198 LNCS, no. PART 1).

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Semidefinite Programming
    Labels
    Cover
    Optimal Solution
    Game

    Sharp kernel clustering algorithms and their associated Grothendieck inequalities

    Khot, S. & Naor, A., 2010, Proceedings of the 21st Annual ACM-SIAM Symposium on Discrete Algorithms. p. 664-683 20 p.

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Positive Semidefinite Matrix
    Clustering algorithms
    Clustering Algorithm
    Partition
    kernel
    2009

    Approximate kernel clustering

    Khot, S. & Naor, A., Jan 2009, In : Mathematika. 55, 1-2, p. 129-165 37 p.

    Research output: Contribution to journalArticle

    Clustering
    kernel
    Positive Semidefinite Matrix
    Unit matrix
    Game

    Inapproximability of vertex cover and independent set in bounded degree graphs

    Austrin, P., Khot, S. & Safra, M., 2009, Proceedings of the 2009 24th Annual IEEE Conference on Computational Complexity, CCC 2009. p. 74-80 7 p. 5231231

    Research output: Chapter in Book/Report/Conference proceedingConference contribution

    Inapproximability
    Vertex Cover
    Independent Set
    Hardness
    Game

    Inapproximability of vertex cover and independent set in bounded degree graphs

    Austrin, P., Khot, S. & Safra, M., 2009, In : Theory of Computing Systems. 7, 1, p. 27-43

    Research output: Contribution to journalArticle

    Inapproximability results for computational problems on lattices

    Khot, S., 2009, The LLL algorithm: Survey and applications. Springer

    Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)