6 Search Results for "Chen, Ning"


Document
Track A: Algorithms, Complexity and Games
Limitations of Local Quantum Algorithms on Random MAX-k-XOR and Beyond

Authors: Chi-Ning Chou, Peter J. Love, Juspreet Singh Sandhu, and Jonathan Shi

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)


Abstract
We introduce a notion of generic local algorithm, which strictly generalizes existing frameworks of local algorithms such as factors of i.i.d. by capturing local quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA). Motivated by a question of Farhi et al. [arXiv:1910.08187, 2019], we then show limitations of generic local algorithms including QAOA on random instances of constraint satisfaction problems (CSPs). Specifically, we show that any generic local algorithm whose assignment to a vertex depends only on a local neighborhood with o(n) other vertices (such as the QAOA at depth less than εlog(n)) cannot arbitrarily-well approximate boolean CSPs if the problem satisfies a geometric property from statistical physics called the coupled overlap-gap property (OGP) [Chen et al., Annals of Probability, 47(3), 2019]. We show that the random MAX-k-XOR problem has this property when k ≥ 4 is even by extending the corresponding result for diluted k-spin glasses. Our concentration lemmas confirm a conjecture of Brandao et al. [arXiv:1812.04170, 2018] asserting that the landscape independence of QAOA extends to logarithmic depth - in other words, for every fixed choice of QAOA angle parameters, the algorithm at logarithmic depth performs almost equally well on almost all instances. One of these lemmas is a strengthening of McDiarmid’s inequality, applicable when the random variables have a highly biased distribution, and may be of independent interest.

Cite as

Chi-Ning Chou, Peter J. Love, Juspreet Singh Sandhu, and Jonathan Shi. Limitations of Local Quantum Algorithms on Random MAX-k-XOR and Beyond. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 41:1-41:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{chou_et_al:LIPIcs.ICALP.2022.41,
  author =	{Chou, Chi-Ning and Love, Peter J. and Sandhu, Juspreet Singh and Shi, Jonathan},
  title =	{{Limitations of Local Quantum Algorithms on Random MAX-k-XOR and Beyond}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{41:1--41:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.41},
  URN =		{urn:nbn:de:0030-drops-163822},
  doi =		{10.4230/LIPIcs.ICALP.2022.41},
  annote =	{Keywords: Quantum Algorithms, Spin Glasses, Hardness of Approximation, Local Algorithms, Concentration Inequalities, Overlap Gap Property}
}
Document
Quantum Meets the Minimum Circuit Size Problem

Authors: Nai-Hui Chia, Chi-Ning Chou, Jiayu Zhang, and Ruizhe Zhang

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)


Abstract
In this work, we initiate the study of the Minimum Circuit Size Problem (MCSP) in the quantum setting. MCSP is a problem to compute the circuit complexity of Boolean functions. It is a fascinating problem in complexity theory - its hardness is mysterious, and a better understanding of its hardness can have surprising implications to many fields in computer science. We first define and investigate the basic complexity-theoretic properties of minimum quantum circuit size problems for three natural objects: Boolean functions, unitaries, and quantum states. We show that these problems are not trivially in NP but in QCMA (or have QCMA protocols). Next, we explore the relations between the three quantum MCSPs and their variants. We discover that some reductions that are not known for classical MCSP exist for quantum MCSPs for unitaries and states, e.g., search-to-decision reductions and self-reductions. Finally, we systematically generalize results known for classical MCSP to the quantum setting (including quantum cryptography, quantum learning theory, quantum circuit lower bounds, and quantum fine-grained complexity) and also find new connections to tomography and quantum gravity. Due to the fundamental differences between classical and quantum circuits, most of our results require extra care and reveal properties and phenomena unique to the quantum setting. Our findings could be of interest for future studies, and we post several open problems for further exploration along this direction.

Cite as

Nai-Hui Chia, Chi-Ning Chou, Jiayu Zhang, and Ruizhe Zhang. Quantum Meets the Minimum Circuit Size Problem. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 47:1-47:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


Copy BibTex To Clipboard

@InProceedings{chia_et_al:LIPIcs.ITCS.2022.47,
  author =	{Chia, Nai-Hui and Chou, Chi-Ning and Zhang, Jiayu and Zhang, Ruizhe},
  title =	{{Quantum Meets the Minimum Circuit Size Problem}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{47:1--47:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.47},
  URN =		{urn:nbn:de:0030-drops-156433},
  doi =		{10.4230/LIPIcs.ITCS.2022.47},
  annote =	{Keywords: Quantum Computation, Quantum Complexity, Minimum Circuit Size Problem}
}
Document
APPROX
Tracking the l_2 Norm with Constant Update Time

Authors: Chi-Ning Chou, Zhixian Lei, and Preetum Nakkiran

Published in: LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)


Abstract
The l_2 tracking problem is the task of obtaining a streaming algorithm that, given access to a stream of items a_1,a_2,a_3,... from a universe [n], outputs at each time t an estimate to the l_2 norm of the frequency vector f^{(t)}in R^n (where f^{(t)}_i is the number of occurrences of item i in the stream up to time t). The previous work [Braverman-Chestnut-Ivkin-Nelson-Wang-Woodruff, PODS 2017] gave a streaming algorithm with (the optimal) space using O(epsilon^{-2}log(1/delta)) words and O(epsilon^{-2}log(1/delta)) update time to obtain an epsilon-accurate estimate with probability at least 1-delta. We give the first algorithm that achieves update time of O(log 1/delta) which is independent of the accuracy parameter epsilon, together with the nearly optimal space using O(epsilon^{-2}log(1/delta)) words. Our algorithm is obtained using the Count Sketch of [Charilkar-Chen-Farach-Colton, ICALP 2002].

Cite as

Chi-Ning Chou, Zhixian Lei, and Preetum Nakkiran. Tracking the l_2 Norm with Constant Update Time. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 2:1-2:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


Copy BibTex To Clipboard

@InProceedings{chou_et_al:LIPIcs.APPROX-RANDOM.2019.2,
  author =	{Chou, Chi-Ning and Lei, Zhixian and Nakkiran, Preetum},
  title =	{{Tracking the l\underline2 Norm with Constant Update Time}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{2:1--2:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.2},
  URN =		{urn:nbn:de:0030-drops-112175},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.2},
  annote =	{Keywords: Streaming algorithms, Sketching algorithms, Tracking, CountSketch}
}
Document
Online Makespan Minimization: The Power of Restart

Authors: Zhiyi Huang, Ning Kang, Zhihao Gavin Tang, Xiaowei Wu, and Yuhao Zhang

Published in: LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)


Abstract
We consider the online makespan minimization problem on identical machines. Chen and Vestjens (ORL 1997) show that the largest processing time first (LPT) algorithm is 1.5-competitive. For the special case of two machines, Noga and Seiden (TCS 2001) introduce the SLEEPY algorithm that achieves a competitive ratio of (5 - sqrt{5})/2 ~~ 1.382, matching the lower bound by Chen and Vestjens (ORL 1997). Furthermore, Noga and Seiden note that in many applications one can kill a job and restart it later, and they leave an open problem whether algorithms with restart can obtain better competitive ratios. We resolve this long-standing open problem on the positive end. Our algorithm has a natural rule for killing a processing job: a newly-arrived job replaces the smallest processing job if 1) the new job is larger than other pending jobs, 2) the new job is much larger than the processing one, and 3) the processed portion is small relative to the size of the new job. With appropriate choice of parameters, we show that our algorithm improves the 1.5 competitive ratio for the general case, and the 1.382 competitive ratio for the two-machine case.

Cite as

Zhiyi Huang, Ning Kang, Zhihao Gavin Tang, Xiaowei Wu, and Yuhao Zhang. Online Makespan Minimization: The Power of Restart. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 14:1-14:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


Copy BibTex To Clipboard

@InProceedings{huang_et_al:LIPIcs.APPROX-RANDOM.2018.14,
  author =	{Huang, Zhiyi and Kang, Ning and Tang, Zhihao Gavin and Wu, Xiaowei and Zhang, Yuhao},
  title =	{{Online Makespan Minimization: The Power of Restart}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{14:1--14:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.14},
  URN =		{urn:nbn:de:0030-drops-94182},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.14},
  annote =	{Keywords: Online Scheduling, Makespan Minimization, Identical Machines}
}
Document
On Computing Pareto Stable Assignments

Authors: Ning Chen

Published in: LIPIcs, Volume 14, 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)


Abstract
Assignment between two parties in a two-sided matching market has been one of the central questions studied in economics, due to its extensive applications, focusing on different solution concepts with different objectives. One of the most important and well-studied ones is that of stability, proposed by Gale and Shapley, which captures fairness condition in a model where every individual in the market has a preference of the other side. When the preferences have indifferences (i.e., ties), a stable outcome need not be Pareto efficient, causing a loss in efficiency. The solution concept Pareto stability, which requires both stability and Pareto efficiency, offers a refinement of the solution concept stability in the sense that it captures both fairness and efficiency. We study the algorithmic question of computing a Pareto stable assignment in a many-to-many matching market model, where both sides of the market can have multiunit capacities (i.e., demands) and can be matched with multiple partners given the capacity constraints. We provide an algorithm to efficiently construct an assignment that is simultaneously stable and Pareto efficient; our result immediately implies the existence of a Pareto stable assignment for this model.

Cite as

Ning Chen. On Computing Pareto Stable Assignments. In 29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012). Leibniz International Proceedings in Informatics (LIPIcs), Volume 14, pp. 384-395, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2012)


Copy BibTex To Clipboard

@InProceedings{chen:LIPIcs.STACS.2012.384,
  author =	{Chen, Ning},
  title =	{{On Computing Pareto Stable Assignments}},
  booktitle =	{29th International Symposium on Theoretical Aspects of Computer Science (STACS 2012)},
  pages =	{384--395},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-35-4},
  ISSN =	{1868-8969},
  year =	{2012},
  volume =	{14},
  editor =	{D\"{u}rr, Christoph and Wilke, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2012.384},
  URN =		{urn:nbn:de:0030-drops-34042},
  doi =		{10.4230/LIPIcs.STACS.2012.384},
  annote =	{Keywords: Algorithm, stable matching, Pareto efficiency}
}
Document
Testing Linear-Invariant Non-Linear Properties

Authors: Arnab Bhattacharyya, Victor Chen, Madhu Sudan, and Ning Xie

Published in: LIPIcs, Volume 3, 26th International Symposium on Theoretical Aspects of Computer Science (2009)


Abstract
We consider the task of testing properties of Boolean functions that are invariant under linear transformations of the Boolean cube. Previous work in property testing, including the linearity test and the test for Reed-Muller codes, has mostly focused on such tasks for linear properties. The one exception is a test due to Green for {}``triangle freeness'': A function $f:\mathbb{F}_{2}^{n}\to\mathbb{F}_{2}$ satisfies this property if $f(x),f(y),f(x+y)$ do not all equal $1$, for any pair $x,y\in\mathbb{F}_{2}^{n}$. Here we extend this test to a more systematic study of testing for linear-invariant non-linear properties. We consider properties that are described by a single forbidden pattern (and its linear transformations), i.e., a property is given by $k$ points $v_{1},\ldots,v_{k}\in\mathbb{F}_{2}^{k}$ and $f:\mathbb{F}_{2}^{n}\to\mathbb{F}_{2}$ satisfies the property that if for all linear maps $L:\mathbb{F}_{2}^{k}\to\mathbb{F}_{2}^{n}$ it is the case that $f(L(v_{1})),\ldots,f(L(v_{k}))$ do not all equal $1$. We show that this property is testable if the underlying matroid specified by $v_{1},\ldots,v_{k}$ is a graphic matroid. This extends Green's result to an infinite class of new properties. Our techniques extend those of Green and in particular we establish a link between the notion of {}``1-complexity linear systems'' of Green and Tao, and graphic matroids, to derive the results.

Cite as

Arnab Bhattacharyya, Victor Chen, Madhu Sudan, and Ning Xie. Testing Linear-Invariant Non-Linear Properties. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 135-146, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)


Copy BibTex To Clipboard

@InProceedings{bhattacharyya_et_al:LIPIcs.STACS.2009.1823,
  author =	{Bhattacharyya, Arnab and Chen, Victor and Sudan, Madhu and Xie, Ning},
  title =	{{Testing Linear-Invariant Non-Linear Properties}},
  booktitle =	{26th International Symposium on Theoretical Aspects of Computer Science},
  pages =	{135--146},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-09-5},
  ISSN =	{1868-8969},
  year =	{2009},
  volume =	{3},
  editor =	{Albers, Susanne and Marion, Jean-Yves},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2009.1823},
  URN =		{urn:nbn:de:0030-drops-18235},
  doi =		{10.4230/LIPIcs.STACS.2009.1823},
  annote =	{Keywords: }
}
  • Refine by Author
  • 3 Chou, Chi-Ning
  • 1 Bhattacharyya, Arnab
  • 1 Chen, Ning
  • 1 Chen, Victor
  • 1 Chia, Nai-Hui
  • Show More...

  • Refine by Classification
  • 2 Theory of computation → Quantum complexity theory
  • 1 Mathematics of computing → Combinatorics
  • 1 Mathematics of computing → Probabilistic algorithms
  • 1 Theory of computation → Approximation algorithms analysis
  • 1 Theory of computation → Online algorithms
  • Show More...

  • Refine by Keyword
  • 1 Algorithm
  • 1 Concentration Inequalities
  • 1 CountSketch
  • 1 Hardness of Approximation
  • 1 Identical Machines
  • Show More...

  • Refine by Type
  • 6 document

  • Refine by Publication Year
  • 2 2022
  • 1 2009
  • 1 2012
  • 1 2018
  • 1 2019

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail