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Documents authored by Liu, Tian

Found 4 Possible Name Variants:

Liu, Tian

Document
DOI: 10.4230/LIPIcs.ISAAC.2017.66
A (1.4 + epsilon)-Approximation Algorithm for the 2-Max-Duo Problem

Authors: Yao Xu, Yong Chen, Guohui Lin, Tian Liu, Taibo Luo, and Peng Zhang

Published in: LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017)

Abstract
The maximum duo-preservation string mapping (Max-Duo) problem is the complement of the well studied minimum common string partition (MCSP) problem, both of which have applications in many fields including text compression and bioinformatics. k-Max-Duo is the restricted version of Max-Duo, where every letter of the alphabet occurs at most k times in each of the strings, which is readily reduced into the well known maximum independent set (MIS) problem on a graph of maximum degree \Delta \le 6(k-1). In particular, 2-Max-Duo can then be approximated arbitrarily close to 1.8 using the state-of-the-art approximation algorithm for the MIS problem. 2-Max-Duo was proved APX-hard and very recently a (1.6 + \epsilon)-approximation was claimed, for any \epsilon > 0. In this paper, we present a vertex-degree reduction technique, based on which, we show that 2-Max-Duo can be approximated arbitrarily close to 1.4.
Cite as

Yao Xu, Yong Chen, Guohui Lin, Tian Liu, Taibo Luo, and Peng Zhang. A (1.4 + epsilon)-Approximation Algorithm for the 2-Max-Duo Problem. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 66:1-66:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{xu_et_al:LIPIcs.ISAAC.2017.66,
  author =	{Xu, Yao and Chen, Yong and Lin, Guohui and Liu, Tian and Luo, Taibo and Zhang, Peng},
  title =	{{A (1.4 + epsilon)-Approximation Algorithm for the 2-Max-Duo Problem}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{66:1--66:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Okamoto, Yoshio and Tokuyama, Takeshi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.66},
  URN =		{urn:nbn:de:0030-drops-82120},
  doi =		{10.4230/LIPIcs.ISAAC.2017.66},
  annote =	{Keywords: Approximation algorithm, duo-preservation string mapping, string partition, independent set}
}

Liu, Tian Rui

Document
DOI: 10.4230/LIPIcs.WABI.2019.19
Faster Pan-Genome Construction for Efficient Differentiation of Naturally Occurring and Engineered Plasmids with Plaster

Authors: Qi Wang, R. A. Leo Elworth, Tian Rui Liu, and Todd J. Treangen

Published in: LIPIcs, Volume 143, 19th International Workshop on Algorithms in Bioinformatics (WABI 2019)

Abstract
As sequence databases grow, characterizing diversity across extremely large collections of genomes requires the development of efficient methods that avoid costly all-vs-all comparisons [Marschall et al., 2018]. In addition to exponential increases in the amount of natural genomes being sequenced, improved techniques for the creation of human engineered sequences is ushering in a new wave of synthetic genome sequence databases that grow alongside naturally occurring genome databases. In this paper, we analyze the full diversity of available sequenced natural and synthetic plasmid genome sequences. This diversity can be represented by a data structure that captures all presently available nucleotide sequences, known as a pan-genome. In our case, we construct a single linear pan-genome nucleotide sequence that captures this diversity. To process such a large number of sequences, we introduce the plaster algorithmic pipeline. Using plaster we are able to construct the full synthetic plasmid pan-genome from 51,047 synthetic plasmid sequences as well as a natural pan-genome from 6,642 natural plasmid sequences. We demonstrate the efficacy of plaster by comparing its speed against another pan-genome construction method as well as demonstrating that nearly all plasmids align well to their corresponding pan-genome. Finally, we explore the use of pan-genome sequence alignment to distinguish between naturally occurring and synthetic plasmids. We believe this approach will lead to new techniques for rapid characterization of engineered plasmids. Applications for this work include detection of genome editing, tracking an unknown plasmid back to its lab of origin, and identifying naturally occurring sequences that may be of use to the synthetic biology community. The source code for fully reconstructing the natural and synthetic plasmid pan-genomes as well for plaster are publicly available and can be downloaded at https://gitlab.com/qiwangrice/plaster.git.
Cite as

Qi Wang, R. A. Leo Elworth, Tian Rui Liu, and Todd J. Treangen. Faster Pan-Genome Construction for Efficient Differentiation of Naturally Occurring and Engineered Plasmids with Plaster. In 19th International Workshop on Algorithms in Bioinformatics (WABI 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 143, pp. 19:1-19:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{wang_et_al:LIPIcs.WABI.2019.19,
  author =	{Wang, Qi and Elworth, R. A. Leo and Liu, Tian Rui and Treangen, Todd J.},
  title =	{{Faster Pan-Genome Construction for Efficient Differentiation of Naturally Occurring and Engineered Plasmids with Plaster}},
  booktitle =	{19th International Workshop on Algorithms in Bioinformatics (WABI 2019)},
  pages =	{19:1--19:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-123-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{143},
  editor =	{Huber, Katharina T. and Gusfield, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2019.19},
  URN =		{urn:nbn:de:0030-drops-110492},
  doi =		{10.4230/LIPIcs.WABI.2019.19},
  annote =	{Keywords: comparative genomics, sequence alignment, pan-genome, engineered plasmids}
}

Liu, Tianyu

Document
DOI: 10.4230/LIPIcs.CCC.2020.4
Approximability of the Eight-Vertex Model

Authors: Jin-Yi Cai, Tianyu Liu, Pinyan Lu, and Jing Yu

Published in: LIPIcs, Volume 169, 35th Computational Complexity Conference (CCC 2020)

Abstract
We initiate a study of the classification of approximation complexity of the eight-vertex model defined over 4-regular graphs. The eight-vertex model, together with its special case the six-vertex model, is one of the most extensively studied models in statistical physics, and can be stated as a problem of counting weighted orientations in graph theory. Our result concerns the approximability of the partition function on all 4-regular graphs, classified according to the parameters of the model. Our complexity results conform to the phase transition phenomenon from physics. We introduce a quantum decomposition of the eight-vertex model and prove a set of closure properties in various regions of the parameter space. Furthermore, we show that there are extra closure properties on 4-regular planar graphs. These regions of the parameter space are concordant with the phase transition threshold. Using these closure properties, we derive polynomial time approximation algorithms via Markov chain Monte Carlo. We also show that the eight-vertex model is NP-hard to approximate on the other side of the phase transition threshold.
Cite as

Jin-Yi Cai, Tianyu Liu, Pinyan Lu, and Jing Yu. Approximability of the Eight-Vertex Model. In 35th Computational Complexity Conference (CCC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 169, pp. 4:1-4:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{cai_et_al:LIPIcs.CCC.2020.4,
  author =	{Cai, Jin-Yi and Liu, Tianyu and Lu, Pinyan and Yu, Jing},
  title =	{{Approximability of the Eight-Vertex Model}},
  booktitle =	{35th Computational Complexity Conference (CCC 2020)},
  pages =	{4:1--4:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-156-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{169},
  editor =	{Saraf, Shubhangi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2020.4},
  URN =		{urn:nbn:de:0030-drops-125564},
  doi =		{10.4230/LIPIcs.CCC.2020.4},
  annote =	{Keywords: Approximate complexity, the eight-vertex model, Markov chain Monte Carlo}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.23
Counting Perfect Matchings and the Eight-Vertex Model

Authors: Jin-Yi Cai and Tianyu Liu

Published in: LIPIcs, Volume 168, 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)

Abstract
We study the approximation complexity of the partition function of the eight-vertex model on general 4-regular graphs. For the first time, we relate the approximability of the eight-vertex model to the complexity of approximately counting perfect matchings, a central open problem in this field. Our results extend those in [Jin-Yi Cai et al., 2018]. In a region of the parameter space where no previous approximation complexity was known, we show that approximating the partition function is at least as hard as approximately counting perfect matchings via approximation-preserving reductions. In another region of the parameter space which is larger than the region that is previously known to admit Fully Polynomial Randomized Approximation Scheme (FPRAS), we show that computing the partition function can be reduced to counting perfect matchings (which is valid for both exact and approximate counting). Moreover, we give a complete characterization of nonnegatively weighted (not necessarily planar) 4-ary matchgates, which has been open for several years. The key ingredient of our proof is a geometric lemma. We also identify a region of the parameter space where approximating the partition function on planar 4-regular graphs is feasible but on general 4-regular graphs is equivalent to approximately counting perfect matchings. To our best knowledge, these are the first problems that exhibit this dichotomic behavior between the planar and the nonplanar settings in approximate counting.
Cite as

Jin-Yi Cai and Tianyu Liu. Counting Perfect Matchings and the Eight-Vertex Model. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 23:1-23:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{cai_et_al:LIPIcs.ICALP.2020.23,
  author =	{Cai, Jin-Yi and Liu, Tianyu},
  title =	{{Counting Perfect Matchings and the Eight-Vertex Model}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{23:1--23:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-138-2},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{168},
  editor =	{Czumaj, Artur and Dawar, Anuj and Merelli, Emanuela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2020.23},
  URN =		{urn:nbn:de:0030-drops-124301},
  doi =		{10.4230/LIPIcs.ICALP.2020.23},
  annote =	{Keywords: Approximate complexity, the eight-vertex model, counting perfect matchings}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.52
Torpid Mixing of Markov Chains for the Six-vertex Model on Z^2

Authors: Tianyu Liu

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

Abstract
In this paper, we study the mixing time of two widely used Markov chain algorithms for the six-vertex model, Glauber dynamics and the directed-loop algorithm, on the square lattice Z^2. We prove, for the first time that, on finite regions of the square lattice these Markov chains are torpidly mixing under parameter settings in the ferroelectric phase and the anti-ferroelectric phase.
Cite as

Tianyu Liu. Torpid Mixing of Markov Chains for the Six-vertex Model on Z^2. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 52:1-52:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{liu:LIPIcs.APPROX-RANDOM.2018.52,
  author =	{Liu, Tianyu},
  title =	{{Torpid Mixing of Markov Chains for the Six-vertex Model on Z^2}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{52:1--52:15},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.52},
  URN =		{urn:nbn:de:0030-drops-94568},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.52},
  annote =	{Keywords: the six-vertex model, Eulerian orientations, square lattice, torpid mixing}
}

Liu, Tianren

Document
DOI: 10.4230/LIPIcs.ITCS.2020.86
On the Complexity of Decomposable Randomized Encodings, Or: How Friendly Can a Garbling-Friendly PRF Be?

Authors: Marshall Ball, Justin Holmgren, Yuval Ishai, Tianren Liu, and Tal Malkin

Published in: LIPIcs, Volume 151, 11th Innovations in Theoretical Computer Science Conference (ITCS 2020)

Abstract
Garbling schemes, also known as decomposable randomized encodings (DRE), have found many applications in cryptography. However, despite a large body of work on constructing such schemes, very little is known about their limitations. We initiate a systematic study of the DRE complexity of Boolean functions, obtaining the following main results: - Near-quadratic lower bounds. We use a classical lower bound technique of Nečiporuk [Dokl. Akad. Nauk SSSR '66] to show an Ω(n²/log n) lower bound on the size of any DRE for many explicit Boolean functions. For some natural functions, we obtain a corresponding upper bound, thus settling their DRE complexity up to polylogarithmic factors. Prior to our work, no superlinear lower bounds were known, even for non-explicit functions. - Garbling-friendly PRFs. We show that any exponentially secure PRF has Ω(n²/log n) DRE size, and present a plausible candidate for a "garbling-optimal" PRF that nearly meets this bound. This candidate establishes a barrier for super-quadratic DRE lower bounds via natural proof techniques. In contrast, we show a candidate for a weak PRF with near-exponential security and linear DRE size. Our results establish several qualitative separations, including near-quadratic separations between computational and information-theoretic DRE size of Boolean functions, and between DRE size of weak vs. strong PRFs.
Cite as

Marshall Ball, Justin Holmgren, Yuval Ishai, Tianren Liu, and Tal Malkin. On the Complexity of Decomposable Randomized Encodings, Or: How Friendly Can a Garbling-Friendly PRF Be?. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 86:1-86:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{ball_et_al:LIPIcs.ITCS.2020.86,
  author =	{Ball, Marshall and Holmgren, Justin and Ishai, Yuval and Liu, Tianren and Malkin, Tal},
  title =	{{On the Complexity of Decomposable Randomized Encodings, Or: How Friendly Can a Garbling-Friendly PRF Be?}},
  booktitle =	{11th Innovations in Theoretical Computer Science Conference (ITCS 2020)},
  pages =	{86:1--86:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-134-4},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{151},
  editor =	{Vidick, Thomas},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2020.86},
  URN =		{urn:nbn:de:0030-drops-117714},
  doi =		{10.4230/LIPIcs.ITCS.2020.86},
  annote =	{Keywords: Randomized Encoding, Private Simultaneous Messages}
}
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