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**Published in:** OASIcs, Volume 31, 1st French Singaporean Workshop on Formal Methods and Applications (FSFMA 2013)

Pervasive computing (PvC) systems are emerging as promising solutions to many practical problems, e.g., elderly care in home. However, such systems have long been developed without sufficient verification. Formal methods, eps. model checking are sound techniques for complex system analysis regarding correctness and reliability requirements. In this work, a formal modelling framework is proposed to model the general the system design (e.g., concurrent communications) and the critical environment inputs (e.g., human behaviours). Correctness requirements are specified in formal logics which are automatically verifiable against a system model. Furthermore, Markov Decision Processes (MDPs) are adopted for modelling probabilistic behaviours of PvC systems. Three problems are analysed which are overall reliability prediction based on component reliabilities, reliability distribution w.r.t., how reliable should the component be to reach an overall reliability requirement and sensitivity analysis w.r.t., how does a component reliability affect the overall reliability. Finally, the usefulness of our approaches are demonstrated on a smart healthcare system with unexpected bugs and system flaws exposed.

Yan Liu. Formal Modelling and Verification of Pervasive Computing Systems. In 1st French Singaporean Workshop on Formal Methods and Applications (FSFMA 2013). Open Access Series in Informatics (OASIcs), Volume 31, pp. 61-67, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

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@InProceedings{liu:OASIcs.FSFMA.2013.61, author = {Liu, Yan}, title = {{Formal Modelling and Verification of Pervasive Computing Systems}}, booktitle = {1st French Singaporean Workshop on Formal Methods and Applications (FSFMA 2013)}, pages = {61--67}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-939897-56-9}, ISSN = {2190-6807}, year = {2013}, volume = {31}, editor = {Choppy, Christine and Sun, Jun}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.FSFMA.2013.61}, URN = {urn:nbn:de:0030-drops-40892}, doi = {10.4230/OASIcs.FSFMA.2013.61}, annote = {Keywords: System Analysis, Formal Modelling and Verification, Reliability Analysis} }

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**Published in:** OASIcs, Volume 66, 2018 Imperial College Computing Student Workshop (ICCSW 2018)

We perform a detailed analysis of the C++ implementation of the Cluster Affiliation Model for Big Networks (BigClam) on the Stanford Network Analysis Project (SNAP). BigClam is a popular graph mining algorithm that is capable of finding overlapping communities in networks containing millions of nodes. Our analysis shows a key stage of the algorithm - determining if a node belongs to a community - dominates the runtime of the implementation, yet the computation is not parallelized. We show that by parallelizing computations across multiple threads using OpenMP we can speed up the algorithm by 5.3 times when solving large networks for communities, while preserving the integrity of the program and the result.

C. H. Bryan Liu and Benjamin Paul Chamberlain. Speeding Up BigClam Implementation on SNAP. In 2018 Imperial College Computing Student Workshop (ICCSW 2018). Open Access Series in Informatics (OASIcs), Volume 66, pp. 1:1-1:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{liu_et_al:OASIcs.ICCSW.2018.1, author = {Liu, C. H. Bryan and Chamberlain, Benjamin Paul}, title = {{Speeding Up BigClam Implementation on SNAP}}, booktitle = {2018 Imperial College Computing Student Workshop (ICCSW 2018)}, pages = {1:1--1:13}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-097-2}, ISSN = {2190-6807}, year = {2019}, volume = {66}, editor = {Pirovano, Edoardo and Graversen, Eva}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ICCSW.2018.1}, URN = {urn:nbn:de:0030-drops-101829}, doi = {10.4230/OASIcs.ICCSW.2018.1}, annote = {Keywords: BigClam, Community Detection, Parallelization, Networks} }

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**Published in:** Dagstuhl Seminar Proceedings, Volume 7281, Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs (2007)

To decide if the {sc parameterized feedback vertex set} problem
in directed graph is fixed-parameter tractable is a long standing
open problem. In this paper, we prove that the {sc parameterized
feedback vertex set} in directed graph is fixed-parameter
tractable and give the first FPT algorithm of running time
$O((1.48k)^kn^{O(1)})$ for it. As the {sc feedback arc set}
problem in directed graph can be transformed to a {sc
feedback vertex set} problem in directed graph,
hence we also show that the {sc parameterized feedback arc set}
problem can be solved in time of $O((1.48k)^kn^{O(1)})$.

Jianer Chen, Yang Liu, and Songiian Lu. Directed Feedback Vertex Set Problem is FPT. In Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs. Dagstuhl Seminar Proceedings, Volume 7281, pp. 1-17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2007)

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@InProceedings{chen_et_al:DagSemProc.07281.5, author = {Chen, Jianer and Liu, Yang and Lu, Songiian}, title = {{Directed Feedback Vertex Set Problem is FPT}}, booktitle = {Structure Theory and FPT Algorithmics for Graphs, Digraphs and Hypergraphs}, pages = {1--17}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2007}, volume = {7281}, editor = {Erik Demaine and Gregory Z. Gutin and Daniel Marx and Ulrike Stege}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.07281.5}, URN = {urn:nbn:de:0030-drops-12333}, doi = {10.4230/DagSemProc.07281.5}, annote = {Keywords: Directed feedback vertex set problem, parameterized algorithm,} }

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**Published in:** LIPIcs, Volume 50, 31st Conference on Computational Complexity (CCC 2016)

We consider the problem of finding a fully colored base triangle on the 2-dimensional Möbius band under the standard boundary condition, proving it to be PPA-complete. The proof is based on a construction for the DPZP problem, that of finding a zero point under a discrete version of continuity condition. It further derives PPA-completeness for versions on the Möbius band of other related discrete fixed point type problems, and a special version of the Tucker problem, finding an edge such that if the value of one end vertex is x, the other is -x, given a special anti-symmetry boundary condition.
More generally, this applies to other non-orientable spaces, including the projective plane and the Klein bottle. However, since those models have a closed boundary, we rely on a version of the PPA that states it as to find another fixed point giving a fixed point. This model also makes it presentationally simple for an extension to a high dimensional discrete fixed point problem on a non-orientable (nearly) hyper-grid with a constant side length.

Xiaotie Deng, Jack R. Edmonds, Zhe Feng, Zhengyang Liu, Qi Qi, and Zeying Xu. Understanding PPA-Completeness. In 31st Conference on Computational Complexity (CCC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 50, pp. 23:1-23:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{deng_et_al:LIPIcs.CCC.2016.23, author = {Deng, Xiaotie and Edmonds, Jack R. and Feng, Zhe and Liu, Zhengyang and Qi, Qi and Xu, Zeying}, title = {{Understanding PPA-Completeness}}, booktitle = {31st Conference on Computational Complexity (CCC 2016)}, pages = {23:1--23:25}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-008-8}, ISSN = {1868-8969}, year = {2016}, volume = {50}, editor = {Raz, Ran}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2016.23}, URN = {urn:nbn:de:0030-drops-58310}, doi = {10.4230/LIPIcs.CCC.2016.23}, annote = {Keywords: Fixed Point Computation, PPA-Completeness} }

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**Published in:** LIPIcs, Volume 64, 27th International Symposium on Algorithms and Computation (ISAAC 2016)

In this paper, we consider the distributed version of Support Vector Machine (SVM) under the coordinator model, where all input data (i.e., points in R^d space) of SVM are arbitrarily distributed among k nodes in some network with a coordinator which can communicate with all nodes. We investigate two variants of this problem, with and without outliers. For distributed SVM without outliers, we prove a lower bound on the communication complexity and give a distributed (1-epsilon)-approximation algorithm to reach this lower bound, where epsilon is a user specified small constant. For distributed SVM with outliers, we present a (1-epsilon)-approximation algorithm to explicitly remove the influence of outliers. Our algorithm is based on a deterministic distributed top t selection algorithm with communication complexity of O(k log (t)) in the coordinator model. Experimental results on benchmark datasets confirm the theoretical guarantees of our algorithms.

Yangwei Liu, Hu Ding, Ziyun Huang, and Jinhui Xu. Distributed and Robust Support Vector Machine. In 27th International Symposium on Algorithms and Computation (ISAAC 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 64, pp. 54:1-54:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{liu_et_al:LIPIcs.ISAAC.2016.54, author = {Liu, Yangwei and Ding, Hu and Huang, Ziyun and Xu, Jinhui}, title = {{Distributed and Robust Support Vector Machine}}, booktitle = {27th International Symposium on Algorithms and Computation (ISAAC 2016)}, pages = {54:1--54:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-026-2}, ISSN = {1868-8969}, year = {2016}, volume = {64}, editor = {Hong, Seok-Hee}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2016.54}, URN = {urn:nbn:de:0030-drops-68221}, doi = {10.4230/LIPIcs.ISAAC.2016.54}, annote = {Keywords: Distributed Algorithm, Communication Complexity, Robust Algorithm, SVM} }

Document

RANDOM

**Published in:** LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

We study parallel repetition of k-player games where the constraints satisfy the projection property. We prove exponential decay in the value of a parallel repetition of projection games with a value less than 1.

Amey Bhangale, Mark Braverman, Subhash Khot, Yang P. Liu, and Dor Minzer. Parallel Repetition of k-Player Projection Games. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 54:1-54:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bhangale_et_al:LIPIcs.APPROX/RANDOM.2024.54, author = {Bhangale, Amey and Braverman, Mark and Khot, Subhash and Liu, Yang P. and Minzer, Dor}, title = {{Parallel Repetition of k-Player Projection Games}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)}, pages = {54:1--54:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-348-5}, ISSN = {1868-8969}, year = {2024}, volume = {317}, editor = {Kumar, Amit and Ron-Zewi, Noga}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.54}, URN = {urn:nbn:de:0030-drops-210475}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2024.54}, annote = {Keywords: Parallel Repetition, Multiplayer games, Projection games} }

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

An important open question in the area of vertex sparsification is whether (1+ε)-approximate cut-preserving vertex sparsifiers with size close to the number of terminals exist. The work [Parinya Chalermsook et al., 2021] (SODA 2021) introduced a relaxation called connectivity-c mimicking networks, which asks to construct a vertex sparsifier which preserves connectivity among k terminals exactly up to the value of c, and showed applications to dynamic connectivity data structures and survivable network design. We show that connectivity-c mimicking networks with Õ(kc³) edges exist and can be constructed in polynomial time in n and c, improving over the results of [Parinya Chalermsook et al., 2021] for any c ≥ log n, whose runtimes depended exponentially on c.

Yang P. Liu. Vertex Sparsification for Edge Connectivity in Polynomial Time. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 83:1-83:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{liu:LIPIcs.ITCS.2023.83, author = {Liu, Yang P.}, title = {{Vertex Sparsification for Edge Connectivity in Polynomial Time}}, booktitle = {14th Innovations in Theoretical Computer Science Conference (ITCS 2023)}, pages = {83:1--83:15}, 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.2023.83}, URN = {urn:nbn:de:0030-drops-175863}, doi = {10.4230/LIPIcs.ITCS.2023.83}, annote = {Keywords: Vertex-sparsification, edge-connectivity, Gammoids} }

Document

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

In this note, we design a discrete random walk on the real line which takes steps 0,±1 (and one with steps in {±1,2}) where at least 96% of the signs are ±1 in expectation, and which has 𝒩(0,1) as a stationary distribution. As an immediate corollary, we obtain an online version of Banaszczyk’s discrepancy result for partial colorings and ±1,2 signings. Additionally, we recover linear time algorithms for logarithmic bounds for the Komlós conjecture in an oblivious online setting.

Yang P. Liu, Ashwin Sah, and Mehtaab Sawhney. A Gaussian Fixed Point Random Walk. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 101:1-101:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{liu_et_al:LIPIcs.ITCS.2022.101, author = {Liu, Yang P. and Sah, Ashwin and Sawhney, Mehtaab}, title = {{A Gaussian Fixed Point Random Walk}}, booktitle = {13th Innovations in Theoretical Computer Science Conference (ITCS 2022)}, pages = {101:1--101:10}, 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.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.101}, URN = {urn:nbn:de:0030-drops-156975}, doi = {10.4230/LIPIcs.ITCS.2022.101}, annote = {Keywords: Discrepancy, Partial Coloring} }

Document

**Published in:** LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Interactive proofs of proximity allow a sublinear-time verifier to check that a given input is close to the language, using a small amount of communication with a powerful (but untrusted) prover. In this work we consider two natural minimally interactive variants of such proofs systems, in which the prover only sends a single message, referred to as the proof.
The first variant, known as MA-proofs of Proximity (MAP), is fully non-interactive, meaning that the proof is a function of the input only. The second variant, known as AM-proofs of Proximity (AMP), allows the proof to additionally depend on the verifier's (entire) random string. The complexity of both MAPs and AMPs is the total number of bits that the verifier observes - namely, the sum of the proof length and query complexity.
Our main result is an exponential separation between the power of MAPs and AMPs. Specifically, we exhibit an explicit and natural property Pi that admits an AMP with complexity O(log n), whereas any MAP for Pi has complexity Omega~(n^{1/4}), where n denotes the length of the input in bits. Our MAP lower bound also yields an alternate proof, which is more general and arguably much simpler, for a recent result of Fischer et al. (ITCS, 2014).
Lastly, we also consider the notion of oblivious proofs of proximity, in which the verifier's queries are oblivious to the proof. In this setting we show that AMPs can only be quadratically stronger than MAPs. As an application of this result, we show an exponential separation between the power of public and private coin for oblivious interactive proofs of proximity.

Tom Gur, Yang P. Liu, and Ron D. Rothblum. An Exponential Separation Between MA and AM Proofs of Proximity. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 73:1-73:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{gur_et_al:LIPIcs.ICALP.2018.73, author = {Gur, Tom and Liu, Yang P. and Rothblum, Ron D.}, title = {{An Exponential Separation Between MA and AM Proofs of Proximity}}, booktitle = {45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)}, pages = {73:1--73:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-076-7}, ISSN = {1868-8969}, year = {2018}, volume = {107}, editor = {Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.73}, URN = {urn:nbn:de:0030-drops-90772}, doi = {10.4230/LIPIcs.ICALP.2018.73}, annote = {Keywords: Property testing, Probabilistic proof systems, Proofs of proximity} }

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