7 Search Results for "Wu, Ke"

Document
DOI: 10.4230/LIPIcs.TQC.2024.3
Efficient Optimal Control of Open Quantum Systems

Authors: Wenhao He, Tongyang Li, Xiantao Li, Zecheng Li, Chunhao Wang, and Ke Wang

Published in: LIPIcs, Volume 310, 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024)

Abstract
The optimal control problem for open quantum systems can be formulated as a time-dependent Lindbladian that is parameterized by a number of time-dependent control variables. Given an observable and an initial state, the goal is to tune the control variables so that the expected value of some observable with respect to the final state is maximized. In this paper, we present algorithms for solving this optimal control problem efficiently, i.e., having a poly-logarithmic dependency on the system dimension, which is exponentially faster than best-known classical algorithms. Our algorithms are hybrid, consisting of both quantum and classical components. The quantum procedure simulates time-dependent Lindblad evolution that drives the initial state to the final state, and it also provides access to the gradients of the objective function via quantum gradient estimation. The classical procedure uses the gradient information to update the control variables. At the technical level, we provide the first (to the best of our knowledge) simulation algorithm for time-dependent Lindbladians with an 𝓁₁-norm dependence. As an alternative, we also present a simulation algorithm in the interaction picture to improve the algorithm for the cases where the time-independent component of a Lindbladian dominates the time-dependent part. On the classical side, we heavily adapt the state-of-the-art classical optimization analysis to interface with the quantum part of our algorithms. Both the quantum simulation techniques and the classical optimization analyses might be of independent interest.
Cite as

Wenhao He, Tongyang Li, Xiantao Li, Zecheng Li, Chunhao Wang, and Ke Wang. Efficient Optimal Control of Open Quantum Systems. In 19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 310, pp. 3:1-3:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{he_et_al:LIPIcs.TQC.2024.3,
  author =	{He, Wenhao and Li, Tongyang and Li, Xiantao and Li, Zecheng and Wang, Chunhao and Wang, Ke},
  title =	{{Efficient Optimal Control of Open Quantum Systems}},
  booktitle =	{19th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2024)},
  pages =	{3:1--3:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-328-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{310},
  editor =	{Magniez, Fr\'{e}d\'{e}ric and Grilo, Alex Bredariol},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2024.3},
  URN =		{urn:nbn:de:0030-drops-206733},
  doi =		{10.4230/LIPIcs.TQC.2024.3},
  annote =	{Keywords: Quantum algorithm, quantum optimal control, Lindbladian simulation, accelerated gradient descent}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.38
Algorithms and Complexity for Path Covers of Temporal DAGs

Authors: Dibyayan Chakraborty, Antoine Dailly, Florent Foucaud, and Ralf Klasing

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
A path cover of a digraph is a collection of paths collectively containing its vertex set. A path cover with minimum cardinality for a directed acyclic graph can be found in polynomial time [Fulkerson, AMS'56; Cáceres et al., SODA'22]. Moreover, Dilworth’s celebrated theorem on chain coverings of partially ordered sets equivalently states that the minimum size of a path cover of a DAG is equal to the maximum size of a set of mutually unreachable vertices. In this paper, we examine how far these classic results can be extended to a dynamic setting. A temporal digraph has an arc set that changes over discrete time-steps; if the underlying digraph is acyclic, then it is a temporal DAG. A temporal path is a directed path in the underlying digraph, such that the time-steps of arcs are strictly increasing along the path. Two temporal paths are temporally disjoint if they do not occupy any vertex at the same time. A temporal path cover is a collection 𝒞 of temporal paths that covers all vertices, and 𝒞 is temporally disjoint if all its temporal paths are pairwise temporally disjoint. We study the computational complexities of the problems of finding a minimum-size temporal (disjoint) path cover (denoted as Temporal Path Cover and Temporally Disjoint Path Cover). On the negative side, we show that both Temporal Path Cover and Temporally Disjoint Path Cover are NP-hard even when the underlying DAG is planar, bipartite, subcubic, and there are only two arc-disjoint time-steps. Moreover, Temporally Disjoint Path Cover remains NP-hard even on temporal oriented trees. We also observe that natural temporal analogues of Dilworth’s theorem on these classes of temporal DAGs do not hold. In contrast, we show that Temporal Path Cover is polynomial-time solvable on temporal oriented trees by a reduction to Clique Cover for (static undirected) weakly chordal graphs (a subclass of perfect graphs for which Clique Cover admits an efficient algorithm). This highlights an interesting algorithmic difference between the two problems. Although it is NP-hard on temporal oriented trees, Temporally Disjoint Path Cover becomes polynomial-time solvable on temporal oriented lines and temporal rooted directed trees. Motivated by the hardness result on trees, we show that, in contrast, Temporal Path Cover admits an XP time algorithm with respect to parameter t_max + tw, where t_max is the maximum time-step and tw is the treewidth of the underlying static undirected graph; moreover, Temporally Disjoint Path Cover admits an FPT algorithm with respect to the same parameterization.
Cite as

Dibyayan Chakraborty, Antoine Dailly, Florent Foucaud, and Ralf Klasing. Algorithms and Complexity for Path Covers of Temporal DAGs. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 38:1-38:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chakraborty_et_al:LIPIcs.MFCS.2024.38,
  author =	{Chakraborty, Dibyayan and Dailly, Antoine and Foucaud, Florent and Klasing, Ralf},
  title =	{{Algorithms and Complexity for Path Covers of Temporal DAGs}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{38:1--38:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.38},
  URN =		{urn:nbn:de:0030-drops-205940},
  doi =		{10.4230/LIPIcs.MFCS.2024.38},
  annote =	{Keywords: Temporal Graphs, Dilworth’s Theorem, DAGs, Path Cover, Temporally Disjoint Paths, Algorithms, Oriented Trees, Treewidth}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2024.84
Faster Approximation Schemes for (Constrained) k-Means with Outliers

Authors: Zhen Zhang, Junyu Huang, and Qilong Feng

Published in: LIPIcs, Volume 306, 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)

Abstract
Given a set of n points in ℝ^d and two positive integers k and m, the Euclidean k-means with outliers problem aims to remove at most m points, referred to as outliers, and minimize the k-means cost function for the remaining points. Developing algorithms for this problem remains an active area of research due to its prevalence in applications involving noisy data. In this paper, we give a (1+ε)-approximation algorithm that runs in n²d((k+m)ε^{-1})^O(kε^{-1}) time for the problem. When combined with a coreset construction method, the running time of the algorithm can be improved to be linear in n. For the case where k is a constant, this represents the first polynomial-time approximation scheme for the problem: Existing algorithms with the same approximation guarantee run in polynomial time only when both k and m are constants. Furthermore, our approach generalizes to variants of k-means with outliers incorporating additional constraints on instances, such as those related to capacities and fairness.
Cite as

Zhen Zhang, Junyu Huang, and Qilong Feng. Faster Approximation Schemes for (Constrained) k-Means with Outliers. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 84:1-84:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{zhang_et_al:LIPIcs.MFCS.2024.84,
  author =	{Zhang, Zhen and Huang, Junyu and Feng, Qilong},
  title =	{{Faster Approximation Schemes for (Constrained) k-Means with Outliers}},
  booktitle =	{49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024)},
  pages =	{84:1--84:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-335-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{306},
  editor =	{Kr\'{a}lovi\v{c}, Rastislav and Ku\v{c}era, Anton{\'\i}n},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2024.84},
  URN =		{urn:nbn:de:0030-drops-206408},
  doi =		{10.4230/LIPIcs.MFCS.2024.84},
  annote =	{Keywords: Approximation algorithms, clustering}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2024.98
Maximizing Miner Revenue in Transaction Fee Mechanism Design

Authors: Ke Wu, Elaine Shi, and Hao Chung

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
Transaction fee mechanism design is a new decentralized mechanism design problem where users bid for space on the blockchain. Several recent works showed that the transaction fee mechanism design fundamentally departs from classical mechanism design. They then systematically explored the mathematical landscape of this new decentralized mechanism design problem in two settings: in the plain setting where no cryptography is employed, and in a cryptography-assisted setting where the rules of the mechanism are enforced by a multi-party computation protocol. Unfortunately, in both settings, prior works showed that if we want the mechanism to incentivize honest behavior for both users as well as miners (possibly colluding with users), then the miner revenue has to be zero. Although adopting a relaxed, approximate notion of incentive compatibility gets around this zero miner-revenue limitation, the scaling of the miner revenue is nonetheless poor. In this paper, we show that if we make a mild reasonable-world assumption that there are sufficiently many honest users, we can circumvent the known limitations on miner revenue, and design auctions that generate asymptotically optimal miner revenue. We also systematically explore the mathematical landscape of transaction fee mechanism design under the new reasonable-world assumptions, and demonstrate how such assumptions can alter the feasibility and infeasibility landscape.
Cite as

Ke Wu, Elaine Shi, and Hao Chung. Maximizing Miner Revenue in Transaction Fee Mechanism Design. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 98:1-98:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{wu_et_al:LIPIcs.ITCS.2024.98,
  author =	{Wu, Ke and Shi, Elaine and Chung, Hao},
  title =	{{Maximizing Miner Revenue in Transaction Fee Mechanism Design}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{98:1--98:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.98},
  URN =		{urn:nbn:de:0030-drops-196266},
  doi =		{10.4230/LIPIcs.ITCS.2024.98},
  annote =	{Keywords: Blockchain, Mechanism Design, Transaction Fee}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.97
What Can Cryptography Do for Decentralized Mechanism Design?

Authors: Elaine Shi, Hao Chung, and Ke Wu

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
Recent works of Roughgarden (EC'21) and Chung and Shi (SODA'23) initiate the study of a new decentralized mechanism design problem called transaction fee mechanism design (TFM). Unlike the classical mechanism design literature, in the decentralized environment, even the auctioneer (i.e., the miner) can be a strategic player, and it can even collude with a subset of the users facilitated by binding side contracts. Chung and Shi showed two main impossibility results that rule out the existence of a dream TFM. First, any TFM that provides incentive compatibility for individual users and miner-user coalitions must always have zero miner revenue, no matter whether the block size is finite or infinite. Second, assuming finite block size, no non-trivial TFM can simultaneously provide incentive compatibility for any individual user and for any miner-user coalition. In this work, we explore what new models and meaningful relaxations can allow us to circumvent the impossibility results of Chung and Shi. Besides today’s model that does not employ cryptography, we introduce a new MPC-assisted model where the TFM is implemented by a joint multi-party computation (MPC) protocol among the miners. We prove several feasibility and infeasibility results for achieving strict and approximate incentive compatibility, respectively, in the plain model as well as the MPC-assisted model. We show that while cryptography is not a panacea, it indeed allows us to overcome some impossibility results pertaining to the plain model, leading to non-trivial mechanisms with useful guarantees that are otherwise impossible in the plain model. Our work is also the first to characterize the mathematical landscape of transaction fee mechanism design under approximate incentive compatibility, as well as in a cryptography-assisted model.
Cite as

Elaine Shi, Hao Chung, and Ke Wu. What Can Cryptography Do for Decentralized Mechanism Design?. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 97:1-97:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{shi_et_al:LIPIcs.ITCS.2023.97,
  author =	{Shi, Elaine and Chung, Hao and Wu, Ke},
  title =	{{What Can Cryptography Do for Decentralized Mechanism Design?}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{97:1--97:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.97},
  URN =		{urn:nbn:de:0030-drops-176005},
  doi =		{10.4230/LIPIcs.ITCS.2023.97},
  annote =	{Keywords: Transaction Fee Mechanism Design}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.8
Beyond Single-Deletion Correcting Codes: Substitutions and Transpositions

Authors: Ryan Gabrys, Venkatesan Guruswami, João Ribeiro, and Ke Wu

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Abstract
We consider the problem of designing low-redundancy codes in settings where one must correct deletions in conjunction with substitutions or adjacent transpositions; a combination of errors that is usually observed in DNA-based data storage. One of the most basic versions of this problem was settled more than 50 years ago by Levenshtein, who proved that binary Varshamov-Tenengolts codes correct one arbitrary edit error, i.e., one deletion or one substitution, with nearly optimal redundancy. However, this approach fails to extend to many simple and natural variations of the binary single-edit error setting. In this work, we make progress on the code design problem above in three such variations: - We construct linear-time encodable and decodable length-n non-binary codes correcting a single edit error with nearly optimal redundancy log n+O(log log n), providing an alternative simpler proof of a result by Cai, Chee, Gabrys, Kiah, and Nguyen (IEEE Trans. Inf. Theory 2021). This is achieved by employing what we call weighted VT sketches, a new notion that may be of independent interest. - We show the existence of a binary code correcting one deletion or one adjacent transposition with nearly optimal redundancy log n+O(log log n). - We construct linear-time encodable and list-decodable binary codes with list-size 2 for one deletion and one substitution with redundancy 4log n+O(log log n). This matches the existential bound up to an O(log log n) additive term.
Cite as

Ryan Gabrys, Venkatesan Guruswami, João Ribeiro, and Ke Wu. Beyond Single-Deletion Correcting Codes: Substitutions and Transpositions. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 8:1-8:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{gabrys_et_al:LIPIcs.APPROX/RANDOM.2022.8,
  author =	{Gabrys, Ryan and Guruswami, Venkatesan and Ribeiro, Jo\~{a}o and Wu, Ke},
  title =	{{Beyond Single-Deletion Correcting Codes: Substitutions and Transpositions}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{8:1--8:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.8},
  URN =		{urn:nbn:de:0030-drops-171302},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.8},
  annote =	{Keywords: Synchronization errors, Optimal redundancy, Explicit codes}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.37
Block Edit Errors with Transpositions: Deterministic Document Exchange Protocols and Almost Optimal Binary Codes

Authors: Kuan Cheng, Zhengzhong Jin, Xin Li, and Ke Wu

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
Document exchange and error correcting codes are two fundamental problems regarding communications. In the first problem, Alice and Bob each holds a string, and the goal is for Alice to send a short sketch to Bob, so that Bob can recover Alice’s string. In the second problem, Alice sends a message with some redundant information to Bob through a channel that can add adversarial errors, and the goal is for Bob to correctly recover the message despite the errors. In both problems, an upper bound is placed on the number of errors between the two strings or that the channel can add, and a major goal is to minimize the size of the sketch or the redundant information. In this paper we focus on deterministic document exchange protocols and binary error correcting codes. Both problems have been studied extensively. In the case of Hamming errors (i.e., bit substitutions) and bit erasures, we have explicit constructions with asymptotically optimal parameters. However, other error types are still rather poorly understood. In a recent work [Kuan Cheng et al., 2018], the authors constructed explicit deterministic document exchange protocols and binary error correcting codes for edit errors with almost optimal parameters. Unfortunately, the constructions in [Kuan Cheng et al., 2018] do not work for other common errors such as block transpositions. In this paper, we generalize the constructions in [Kuan Cheng et al., 2018] to handle a much larger class of errors. These include bursts of insertions and deletions, as well as block transpositions. Specifically, we consider document exchange and error correcting codes where the total number of block insertions, block deletions, and block transpositions is at most k <= alpha n/log n for some constant 0<alpha<1. In addition, the total number of bits inserted and deleted by the first two kinds of operations is at most t <= beta n for some constant 0<beta<1, where n is the length of Alice’s string or message. We construct explicit, deterministic document exchange protocols with sketch size O((k log n +t) log^2 n/{k log n + t}) and explicit binary error correcting code with O(k log n log log log n+t) redundant bits. As a comparison, the information-theoretic optimum for both problems is Theta(k log n+t). As far as we know, previously there are no known explicit deterministic document exchange protocols in this case, and the best known binary code needs Omega(n) redundant bits even to correct just one block transposition [L. J. Schulman and D. Zuckerman, 1999].
Cite as

Kuan Cheng, Zhengzhong Jin, Xin Li, and Ke Wu. Block Edit Errors with Transpositions: Deterministic Document Exchange Protocols and Almost Optimal Binary Codes. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 37:1-37:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{cheng_et_al:LIPIcs.ICALP.2019.37,
  author =	{Cheng, Kuan and Jin, Zhengzhong and Li, Xin and Wu, Ke},
  title =	{{Block Edit Errors with Transpositions: Deterministic Document Exchange Protocols and Almost Optimal Binary Codes}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{37:1--37:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.37},
  URN =		{urn:nbn:de:0030-drops-106137},
  doi =		{10.4230/LIPIcs.ICALP.2019.37},
  annote =	{Keywords: Deterministic document exchange, error correcting code, block edit error}
}
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