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**Published in:** LIPIcs, Volume 210, 27th International Conference on Principles and Practice of Constraint Programming (CP 2021)

Linear programming is a key technique for analysis and verification of numerical properties in programs, neural networks, etc. In particular, in program analysis based on abstract interpretation, many numerical abstract domains (such as Template Constraint Matrix, constraint-only polyhedra, etc.) are designed on top of linear programming. However, most state-of-the-art linear programming solvers use floating-point arithmetic in their implementations, leading to an approximate result that may be unsound. On the other hand, the solvers implemented using exact arithmetic are too costly. To this end, this paper focuses on advancing rigorous linear programming techniques based on floating-point arithmetic for building sound and efficient program analysis. Particularly, as a supplement to existing techniques, we present a novel rigorous linear programming technique based on Fourier-Mozkin elimination. On this basis, we implement a tool, namely, RlpSolver, combining our technique with existing techniques to lift effectiveness of rigorous linear programming in the scene of analysis and verification. Experimental results show that our technique is complementary to existing techniques, and their combination (RlpSolver) can achieve a better trade-off between cost and precision via heuristic rules.

Tengbin Wang, Liqian Chen, Taoqing Chen, Guangsheng Fan, and Ji Wang. Making Rigorous Linear Programming Practical for Program Analysis. In 27th International Conference on Principles and Practice of Constraint Programming (CP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 210, pp. 57:1-57:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)

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@InProceedings{wang_et_al:LIPIcs.CP.2021.57, author = {Wang, Tengbin and Chen, Liqian and Chen, Taoqing and Fan, Guangsheng and Wang, Ji}, title = {{Making Rigorous Linear Programming Practical for Program Analysis}}, booktitle = {27th International Conference on Principles and Practice of Constraint Programming (CP 2021)}, pages = {57:1--57:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-211-2}, ISSN = {1868-8969}, year = {2021}, volume = {210}, editor = {Michel, Laurent D.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2021.57}, URN = {urn:nbn:de:0030-drops-153486}, doi = {10.4230/LIPIcs.CP.2021.57}, annote = {Keywords: Linear programming, rigorous linear programming, abstract interpretation, program analysis, Fourier-Mozkin elimination} }

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

This paper presents the first dataset for eye segmentation in low resolution images. Although eye segmentation has long been a vital preprocessing step in biometric applications, this work is the first to focus on low resolutions image that can be expected from a consumer-grade camera under conventional human-computer interaction and / or video-chat scenarios. Existing eye datasets have multiple limitations, including: (a) datasets only contain high resolution images; (b) datasets did not include enough pose variations; (c) a utility landmark ground truth did not be provided; (d) high accurate pixel-level ground truths had not be given. Our dataset meets all the above conditions and requirements for different segmentation methods. Besides, a baseline experiment has been performed on our dataset to evaluate the performances of landmark models (Active Appearance Model, Ensemble Regression Tree and Supervised Descent Method) and deep semantic segmentation models (Atrous convolutional neural network with conditional random field). Since the novelty of our dataset is to segment the iris and the sclera areas, we evaluate above models on sclera and iris only respectively in order to indicate the feasibility on eye-partial segmentation tasks. In conclusion, based on our dataset, deep segmentation methods performed better in terms of IOU-based ROC curves and it showed potential abilities on low-resolution eye segmentation task.

Bingnan Luo, Jie Shen, Yujiang Wang, and Maja Pantic. The iBUG Eye Segmentation Dataset. In 2018 Imperial College Computing Student Workshop (ICCSW 2018). Open Access Series in Informatics (OASIcs), Volume 66, pp. 7:1-7:9, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{luo_et_al:OASIcs.ICCSW.2018.7, author = {Luo, Bingnan and Shen, Jie and Wang, Yujiang and Pantic, Maja}, title = {{The iBUG Eye Segmentation Dataset}}, booktitle = {2018 Imperial College Computing Student Workshop (ICCSW 2018)}, pages = {7:1--7:9}, 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.2018.7}, URN = {urn:nbn:de:0030-drops-101883}, doi = {10.4230/OASIcs.ICCSW.2018.7}, annote = {Keywords: dataset, eye, segmentation, landmark, pixel-level} }

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**Published in:** LIPIcs, Volume 9, 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)

The visibility representation (VR for short) is a classical representation of plane graphs. It has various applications and has been extensively studied. A main focus of the study is to minimize the size of the VR. It is known that there exists a plane graph $G$ with $n$ vertices where any VR of $G$ requires a grid of size at least (2/3)n x((4/3)n-3) (width x height). For upper bounds, it is known that every plane graph has a VR with grid size at most (2/3)n x (2n-5), and a VR with grid size at most (n-1) x (4/3)n. It has been an open problem to find a VR with both height and width simultaneously bounded away from the trivial upper bounds (namely with size at most c_h n x c_w n with c_h < 1 and c_w < 2$).
In this paper, we provide the first VR construction with this property. We prove that every plane graph of n vertices has a VR with height <= max{23/24 n + 2 Ceil(sqrt(n))+4, 11/12 n + 13} and width <= 23/12 n. The area (height x width) of our VR is larger than the area of some of previous results. However, bounding one dimension of the VR only requires finding a good st-orientation or a good dual s^*t^*-orientation of G. On the other hand, to bound both dimensions of VR simultaneously, one must find a good $st$-orientation and a good dual s^*t^*-orientation at the same time, and thus is far more challenging. Since st-orientation is a very useful concept in other applications, this result may be of independent interests.

Jiun-Jie Wang and Xin He. Compact Visibility Representation of Plane Graphs. In 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 9, pp. 141-152, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2011)

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@InProceedings{wang_et_al:LIPIcs.STACS.2011.141, author = {Wang, Jiun-Jie and He, Xin}, title = {{Compact Visibility Representation of Plane Graphs}}, booktitle = {28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)}, pages = {141--152}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-25-5}, ISSN = {1868-8969}, year = {2011}, volume = {9}, editor = {Schwentick, Thomas and D\"{u}rr, Christoph}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2011.141}, URN = {urn:nbn:de:0030-drops-30064}, doi = {10.4230/LIPIcs.STACS.2011.141}, annote = {Keywords: plane graph, plane triangulation, visibility representation, st-orientation} }

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**Published in:** LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018)

Recovering hidden graph-like structures from potentially noisy data is a fundamental task in modern data analysis. Recently, a persistence-guided discrete Morse-based framework to extract a geometric graph from low-dimensional data has become popular. However, to date, there is very limited theoretical understanding of this framework in terms of graph reconstruction. This paper makes a first step towards closing this gap. Specifically, first, leveraging existing theoretical understanding of persistence-guided discrete Morse cancellation, we provide a simplified version of the existing discrete Morse-based graph reconstruction algorithm. We then introduce a simple and natural noise model and show that the aforementioned framework can correctly reconstruct a graph under this noise model, in the sense that it has the same loop structure as the hidden ground-truth graph, and is also geometrically close. We also provide some experimental results for our simplified graph-reconstruction algorithm.

Tamal K. Dey, Jiayuan Wang, and Yusu Wang. Graph Reconstruction by Discrete Morse Theory. In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 31:1-31:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{dey_et_al:LIPIcs.SoCG.2018.31, author = {Dey, Tamal K. and Wang, Jiayuan and Wang, Yusu}, title = {{Graph Reconstruction by Discrete Morse Theory}}, booktitle = {34th International Symposium on Computational Geometry (SoCG 2018)}, pages = {31:1--31:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-066-8}, ISSN = {1868-8969}, year = {2018}, volume = {99}, editor = {Speckmann, Bettina and T\'{o}th, Csaba D.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.31}, URN = {urn:nbn:de:0030-drops-87443}, doi = {10.4230/LIPIcs.SoCG.2018.31}, annote = {Keywords: graph reconstruction, discrete Morse theory, persistence} }

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**Published in:** LIPIcs, Volume 77, 33rd International Symposium on Computational Geometry (SoCG 2017)

In many data analysis applications the following scenario is commonplace: we are given a point set that is supposed to sample a hidden ground truth K in a metric space, but it got corrupted with noise so that some of the data points lie far away from K creating outliers also termed as ambient noise. One of the main goals of denoising algorithms is to eliminate such noise so that the curated data lie within a bounded Hausdorff distance of K. Popular denoising approaches such as deconvolution and thresholding often require the user to set several parameters and/or to choose an appropriate noise model while guaranteeing only asymptotic convergence. Our goal is to lighten this burden as much as possible while ensuring theoretical guarantees in all cases.
Specifically, first, we propose a simple denoising algorithm that requires only a single parameter but provides a theoretical guarantee on the quality of the output on general input points. We argue that this single parameter cannot be avoided. We next present a simple algorithm that avoids even this parameter by paying for it with a slight strengthening of the sampling condition on the input points which is not unrealistic. We also provide some preliminary empirical evidence that our algorithms
are effective in practice.

Mickael Buchet, Tamal K. Dey, Jiayuan Wang, and Yusu Wang. Declutter and Resample: Towards Parameter Free Denoising. In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 23:1-23:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{buchet_et_al:LIPIcs.SoCG.2017.23, author = {Buchet, Mickael and Dey, Tamal K. and Wang, Jiayuan and Wang, Yusu}, title = {{Declutter and Resample: Towards Parameter Free Denoising}}, booktitle = {33rd International Symposium on Computational Geometry (SoCG 2017)}, pages = {23:1--23:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-038-5}, ISSN = {1868-8969}, year = {2017}, volume = {77}, editor = {Aronov, Boris and Katz, Matthew J.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.23}, URN = {urn:nbn:de:0030-drops-72133}, doi = {10.4230/LIPIcs.SoCG.2017.23}, annote = {Keywords: denoising, parameter free, k-distance,compact sets} }

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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 241, 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)

When we bundle quantifiers and modalities together (as in ∃x□, ◇∀x etc.) in first-order modal logic (FOML), we get new logical operators whose combinations produce interesting bundled fragments of FOML. It is well-known that finding decidable fragments of FOML is hard, but existing work shows that certain bundled fragments are decidable [Anantha Padmanabha et al., 2018], without any restriction on the arity of predicates, the number of variables, or the modal scope. In this paper, we explore generalized bundles such as ∀x∀y□, ∀x∃y◇ etc., and map the terrain with regard to decidability, presenting both decidability and undecidability results. In particular, we propose the loosely bundled fragment, which is decidable over increasing domains and encompasses all known decidable bundled fragments.

Mo Liu, Anantha Padmanabha, R. Ramanujam, and Yanjing Wang. Generalized Bundled Fragments for First-Order Modal Logic. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 70:1-70:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{liu_et_al:LIPIcs.MFCS.2022.70, author = {Liu, Mo and Padmanabha, Anantha and Ramanujam, R. and Wang, Yanjing}, title = {{Generalized Bundled Fragments for First-Order Modal Logic}}, booktitle = {47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)}, pages = {70:1--70:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-256-3}, ISSN = {1868-8969}, year = {2022}, volume = {241}, editor = {Szeider, Stefan and Ganian, Robert and Silva, Alexandra}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2022.70}, URN = {urn:nbn:de:0030-drops-168684}, doi = {10.4230/LIPIcs.MFCS.2022.70}, annote = {Keywords: bundled fragments, first-order modal logic, decidability, tableaux} }

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**Published in:** LIPIcs, Volume 122, 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)

Quantified modal logic is notorious for being undecidable, with very few known decidable fragments such as the monodic ones. For instance, even the two-variable fragment over unary predicates is undecidable. In this paper, we study a particular fragment, namely the bundled fragment, where a first-order quantifier is always followed by a modality when occurring in the formula, inspired by the proposal of [Yanjing Wang, 2017] in the context of non-standard epistemic logics of know-what, know-how, know-why, and so on.
As always with quantified modal logics, it makes a significant difference whether the domain stays the same across possible worlds. In particular, we show that the predicate logic with the bundle "forall Box" alone is undecidable over constant domain interpretations, even with only monadic predicates, whereas having the "exists Box" bundle instead gives us a decidable logic. On the other hand, over increasing domain interpretations, we get decidability with both "forall Box" and "exists Box" bundles with unrestricted predicates, where we obtain tableau based procedures that run in PSPACE. We further show that the "exists Box" bundle cannot distinguish between constant domain and variable domain interpretations.

Anantha Padmanabha, R Ramanujam, and Yanjing Wang. Bundled Fragments of First-Order Modal Logic: (Un)Decidability. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 43:1-43:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)

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@InProceedings{padmanabha_et_al:LIPIcs.FSTTCS.2018.43, author = {Padmanabha, Anantha and Ramanujam, R and Wang, Yanjing}, title = {{Bundled Fragments of First-Order Modal Logic: (Un)Decidability}}, booktitle = {38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)}, pages = {43:1--43:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-093-4}, ISSN = {1868-8969}, year = {2018}, volume = {122}, editor = {Ganguly, Sumit and Pandya, Paritosh}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2018.43}, URN = {urn:nbn:de:0030-drops-99424}, doi = {10.4230/LIPIcs.FSTTCS.2018.43}, annote = {Keywords: First-order modal logic, decidability, bundled fragments} }

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**Published in:** LIPIcs, Volume 127, 22nd International Conference on Database Theory (ICDT 2019)

Given a database of vectors, a cosine threshold query returns all vectors in the database having cosine similarity to a query vector above a given threshold. These queries arise naturally in many applications, such as document retrieval, image search, and mass spectrometry. The present paper considers the efficient evaluation of such queries, providing novel optimality guarantees and exhibiting good performance on real datasets. We take as a starting point Fagin’s well-known Threshold Algorithm (TA), which can be used to answer cosine threshold queries as follows: an inverted index is first built from the database vectors during pre-processing; at query time, the algorithm traverses the index partially to gather a set of candidate vectors to be later verified against the similarity threshold. However, directly applying TA in its raw form misses significant optimization opportunities. Indeed, we first show that one can take advantage of the fact that the vectors can be assumed to be normalized, to obtain an improved, tight stopping condition for index traversal and to efficiently compute it incrementally. Then we show that one can take advantage of data skewness to obtain better traversal strategies. In particular, we show a novel traversal strategy that exploits a common data skewness condition which holds in multiple domains including mass spectrometry, documents, and image databases. We show that under the skewness assumption, the new traversal strategy has a strong, near-optimal performance guarantee. The techniques developed in the paper are quite general since they can be applied to a large class of similarity functions beyond cosine.

Yuliang Li, Jianguo Wang, Benjamin Pullman, Nuno Bandeira, and Yannis Papakonstantinou. Index-Based, High-Dimensional, Cosine Threshold Querying with Optimality Guarantees. In 22nd International Conference on Database Theory (ICDT 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 127, pp. 11:1-11:20, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{li_et_al:LIPIcs.ICDT.2019.11, author = {Li, Yuliang and Wang, Jianguo and Pullman, Benjamin and Bandeira, Nuno and Papakonstantinou, Yannis}, title = {{Index-Based, High-Dimensional, Cosine Threshold Querying with Optimality Guarantees}}, booktitle = {22nd International Conference on Database Theory (ICDT 2019)}, pages = {11:1--11:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-101-6}, ISSN = {1868-8969}, year = {2019}, volume = {127}, editor = {Barcelo, Pablo and Calautti, Marco}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2019.11}, URN = {urn:nbn:de:0030-drops-103135}, doi = {10.4230/LIPIcs.ICDT.2019.11}, annote = {Keywords: Vector databases, Similarity search, Cosine, Threshold Algorithm} }

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RANDOM

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

We study the problem of sampling almost uniform proper q-colourings in k-uniform simple hypergraphs with maximum degree Δ. For any δ > 0, if k ≥ 20(1+δ)/δ and q ≥ 100Δ^({2+δ}/{k-4/δ-4}), the running time of our algorithm is Õ(poly(Δ k)⋅ n^1.01), where n is the number of vertices. Our result requires fewer colours than previous results for general hypergraphs (Jain, Pham, and Vuong, 2021; He, Sun, and Wu, 2021), and does not require Ω(log n) colours unlike the work of Frieze and Anastos (2017).

Weiming Feng, Heng Guo, and Jiaheng Wang. Improved Bounds for Randomly Colouring Simple Hypergraphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 25:1-25:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

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@InProceedings{feng_et_al:LIPIcs.APPROX/RANDOM.2022.25, author = {Feng, Weiming and Guo, Heng and Wang, Jiaheng}, title = {{Improved Bounds for Randomly Colouring Simple Hypergraphs}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)}, pages = {25:1--25:17}, 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.2022.25}, URN = {urn:nbn:de:0030-drops-171477}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2022.25}, annote = {Keywords: Approximate counting, Markov chain, Mixing time, Hypergraph colouring} }

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Track A: Algorithms, Complexity and Games

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

Polynomial representations of Boolean functions over various rings such as ℤ and ℤ_m have been studied since Minsky and Papert (1969). From then on, they have been employed in a large variety of areas including communication complexity, circuit complexity, learning theory, coding theory and so on. For any integer m ≥ 2, each Boolean function has a unique multilinear polynomial representation over ring ℤ_m. The degree of such polynomial is called modulo-m degree, denoted as deg_m(⋅).
In this paper, we investigate the lower bound of modulo-m degree of Boolean functions. When m = p^k (k ≥ 1) for some prime p, we give a tight lower bound deg_m(f) ≥ k(p-1) for any non-degenerate function f:{0,1}ⁿ → {0,1}, provided that n is sufficient large. When m contains two different prime factors p and q, we give a nearly optimal lower bound for any symmetric function f:{0,1}ⁿ → {0,1} that deg_m(f) ≥ n/{2+1/(p-1)+1/(q-1)}.

Xiaoming Sun, Yuan Sun, Jiaheng Wang, Kewen Wu, Zhiyu Xia, and Yufan Zheng. On the Degree of Boolean Functions as Polynomials over ℤ_m. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 100:1-100:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{sun_et_al:LIPIcs.ICALP.2020.100, author = {Sun, Xiaoming and Sun, Yuan and Wang, Jiaheng and Wu, Kewen and Xia, Zhiyu and Zheng, Yufan}, title = {{On the Degree of Boolean Functions as Polynomials over \mathbb{Z}\underlinem}}, booktitle = {47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)}, pages = {100:1--100:19}, 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.2020.100}, URN = {urn:nbn:de:0030-drops-125070}, doi = {10.4230/LIPIcs.ICALP.2020.100}, annote = {Keywords: Boolean function, polynomial, modular degree, Ramsey theory} }

Document

**Published in:** LIPIcs, Volume 177, 11th International Conference on Geographic Information Science (GIScience 2021) - Part I (2020)

Social media platforms, such as Twitter, have been increasingly used by people during natural disasters to share information and request for help. Hurricane Harvey was a category 4 hurricane that devastated Houston, Texas, USA in August 2017 and caused catastrophic flooding in the Houston metropolitan area. Hurricane Harvey also witnessed the widespread use of social media by the general public in response to this major disaster, and geographic locations are key information pieces described in many of the social media messages. A geoparsing system, or a geoparser, can be utilized to automatically extract and locate the described locations, which can help first responders reach the people in need. While a number of geoparsers have already been developed, it is unclear how effective they are in recognizing and geo-locating the locations described by people during natural disasters. To fill this gap, this work seeks to understand how people describe locations during a natural disaster by analyzing a sample of tweets posted during Hurricane Harvey. We then identify the limitations of existing geoparsers in processing these tweets, and discuss possible approaches to overcoming these limitations.

Yingjie Hu and Jimin Wang. How Do People Describe Locations During a Natural Disaster: An Analysis of Tweets from Hurricane Harvey. In 11th International Conference on Geographic Information Science (GIScience 2021) - Part I. Leibniz International Proceedings in Informatics (LIPIcs), Volume 177, pp. 6:1-6:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)

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@InProceedings{hu_et_al:LIPIcs.GIScience.2021.I.6, author = {Hu, Yingjie and Wang, Jimin}, title = {{How Do People Describe Locations During a Natural Disaster: An Analysis of Tweets from Hurricane Harvey}}, booktitle = {11th International Conference on Geographic Information Science (GIScience 2021) - Part I}, pages = {6:1--6:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-166-5}, ISSN = {1868-8969}, year = {2020}, volume = {177}, editor = {Janowicz, Krzysztof and Verstegen, Judith A.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.GIScience.2021.I.6}, URN = {urn:nbn:de:0030-drops-130410}, doi = {10.4230/LIPIcs.GIScience.2021.I.6}, annote = {Keywords: Geoparsing, geographic informational retrieval, social media, tweet analysis, disaster response} }

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