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**Published in:** LIPIcs, Volume 263, 37th European Conference on Object-Oriented Programming (ECOOP 2023)

Reliable storage systems must be crash consistent - guaranteed to recover to a consistent state after a crash. Crash consistency is non-trivial as it requires maintaining complex invariants about persistent data structures in the presence of caching, reordering, and system failures. Current programming models offer little support for implementing crash consistency, forcing storage system developers to roll their own consistency mechanisms. Bugs in these mechanisms can lead to severe data loss for applications that rely on persistent storage.
This paper presents a new synthesis-aided programming model for building crash-consistent storage systems. In this approach, storage systems can assume an angelic crash-consistency model, where the underlying storage stack promises to resolve crashes in favor of consistency whenever possible. To realize this model, we introduce a new labeled writes interface for developers to identify their writes to disk, and develop a program synthesis tool, DepSynth, that generates dependency rules to enforce crash consistency over these labeled writes. We evaluate our model in a case study on a production storage system at Amazon Web Services. We find that DepSynth can automate crash consistency for this complex storage system, with similar results to existing expert-written code, and can automatically identify and correct consistency and performance issues.

Jacob Van Geffen, Xi Wang, Emina Torlak, and James Bornholt. Synthesis-Aided Crash Consistency for Storage Systems. In 37th European Conference on Object-Oriented Programming (ECOOP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 263, pp. 35:1-35:26, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{vangeffen_et_al:LIPIcs.ECOOP.2023.35, author = {Van Geffen, Jacob and Wang, Xi and Torlak, Emina and Bornholt, James}, title = {{Synthesis-Aided Crash Consistency for Storage Systems}}, booktitle = {37th European Conference on Object-Oriented Programming (ECOOP 2023)}, pages = {35:1--35:26}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-281-5}, ISSN = {1868-8969}, year = {2023}, volume = {263}, editor = {Ali, Karim and Salvaneschi, Guido}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2023.35}, URN = {urn:nbn:de:0030-drops-182285}, doi = {10.4230/LIPIcs.ECOOP.2023.35}, annote = {Keywords: program synthesis, crash consistency, file systems} }

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**Published in:** LIPIcs, Volume 32, 1st Summit on Advances in Programming Languages (SNAPL 2015)

We present a near-future research agenda for bringing a suite of modern programming-languages verification tools - specifically interactive theorem proving, solver-aided languages, and formally defined domain-specific languages - to the development of a specific safety-critical system, a radiotherapy medical device. We sketch how we believe recent programming-languages research advances can merge with existing best practices for safety-critical systems to increase system assurance and developer productivity. We motivate hypotheses central to our agenda: That we should start with a single specific system and that we need to integrate a variety of complementary verification and synthesis tools into system development.

Michael D. Ernst, Dan Grossman, Jon Jacky, Calvin Loncaric, Stuart Pernsteiner, Zachary Tatlock, Emina Torlak, and Xi Wang. Toward a Dependability Case Language and Workflow for a Radiation Therapy System. In 1st Summit on Advances in Programming Languages (SNAPL 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 32, pp. 103-112, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{ernst_et_al:LIPIcs.SNAPL.2015.103, author = {Ernst, Michael D. and Grossman, Dan and Jacky, Jon and Loncaric, Calvin and Pernsteiner, Stuart and Tatlock, Zachary and Torlak, Emina and Wang, Xi}, title = {{Toward a Dependability Case Language and Workflow for a Radiation Therapy System}}, booktitle = {1st Summit on Advances in Programming Languages (SNAPL 2015)}, pages = {103--112}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-80-4}, ISSN = {1868-8969}, year = {2015}, volume = {32}, editor = {Ball, Thomas and Bodík, Rastislav and Krishnamurthi, Shriram and Lerner, Benjamin S. and Morriset, Greg}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SNAPL.2015.103}, URN = {urn:nbn:de:0030-drops-50208}, doi = {10.4230/LIPIcs.SNAPL.2015.103}, annote = {Keywords: Synthesis, Proof Assistants, Verification, Dependability Cases, Domain Specific Languages, Radiation Therapy} }

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**Published in:** LIPIcs, Volume 272, 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)

We present a 9^k ⋅ n^O(1)-time algorithm for the proper circular-arc vertex deletion problem, resolving an open problem of van ’t Hof and Villanger [Algorithmica 2013] and Crespelle et al. [Computer Science Review 2023]. Our structural study also implies parameterized algorithms for modification problems toward proper Helly circular-arc graphs.

Yixin Cao, Hanchun Yuan, and Jianxin Wang. Modification Problems Toward Proper (Helly) Circular-Arc Graphs. In 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 272, pp. 31:1-31:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cao_et_al:LIPIcs.MFCS.2023.31, author = {Cao, Yixin and Yuan, Hanchun and Wang, Jianxin}, title = {{Modification Problems Toward Proper (Helly) Circular-Arc Graphs}}, booktitle = {48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)}, pages = {31:1--31:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-292-1}, ISSN = {1868-8969}, year = {2023}, volume = {272}, editor = {Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2023.31}, URN = {urn:nbn:de:0030-drops-185652}, doi = {10.4230/LIPIcs.MFCS.2023.31}, annote = {Keywords: proper (Helly) circular-arc graph, graph modification problem} }

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**Published in:** LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020)

In this paper, we present a framework for designing FPT approximation algorithms for many k-clustering problems. Our results are based on a new technique for reducing search spaces. A reduced search space is a small subset of the input data that has the guarantee of containing k clients close to the facilities opened in an optimal solution for any clustering problem we consider. We show, somewhat surprisingly, that greedily sampling O(k) clients yields the desired reduced search space, based on which we obtain FPT(k)-time algorithms with improved approximation guarantees for problems such as capacitated clustering, lower-bounded clustering, clustering with service installation costs, fault tolerant clustering, and priority clustering.

Qilong Feng, Zhen Zhang, Ziyun Huang, Jinhui Xu, and Jianxin Wang. A Unified Framework of FPT Approximation Algorithms for Clustering Problems. In 31st International Symposium on Algorithms and Computation (ISAAC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 181, pp. 5:1-5:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{feng_et_al:LIPIcs.ISAAC.2020.5, author = {Feng, Qilong and Zhang, Zhen and Huang, Ziyun and Xu, Jinhui and Wang, Jianxin}, title = {{A Unified Framework of FPT Approximation Algorithms for Clustering Problems}}, booktitle = {31st International Symposium on Algorithms and Computation (ISAAC 2020)}, pages = {5:1--5:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-173-3}, ISSN = {1868-8969}, year = {2020}, volume = {181}, editor = {Cao, Yixin and Cheng, Siu-Wing and Li, Minming}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.5}, URN = {urn:nbn:de:0030-drops-133495}, doi = {10.4230/LIPIcs.ISAAC.2020.5}, annote = {Keywords: clustering, approximation algorithms, fixed-parameter tractability} }

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**Published in:** LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

Graph search, the process of visiting vertices in a graph in a specific order, has demonstrated magical powers in many important algorithms. But a systematic study was only initiated by Corneil et al. a decade ago, and only by then we started to realize how little we understand it. Even the apparently naïve question "which vertex can be the last visited by a graph search algorithm," known as the end vertex problem, turns out to be quite elusive. We give a full picture of all maximum cardinality searches on chordal graphs, which implies a polynomial-time algorithm for the end vertex problem of maximum cardinality search. It is complemented by a proof of NP-completeness of the same problem on weakly chordal graphs. We also show linear-time algorithms for deciding end vertices of breadth-first searches on interval graphs, and end vertices of lexicographic depth-first searches on chordal graphs. Finally, we present 2^n * n^O(1)-time algorithms for deciding the end vertices of breadth-first searches, depth-first searches, and maximum cardinality searches on general graphs.

Yixin Cao, Zhifeng Wang, Guozhen Rong, and Jianxin Wang. Graph Searches and Their End Vertices. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 1:1-1:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{cao_et_al:LIPIcs.ISAAC.2019.1, author = {Cao, Yixin and Wang, Zhifeng and Rong, Guozhen and Wang, Jianxin}, title = {{Graph Searches and Their End Vertices}}, booktitle = {30th International Symposium on Algorithms and Computation (ISAAC 2019)}, pages = {1:1--1:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-130-6}, ISSN = {1868-8969}, year = {2019}, volume = {149}, editor = {Lu, Pinyan and Zhang, Guochuan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.1}, URN = {urn:nbn:de:0030-drops-114973}, doi = {10.4230/LIPIcs.ISAAC.2019.1}, annote = {Keywords: maximum cardinality search, (lexicographic) breadth-first search, (lexicographic) depth-first search, chordal graph, weighted clique graph, end vertex} }

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**Published in:** LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

In this paper, we study the following pattern search problem: Given a pair of point sets A and B in fixed dimensional space R^d, with |B| = n, |A| = m and n >= m, the pattern search problem is to find the translations T’s of A such that each of the identified translations induces a matching between T(A) and a subset B' of B with cost no more than some given threshold, where the cost is defined as the minimum bipartite matching cost of T(A) and B'. We present a novel algorithm to produce a small set of candidate translations for the pattern search problem. For any B' subseteq B with |B'| = |A|, there exists at least one translation T in the candidate set such that the minimum bipartite matching cost between T(A) and B' is no larger than (1+epsilon) times the minimum bipartite matching cost between A and B' under any translation (i.e., the optimal translational matching cost). We also show that there exists an alternative solution to this problem, which constructs a candidate set of size O(n log^2 n) in O(n log^2 n) time with high probability of success. As a by-product of our construction, we obtain a weak epsilon-net for hypercube ranges, which significantly improves the construction time and the size of the candidate set. Our technique can be applied to a number of applications, including the translational pattern matching problem.

Ziyun Huang, Qilong Feng, Jianxin Wang, and Jinhui Xu. Small Candidate Set for Translational Pattern Search. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{huang_et_al:LIPIcs.ISAAC.2019.26, author = {Huang, Ziyun and Feng, Qilong and Wang, Jianxin and Xu, Jinhui}, title = {{Small Candidate Set for Translational Pattern Search}}, booktitle = {30th International Symposium on Algorithms and Computation (ISAAC 2019)}, pages = {26:1--26:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-130-6}, ISSN = {1868-8969}, year = {2019}, volume = {149}, editor = {Lu, Pinyan and Zhang, Guochuan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.26}, URN = {urn:nbn:de:0030-drops-115222}, doi = {10.4230/LIPIcs.ISAAC.2019.26}, annote = {Keywords: Bipartite matching, Alignment, Discretization, Approximate algorithm} }

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**Published in:** LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

Clustering is a fundamental problem in unsupervised learning. In many real-world applications, the to-be-clustered data often contains various types of noises and thus needs to be removed from the learning process. To address this issue, we consider in this paper two variants of such clustering problems, called k-median with m outliers and k-means with m outliers. Existing techniques for both problems either incur relatively large approximation ratios or can only efficiently deal with a small number of outliers. In this paper, we present improved solution to each of them for the case where k is a fixed number and m could be quite large. Particularly, we gave the first PTAS for the k-median problem with outliers in Euclidean space R^d for possibly high m and d. Our algorithm runs in O(nd((1/epsilon)(k+m))^(k/epsilon)^O(1)) time, which considerably improves the previous result (with running time O(nd(m+k)^O(m+k) + (1/epsilon)k log n)^O(1))) given by [Feldman and Schulman, SODA 2012]. For the k-means with outliers problem, we introduce a (6+epsilon)-approximation algorithm for general metric space with running time O(n(beta (1/epsilon)(k+m))^k) for some constant beta>1. Our algorithm first uses the k-means++ technique to sample O((1/epsilon)(k+m)) points from input and then select the k centers from them. Compared to the more involving existing techniques, our algorithms are much simpler, i.e., using only random sampling, and achieving better performance ratios.

Qilong Feng, Zhen Zhang, Ziyun Huang, Jinhui Xu, and Jianxin Wang. Improved Algorithms for Clustering with Outliers. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 61:1-61:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{feng_et_al:LIPIcs.ISAAC.2019.61, author = {Feng, Qilong and Zhang, Zhen and Huang, Ziyun and Xu, Jinhui and Wang, Jianxin}, title = {{Improved Algorithms for Clustering with Outliers}}, booktitle = {30th International Symposium on Algorithms and Computation (ISAAC 2019)}, pages = {61:1--61:12}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-130-6}, ISSN = {1868-8969}, year = {2019}, volume = {149}, editor = {Lu, Pinyan and Zhang, Guochuan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.61}, URN = {urn:nbn:de:0030-drops-115573}, doi = {10.4230/LIPIcs.ISAAC.2019.61}, annote = {Keywords: Clustering with Outliers, Approximation, Random Sampling} }

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**Published in:** LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

König-Egerváry graphs form an important graph class which has been studied extensively in graph theory. Much attention has also been paid on König-Egerváry subgraphs and König-Egerváry graph modification problems. In this paper, we focus on one König-Egerváry subgraph problem, called the Maximum Edge Induced König Subgraph problem. By exploiting the classical Gallai-Edmonds decomposition, we establish connections between minimum vertex cover, Gallai-Edmonds decomposition structure, maximum matching, maximum bisection, and König-Egerváry subgraph structure. We obtain a new structural property of König-Egerváry subgraph: every graph G=(V, E) has an edge induced König-Egerváry subgraph with at least 2|E|/3 edges. Based on the new structural property proposed, an approximation algorithm with ratio 10/7 for the Maximum Edge Induced König Subgraph problem is presented, improving the current best ratio of 5/3. To the best of our knowledge, this paper is the first one establishing the connection between Gallai-Edmonds decomposition and König-Egerváry graphs. Using 2|E|/3 as a lower bound, we define the Edge Induced König Subgraph above lower bound problem, and give a kernel of at most 30k edges for the problem.

Qilong Feng, Guanlan Tan, Senmin Zhu, Bin Fu, and Jianxin Wang. New Algorithms for Edge Induced König-Egerváry Subgraph Based on Gallai-Edmonds Decomposition. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 31:1-31:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{feng_et_al:LIPIcs.ISAAC.2018.31, author = {Feng, Qilong and Tan, Guanlan and Zhu, Senmin and Fu, Bin and Wang, Jianxin}, title = {{New Algorithms for Edge Induced K\"{o}nig-Egerv\'{a}ry Subgraph Based on Gallai-Edmonds Decomposition}}, booktitle = {29th International Symposium on Algorithms and Computation (ISAAC 2018)}, pages = {31:1--31:12}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-094-1}, ISSN = {1868-8969}, year = {2018}, volume = {123}, editor = {Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.31}, URN = {urn:nbn:de:0030-drops-99790}, doi = {10.4230/LIPIcs.ISAAC.2018.31}, annote = {Keywords: K\"{o}nig-Egerv\'{a}ry graph, Gallai-Edmonds decomposition} }

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**Published in:** LIPIcs, Volume 83, 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)

Given a set \cal P of points in the Euclidean plane and two triangulations of \cal P, the flip distance between these two triangulations is the minimum number of flips required to transform one triangulation into the other. The Parameterized Flip Distance problem is to decide if the flip distance between two given triangulations is equal to a given integer k. The previous best FPT algorithm runs in time O^*(k\cdot c^k) (c\leq 2\times 14^11), where each step has fourteen possible choices, and the length of the action sequence is bounded by 11k. By applying the backtracking strategy and analyzing the underlying property of the flip sequence, each step of our algorithm has only five possible choices. Based on an auxiliary graph G, we prove that the length of the action sequence for our algorithm is bounded by 2|G|. As a result, we present an FPT algorithm running in time O^*(k\cdot 32^k).

Shaohua Li, Qilong Feng, Xiangzhong Meng, and Jianxin Wang. An Improved FPT Algorithm for the Flip Distance Problem. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 65:1-65:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{li_et_al:LIPIcs.MFCS.2017.65, author = {Li, Shaohua and Feng, Qilong and Meng, Xiangzhong and Wang, Jianxin}, title = {{An Improved FPT Algorithm for the Flip Distance Problem}}, booktitle = {42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)}, pages = {65:1--65:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-046-0}, ISSN = {1868-8969}, year = {2017}, volume = {83}, editor = {Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.65}, URN = {urn:nbn:de:0030-drops-81100}, doi = {10.4230/LIPIcs.MFCS.2017.65}, annote = {Keywords: triangulation, flip distance, FPT algorithm} }

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**Published in:** LIPIcs, Volume 163, 1st Conference on Information-Theoretic Cryptography (ITC 2020)

Leakage-resilient secret sharing has mostly been studied in the compartmentalized models, where a leakage oracle can arbitrarily leak bounded number of bits from all shares, provided that the oracle only has access to a bounded number of shares when the leakage is taking place. We start a systematic study of leakage-resilient secret sharing against global leakage, where the leakage oracle can access the full set of shares simultaneously, but the access is restricted to a special class of leakage functions. More concretely, the adversary can corrupt several players and obtain their shares, as well as applying a leakage function from a specific class to the full share vector. We explicitly construct such leakage-resilient secret sharing with respect to affine leakage functions and low-degree multi-variate polynomial leakage functions, respectively. For affine leakage functions, we obtain schemes with threshold access structure that are leakage-resilient as long as there is a substantial difference between the total amount of information obtained by the adversary, through corrupting individual players and leaking from the full share vector, and the amount that the reconstruction algorithm requires for reconstructing the secret. Furthermore, if we assume the adversary is non-adaptive, we can even make the secret length asymptotically equal to the difference, as the share length grows. Specifically, we have a threshold scheme with parameters similar to Shamir’s scheme and is leakage-resilient against affine leakage. For multi-variate polynomial leakage functions with degree bigger than one, our constructions here only yield ramp schemes that are leakage-resilient against such leakage. Finally, as a result of independent interest, we show that our approach to leakage-resilient secret sharing also yields a competitive scheme compared with the state-of-the-art construction in the compartmentalized models.

Fuchun Lin, Mahdi Cheraghchi, Venkatesan Guruswami, Reihaneh Safavi-Naini, and Huaxiong Wang. Leakage-Resilient Secret Sharing in Non-Compartmentalized Models. In 1st Conference on Information-Theoretic Cryptography (ITC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 163, pp. 7:1-7:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{lin_et_al:LIPIcs.ITC.2020.7, author = {Lin, Fuchun and Cheraghchi, Mahdi and Guruswami, Venkatesan and Safavi-Naini, Reihaneh and Wang, Huaxiong}, title = {{Leakage-Resilient Secret Sharing in Non-Compartmentalized Models}}, booktitle = {1st Conference on Information-Theoretic Cryptography (ITC 2020)}, pages = {7:1--7:24}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-151-1}, ISSN = {1868-8969}, year = {2020}, volume = {163}, editor = {Tauman Kalai, Yael and Smith, Adam D. and Wichs, Daniel}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2020.7}, URN = {urn:nbn:de:0030-drops-121124}, doi = {10.4230/LIPIcs.ITC.2020.7}, annote = {Keywords: Leakage-resilient cryptography, Secret sharing scheme, Randomness extractor} }

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**Published in:** LIPIcs, Volume 124, 10th Innovations in Theoretical Computer Science Conference (ITCS 2019)

Shamir's celebrated secret sharing scheme provides an efficient method for encoding a secret of arbitrary length l among any N <= 2^l players such that for a threshold parameter t, (i) the knowledge of any t shares does not reveal any information about the secret and, (ii) any choice of t+1 shares fully reveals the secret. It is known that any such threshold secret sharing scheme necessarily requires shares of length l, and in this sense Shamir's scheme is optimal. The more general notion of ramp schemes requires the reconstruction of secret from any t+g shares, for a positive integer gap parameter g. Ramp secret sharing scheme necessarily requires shares of length l/g. Other than the bound related to secret length l, the share lengths of ramp schemes can not go below a quantity that depends only on the gap ratio g/N.
In this work, we study secret sharing in the extremal case of bit-long shares and arbitrarily small gap ratio g/N, where standard ramp secret sharing becomes impossible. We show, however, that a slightly relaxed but equally effective notion of semantic security for the secret, and negligible reconstruction error probability, eliminate the impossibility. Moreover, we provide explicit constructions of such schemes. One of the consequences of our relaxation is that, unlike standard ramp schemes with perfect secrecy, adaptive and non-adaptive adversaries need different analysis and construction. For non-adaptive adversaries, we explicitly construct secret sharing schemes that provide secrecy against any tau fraction of observed shares, and reconstruction from any rho fraction of shares, for any choices of 0 <= tau < rho <= 1. Our construction achieves secret length N(rho-tau-o(1)), which we show to be optimal. For adaptive adversaries, we construct explicit schemes attaining a secret length Omega(N(rho-tau)). We discuss our results and open questions.

Fuchun Lin, Mahdi Cheraghchi, Venkatesan Guruswami, Reihaneh Safavi-Naini, and Huaxiong Wang. Secret Sharing with Binary Shares. In 10th Innovations in Theoretical Computer Science Conference (ITCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 124, pp. 53:1-53:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{lin_et_al:LIPIcs.ITCS.2019.53, author = {Lin, Fuchun and Cheraghchi, Mahdi and Guruswami, Venkatesan and Safavi-Naini, Reihaneh and Wang, Huaxiong}, title = {{Secret Sharing with Binary Shares}}, booktitle = {10th Innovations in Theoretical Computer Science Conference (ITCS 2019)}, pages = {53:1--53:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-095-8}, ISSN = {1868-8969}, year = {2019}, volume = {124}, editor = {Blum, Avrim}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2019.53}, URN = {urn:nbn:de:0030-drops-101461}, doi = {10.4230/LIPIcs.ITCS.2019.53}, annote = {Keywords: Secret sharing scheme, Wiretap channel} }

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**Published in:** LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

We study the problem of k-center clustering with outliers in arbitrary metrics and Euclidean space. Though a number of methods have been developed in the past decades, it is still quite challenging to design quality guaranteed algorithm with low complexity for this problem. Our idea is inspired by the greedy method, Gonzalez’s algorithm, for solving the problem of ordinary k-center clustering. Based on some novel observations, we show that this greedy strategy actually can handle k-center clustering with outliers efficiently, in terms of clustering quality and time complexity. We further show that the greedy approach yields small coreset for the problem in doubling metrics, so as to reduce the time complexity significantly. Our algorithms are easy to implement in practice. We test our method on both synthetic and real datasets. The experimental results suggest that our algorithms can achieve near optimal solutions and yield lower running times comparing with existing methods.

Hu Ding, Haikuo Yu, and Zixiu Wang. Greedy Strategy Works for k-Center Clustering with Outliers and Coreset Construction. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 40:1-40:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{ding_et_al:LIPIcs.ESA.2019.40, author = {Ding, Hu and Yu, Haikuo and Wang, Zixiu}, title = {{Greedy Strategy Works for k-Center Clustering with Outliers and Coreset Construction}}, booktitle = {27th Annual European Symposium on Algorithms (ESA 2019)}, pages = {40:1--40:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-124-5}, ISSN = {1868-8969}, year = {2019}, volume = {144}, editor = {Bender, Michael A. and Svensson, Ola and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.40}, URN = {urn:nbn:de:0030-drops-111613}, doi = {10.4230/LIPIcs.ESA.2019.40}, annote = {Keywords: k-center clustering, outliers, coreset, doubling metrics, random sampling} }

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

Let F be a multivariate function from a product set Σ^n to an Abelian group G. A k-partition of F with cost δ is a partition of the set of variables V into k non-empty subsets (X_1, ̇s, X_k) such that F(V) is δ-close to F_1(X_1)+ ̇s+F_k(X_k) for some F_1, ̇s, F_k with respect to a given error metric. We study algorithms for agnostically learning k partitions and testing k-partitionability over various groups and error metrics given query access to F. In particular we show that
1) Given a function that has a k-partition of cost δ, a partition of cost O(k n^2)(δ + ε) can be learned in time Õ(n^2 poly 1/ε) for any ε > 0. In contrast, for k = 2 and n = 3 learning a partition of cost δ + ε is NP-hard.
2) When F is real-valued and the error metric is the 2-norm, a 2-partition of cost √(δ^2 + ε) can be learned in time Õ(n^5/ε^2).
3) When F is Z_q-valued and the error metric is Hamming weight, k-partitionability is testable with one-sided error and O(kn^3/ε) non-adaptive queries. We also show that even two-sided testers require Ω(n) queries when k = 2.
This work was motivated by reinforcement learning control tasks in which the set of control variables can be partitioned. The partitioning reduces the task into multiple lower-dimensional ones that are relatively easier to learn. Our second algorithm empirically increases the scores attained over previous heuristic partitioning methods applied in this context.

Andrej Bogdanov and Baoxiang Wang. Learning and Testing Variable Partitions. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 151, pp. 37:1-37:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bogdanov_et_al:LIPIcs.ITCS.2020.37, author = {Bogdanov, Andrej and Wang, Baoxiang}, title = {{Learning and Testing Variable Partitions}}, booktitle = {11th Innovations in Theoretical Computer Science Conference (ITCS 2020)}, pages = {37:1--37:22}, 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.2020.37}, URN = {urn:nbn:de:0030-drops-117221}, doi = {10.4230/LIPIcs.ITCS.2020.37}, annote = {Keywords: partitioning, agnostic learning, property testing, sublinear-time algorithms, hypergraph cut, reinforcement learning} }

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**Published in:** LIPIcs, Volume 153, 23rd International Conference on Principles of Distributed Systems (OPODIS 2019)

Persistent memory makes it possible to recover in-memory data structures following a failure instead of rebuilding them from state saved in slow secondary storage. Implementing such recoverable data structures correctly is challenging as their underlying algorithms must deal with both parallelism and failures, which makes them especially susceptible to programming errors. Traditional proofs of correctness should therefore be combined with other methods, such as model checking or software testing, to minimize the likelihood of uncaught defects. This research focuses specifically on the algorithmic principles of software testing, particularly linearizability analysis, for multi-word persistent synchronization primitives such as conditional swap operations. We describe an efficient decision procedure for linearizability in this context, and discuss its practical applications in detecting previously-unknown bugs in implementations of multi-word persistent primitives.

Diego Cepeda, Sakib Chowdhury, Nan Li, Raphael Lopez, Xinzhe Wang, and Wojciech Golab. Toward Linearizability Testing for Multi-Word Persistent Synchronization Primitives. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 19:1-19:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{cepeda_et_al:LIPIcs.OPODIS.2019.19, author = {Cepeda, Diego and Chowdhury, Sakib and Li, Nan and Lopez, Raphael and Wang, Xinzhe and Golab, Wojciech}, title = {{Toward Linearizability Testing for Multi-Word Persistent Synchronization Primitives}}, booktitle = {23rd International Conference on Principles of Distributed Systems (OPODIS 2019)}, pages = {19:1--19:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-133-7}, ISSN = {1868-8969}, year = {2020}, volume = {153}, editor = {Felber, Pascal and Friedman, Roy and Gilbert, Seth and Miller, Avery}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2019.19}, URN = {urn:nbn:de:0030-drops-118050}, doi = {10.4230/LIPIcs.OPODIS.2019.19}, annote = {Keywords: Shared memory, persistent memory, synchronization, multi-word primitives, concurrency, correctness, software testing} }

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**Published in:** LIPIcs, Volume 184, 24th International Conference on Principles of Distributed Systems (OPODIS 2020)

In distributed systems, a group of learners achieve consensus when, by observing the output of some acceptors, they all arrive at the same value. Consensus is crucial for ordering transactions in failure-tolerant systems. Traditional consensus algorithms are homogeneous in three ways:
- all learners are treated equally,
- all acceptors are treated equally, and
- all failures are treated equally. These assumptions, however, are unsuitable for cross-domain applications, including blockchains, where not all acceptors are equally trustworthy, and not all learners have the same assumptions and priorities. We present the first consensus algorithm to be heterogeneous in all three respects. Learners set their own mixed failure tolerances over differently trusted sets of acceptors. We express these assumptions in a novel Learner Graph, and demonstrate sufficient conditions for consensus.
We present Heterogeneous Paxos, an extension of Byzantine Paxos. Heterogeneous Paxos achieves consensus for any viable Learner Graph in best-case three message sends, which is optimal. We present a proof-of-concept implementation and demonstrate how tailoring for heterogeneous scenarios can save resources and reduce latency.

Isaac Sheff, Xinwen Wang, Robbert van Renesse, and Andrew C. Myers. Heterogeneous Paxos. In 24th International Conference on Principles of Distributed Systems (OPODIS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 184, pp. 5:1-5:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{sheff_et_al:LIPIcs.OPODIS.2020.5, author = {Sheff, Isaac and Wang, Xinwen and van Renesse, Robbert and Myers, Andrew C.}, title = {{Heterogeneous Paxos}}, booktitle = {24th International Conference on Principles of Distributed Systems (OPODIS 2020)}, pages = {5:1--5:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-176-4}, ISSN = {1868-8969}, year = {2021}, volume = {184}, editor = {Bramas, Quentin and Oshman, Rotem and Romano, Paolo}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2020.5}, URN = {urn:nbn:de:0030-drops-134909}, doi = {10.4230/LIPIcs.OPODIS.2020.5}, annote = {Keywords: Consensus, Trust, Heterogeneous Trust} }

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