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

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.

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} }

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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)

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:** OASIcs, Volume 64, Technical Communications of the 34th International Conference on Logic Programming (ICLP 2018)

This paper develops a logic programming language, ASP^EP, that extends answer set programming language with a new epistemic operator >~_x where x in {#,supseteq}. The operator are used between two literals in rules bodies, and thus allows for the representation of introspections of preferences in the presence of multiple belief sets: G >~_# F expresses that G is preferred to F by the cardinality of the sets, and G >~_supseteq F expresses G is preferred to F by the set-theoretic inclusion. We define the semantics of ASP^EP, explore the relation to the languages of strong introspections, and study the applications of ASP^EP by modeling the Monty Hall problem and the principle of majority.

Zhizheng Zhang. Introspecting Preferences in Answer Set Programming. In Technical Communications of the 34th International Conference on Logic Programming (ICLP 2018). Open Access Series in Informatics (OASIcs), Volume 64, pp. 3:1-3:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{zhang:OASIcs.ICLP.2018.3, author = {Zhang, Zhizheng}, title = {{Introspecting Preferences in Answer Set Programming}}, booktitle = {Technical Communications of the 34th International Conference on Logic Programming (ICLP 2018)}, pages = {3:1--3:13}, series = {Open Access Series in Informatics (OASIcs)}, ISBN = {978-3-95977-090-3}, ISSN = {2190-6807}, year = {2018}, volume = {64}, editor = {Dal Palu', Alessandro and Tarau, Paul and Saeedloei, Neda and Fodor, Paul}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.ICLP.2018.3}, URN = {urn:nbn:de:0030-drops-98694}, doi = {10.4230/OASIcs.ICLP.2018.3}, annote = {Keywords: Answer Set, Preference, Introspection} }

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**Published in:** LIPIcs, Volume 199, 2nd Conference on Information-Theoretic Cryptography (ITC 2021)

This article is motivated by the classical results from Shannon that put the simple and elegant one-time pad away from practice: key length has to be as large as message length and the same key could not be used more than once. In particular, we consider encryption algorithm to be defined relative to specific message distributions in order to trade for unconditional security. Such a notion named honey encryption (HE) was originally proposed for achieving best possible security for password based encryption where secrete key may have very small amount of entropy.
Exploring message distributions as in HE indeed helps circumvent the classical restrictions on secret keys.We give a new and very simple honey encryption scheme satisfying the unconditional semantic security (for the targeted message distribution) in the standard model (all previous constructions are in the random oracle model, even for message recovery security only). Our new construction can be paired with an extremely simple yet "tighter" analysis, while all previous analyses (even for message recovery security only) were fairly complicated and require stronger assumptions. We also show a concrete instantiation further enables the secret key to be used for encrypting multiple messages.

Xinze Li, Qiang Tang, and Zhenfeng Zhang. Fooling an Unbounded Adversary with a Short Key, Repeatedly: The Honey Encryption Perspective. In 2nd Conference on Information-Theoretic Cryptography (ITC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 199, pp. 23:1-23:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{li_et_al:LIPIcs.ITC.2021.23, author = {Li, Xinze and Tang, Qiang and Zhang, Zhenfeng}, title = {{Fooling an Unbounded Adversary with a Short Key, Repeatedly: The Honey Encryption Perspective}}, booktitle = {2nd Conference on Information-Theoretic Cryptography (ITC 2021)}, pages = {23:1--23:21}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-197-9}, ISSN = {1868-8969}, year = {2021}, volume = {199}, editor = {Tessaro, Stefano}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITC.2021.23}, URN = {urn:nbn:de:0030-drops-143425}, doi = {10.4230/LIPIcs.ITC.2021.23}, annote = {Keywords: unconditional security, information theoretic encryption, honey encryption} }