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Documents authored by Zhang, Xin

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Zhang, Xin

Document
DOI: 10.4230/LIPIcs.SWAT.2022.25
An Almost Optimal Algorithm for Unbounded Search with Noisy Information

Authors: Junhao Gan, Anthony Wirth, and Xin Zhang

Published in: LIPIcs, Volume 227, 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)

Abstract
Given a sequence of integers, 𝒮 = s₁, s₂,… in ascending order, called the search domain, and an integer t, called the target, the predecessor problem asks for the target index N such that s_N is the largest integer in 𝒮 satisfying s_N ≤ t. We consider solving the predecessor problem with the least number of queries to a binary comparison oracle. For each query index i, the oracle returns whether s_i ≤ t or s_i > t. In particular, we study the predecessor problem under the UnboundedNoisy setting, where (i) the search domain 𝒮 is unbounded, i.e., n = |𝒮| is unknown or infinite, and (ii) the binary comparison oracle is noisy. We denote the former setting by Unbounded and the latter by Noisy. In Noisy, the oracle, for each query, independently returns a wrong answer with a fixed constant probability 0 < p < 1/2. In particular, even for two queries on the same index i, the answers from the oracle may be different. Furthermore, with a noisy oracle, the goal is to correctly return the target index with probability at least 1- Q, where 0 < Q < 1/2 is the failure probability. Our first result is an algorithm, called NoS, for Noisy that improves the previous result by Ben-Or and Hassidim [FOCS 2008] from an expected query complexity bound to a worst-case bound. We also achieve an expected query complexity bound, whose leading term has an optimal constant factor, matching the lower bound of Ben-Or and Hassidim. Building on NoS, we propose our NoSU algorithm, which correctly solves the predecessor problem in the UnboundedNoisy setting. We prove that the query complexity of NoSU is ∑_{i = 1}^k (log^{(i)} N) /(1-H(p))+ o(log N) when log Q^{-1} ∈ o(log N), where N is the target index, k = log^* N, the iterated logarithm, and H(p) is the entropy function. This improves the previous bound of O(log (N/Q) / (1-H(p))) by reducing the coefficient of the leading term from a large constant to 1. Moreover, we show that this upper bound can be further improved to (1 - Q) ∑_{i = 1}^k (log^{(i)} N) /(1-H(p))+ o(log N) in expectation, with the constant in the leading term reduced to 1 - Q. Finally, we show that an information-theoretic lower bound on the expected query cost of the predecessor problem in UnboundedNoisy is at least (1 - Q)(∑_{i = 1}^k log^{(i)} N - 2k)/(1-H(p)) - 10. This implies the constant factor in the leading term of our expected upper bound is indeed optimal.
Cite as

Junhao Gan, Anthony Wirth, and Xin Zhang. An Almost Optimal Algorithm for Unbounded Search with Noisy Information. In 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 227, pp. 25:1-25:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{gan_et_al:LIPIcs.SWAT.2022.25,
  author =	{Gan, Junhao and Wirth, Anthony and Zhang, Xin},
  title =	{{An Almost Optimal Algorithm for Unbounded Search with Noisy Information}},
  booktitle =	{18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)},
  pages =	{25:1--25:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-236-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{227},
  editor =	{Czumaj, Artur and Xin, Qin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2022.25},
  URN =		{urn:nbn:de:0030-drops-161854},
  doi =		{10.4230/LIPIcs.SWAT.2022.25},
  annote =	{Keywords: Fault-tolerant search, noisy binary search, query complexity}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2020.39
Graph Clustering in All Parameter Regimes

Authors: Junhao Gan, David F. Gleich, Nate Veldt, Anthony Wirth, and Xin Zhang

Published in: LIPIcs, Volume 170, 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)

Abstract
Resolution parameters in graph clustering control the size and structure of clusters formed by solving a parametric objective function. Typically there is more than one meaningful way to cluster a graph, and solving the same objective function for different resolution parameters produces clusterings at different levels of granularity, each of which can be meaningful depending on the application. In this paper, we address the task of efficiently solving a parameterized graph clustering objective for all values of a resolution parameter. Specifically, we consider a new analysis-friendly objective we call LambdaPrime, involving a parameter λ ∈ (0,1). LambdaPrime is an adaptation of LambdaCC, a significant family of instances of the Correlation Clustering (minimization) problem. Indeed, LambdaPrime and LambdaCC are closely related to other parameterized clustering problems, such as parametric generalizations of modularity. They capture a number of specific clustering problems as special cases, including sparsest cut and cluster deletion. While previous work provides approximation results for a single value of the resolution parameter, we seek a set of approximately optimal clusterings for all values of λ in polynomial time. More specifically, we show that when a graph has m edges and n nodes, there exists a set of at most m clusterings such that, for every λ ∈ (0,1), the family contains an optimal solution to the LambdaPrime objective. This bound is tight on star graphs. We obtain a family of O(log n) clusterings by solving the parametric linear programming (LP) relaxation of LambdaPrime at O(log n) λ values, and rounding each LP solution using existing approximation algorithms. We prove that this is asymptotically tight: for a certain class of ring graphs, for all values of λ, Ω(log n) feasible solutions are required to provide a constant-factor approximation for the LambdaPrime LP relaxation. To minimize the size of the clustering family, we further propose an algorithm that yields a family of solutions of a size no more than twice of the minimum LP-approximating family.
Cite as

Junhao Gan, David F. Gleich, Nate Veldt, Anthony Wirth, and Xin Zhang. Graph Clustering in All Parameter Regimes. In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 39:1-39:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{gan_et_al:LIPIcs.MFCS.2020.39,
  author =	{Gan, Junhao and Gleich, David F. and Veldt, Nate and Wirth, Anthony and Zhang, Xin},
  title =	{{Graph Clustering in All Parameter Regimes}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{39:1--39:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.39},
  URN =		{urn:nbn:de:0030-drops-127065},
  doi =		{10.4230/LIPIcs.MFCS.2020.39},
  annote =	{Keywords: Graph Clustering, Algorithms, Parametric Linear Programming}
}

Zhang, Weixin

Document
Artifact
DOI: 10.4230/DARTS.7.2.11
Compositional Programming (Artifact)

Authors: Weixin Zhang, Yaozhu Sun, and Bruno C. d. S. Oliveira

Published in: DARTS, Volume 7, Issue 2, Special Issue of the 35th European Conference on Object-Oriented Programming (ECOOP 2021)

Abstract
Our main paper presents CP, a Compositional Programming language in a statically typed modular programming style. This artifact includes its Haskell implementation, together with several examples and three case studies written in CP. All code snippets in our main paper can be type-checked and run using our CP interpreter.
Cite as

Weixin Zhang, Yaozhu Sun, and Bruno C. d. S. Oliveira. Compositional Programming (Artifact). In Special Issue of the 35th European Conference on Object-Oriented Programming (ECOOP 2021). Dagstuhl Artifacts Series (DARTS), Volume 7, Issue 2, pp. 11:1-11:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@Article{zhang_et_al:DARTS.7.2.11,
  author =	{Zhang, Weixin and Sun, Yaozhu and Oliveira, Bruno C. d. S.},
  title =	{{Compositional Programming (Artifact)}},
  pages =	{11:1--11:2},
  journal =	{Dagstuhl Artifacts Series},
  ISSN =	{2509-8195},
  year =	{2021},
  volume =	{7},
  number =	{2},
  editor =	{Zhang, Weixin and Sun, Yaozhu and Oliveira, Bruno C. d. S.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DARTS.7.2.11},
  URN =		{urn:nbn:de:0030-drops-140356},
  doi =		{10.4230/DARTS.7.2.11},
  annote =	{Keywords: Expression Problem, Compositionality, Traits}
}
Document
DOI: 10.4230/DARTS.3.2.10
EVF: An Extensible and Expressive Visitor Framework for Programming Language Reuse (Artifact)

Authors: Weixin Zhang and Bruno C. d. S. Oliveira

Published in: DARTS, Volume 3, Issue 2, Special Issue of the 31st European Conference on Object-Oriented Programming (ECOOP 2017)

Abstract
This artifact is based on EVF, an extensible and expressive Java visitor framework. EVF aims at reducing the effort involved in creation and reuse of programming languages. EVF an annotation processor that automatically generate boilerplate ASTs and AST for a given an Object Algebra interface. This artifact contains source code of the case study on "Types and Programming Languages", illustrating how effective EVF is in modularizing programming languages. There is also a microbenchmark in the artifact that shows that EVF has reasonable performance with respect to traditional visitors.
Cite as

Weixin Zhang and Bruno C. d. S. Oliveira. EVF: An Extensible and Expressive Visitor Framework for Programming Language Reuse (Artifact). In Special Issue of the 31st European Conference on Object-Oriented Programming (ECOOP 2017). Dagstuhl Artifacts Series (DARTS), Volume 3, Issue 2, pp. 10:1-10:2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@Article{zhang_et_al:DARTS.3.2.10,
  author =	{Zhang, Weixin and Oliveira, Bruno C. d. S.},
  title =	{{EVF: An Extensible and Expressive Visitor Framework for Programming Language Reuse (Artifact)}},
  pages =	{10:1--10:2},
  journal =	{Dagstuhl Artifacts Series},
  ISSN =	{2509-8195},
  year =	{2017},
  volume =	{3},
  number =	{2},
  editor =	{Zhang, Weixin and Oliveira, Bruno C. d. S.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DARTS.3.2.10},
  URN =		{urn:nbn:de:0030-drops-72918},
  doi =		{10.4230/DARTS.3.2.10},
  annote =	{Keywords: visitor pattern, object algebras, modularity, domain-specific languages}
}
Document
DOI: 10.4230/LIPIcs.ECOOP.2017.29
EVF: An Extensible and Expressive Visitor Framework for Programming Language Reuse

Authors: Weixin Zhang and Bruno C. d. S. Oliveira

Published in: LIPIcs, Volume 74, 31st European Conference on Object-Oriented Programming (ECOOP 2017)

Abstract
Object Algebras are a design pattern that enables extensibility, modularity, and reuse in mainstream object-oriented languages such as Java. The theoretical foundations of Object Algebras are rooted on Church encodings of datatypes, which are in turn closely related to folds in functional programming. Unfortunately, it is well-known that certain programs are difficult to write, and may incur performance penalties when using Church-encodings/folds. This paper presents EVF: an extensible and expressive Java Visitor framework. The visitors supported by EVF generalize Object Algebras and enable writing programs using a generally recursive style rather than folds. The use of such generally recursive style enables users to more naturally write programs, which would otherwise require contrived workarounds using a fold-like structure. EVF visitors retain the type-safe extensibility of Object Algebras. The key advance in EVF is a novel technique to support extensible external visitors. Extensible external visitors are able to control traversals with direct access to the data structure being traversed, allowing dependent operations to be defined modularly without the need of advanced type system features. To make EVF practical, the framework employs annotations to automatically generate large amounts of boilerplate code related to visitors and traversals. To illustrate the applicability of EVF we conduct a case study, which refactors a large number of non-modular interpreters from the “Types and Programming Languages” (TAPL) book. Using EVF we are able to create a modular software product line (SPL) of the TAPL interpreters, enabling sharing of large portions of code and features. The TAPL software product line contains several modular operations, which would be non-trivial to define with standard Object Algebras.
Cite as

Weixin Zhang and Bruno C. d. S. Oliveira. EVF: An Extensible and Expressive Visitor Framework for Programming Language Reuse. In 31st European Conference on Object-Oriented Programming (ECOOP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 74, pp. 29:1-29:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{zhang_et_al:LIPIcs.ECOOP.2017.29,
  author =	{Zhang, Weixin and Oliveira, Bruno C. d. S.},
  title =	{{EVF: An Extensible and Expressive Visitor Framework for Programming Language Reuse}},
  booktitle =	{31st European Conference on Object-Oriented Programming (ECOOP 2017)},
  pages =	{29:1--29:32},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-035-4},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{74},
  editor =	{M\"{u}ller, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2017.29},
  URN =		{urn:nbn:de:0030-drops-72749},
  doi =		{10.4230/LIPIcs.ECOOP.2017.29},
  annote =	{Keywords: Visitor Pattern, Object Algebras, Modularity, Domain-Specific Languages}
}

Zhang, Louxin

Document
DOI: 10.4230/LIPIcs.WABI.2020.14
The Bourque Distances for Mutation Trees of Cancers

Authors: Katharina Jahn, Niko Beerenwinkel, and Louxin Zhang

Published in: LIPIcs, Volume 172, 20th International Workshop on Algorithms in Bioinformatics (WABI 2020)

Abstract
Mutation trees are rooted trees of arbitrary node degree in which each node is labeled with a mutation set. These trees, also referred to as clonal trees, are used in computational oncology to represent the mutational history of tumours. Classical tree metrics such as the popular Robinson - Foulds distance are of limited use for the comparison of mutation trees. One reason is that mutation trees inferred with different methods or for different patients often contain different sets of mutation labels. Here, we generalize the Robinson - Foulds distance into a set of distance metrics called Bourque distances for comparing mutation trees. A connection between the Robinson - Foulds distance and the nearest neighbor interchange distance is also presented.
Cite as

Katharina Jahn, Niko Beerenwinkel, and Louxin Zhang. The Bourque Distances for Mutation Trees of Cancers. In 20th International Workshop on Algorithms in Bioinformatics (WABI 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 172, pp. 14:1-14:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{jahn_et_al:LIPIcs.WABI.2020.14,
  author =	{Jahn, Katharina and Beerenwinkel, Niko and Zhang, Louxin},
  title =	{{The Bourque Distances for Mutation Trees of Cancers}},
  booktitle =	{20th International Workshop on Algorithms in Bioinformatics (WABI 2020)},
  pages =	{14:1--14:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-161-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{172},
  editor =	{Kingsford, Carl and Pisanti, Nadia},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2020.14},
  URN =		{urn:nbn:de:0030-drops-128039},
  doi =		{10.4230/LIPIcs.WABI.2020.14},
  annote =	{Keywords: mutation trees, clonal trees, tree distance, phylogenetic trees, tree metric, Robinson - Foulds distance, Bourque distance}
}

Zhang, Xindi

Document
Short Paper
DOI: 10.4230/LIPIcs.CP.2021.5
Improving Local Search for Structured SAT Formulas via Unit Propagation Based Construct and Cut Initialization (Short Paper)

Authors: Shaowei Cai, Chuan Luo, Xindi Zhang, and Jian Zhang

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

Abstract
This work is dedicated to improving local search solvers for the Boolean satisfiability (SAT) problem on structured instances. We propose a construct-and-cut (CnC) algorithm based on unit propagation, which is used to produce initial assignments for local search. We integrate our CnC initialization procedure within several state-of-the-art local search SAT solvers, and obtain the improved solvers. Experiments are carried out with a benchmark encoded from a spectrum repacking project as well as benchmarks encoded from two important mathematical problems namely Boolean Pythagorean Triple and Schur Number Five. The experiments show that the CnC initialization improves the local search solvers, leading to better performance than state-of-the-art SAT solvers based on Conflict Driven Clause Learning (CDCL) solvers.
Cite as

Shaowei Cai, Chuan Luo, Xindi Zhang, and Jian Zhang. Improving Local Search for Structured SAT Formulas via Unit Propagation Based Construct and Cut Initialization (Short Paper). In 27th International Conference on Principles and Practice of Constraint Programming (CP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 210, pp. 5:1-5:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{cai_et_al:LIPIcs.CP.2021.5,
  author =	{Cai, Shaowei and Luo, Chuan and Zhang, Xindi and Zhang, Jian},
  title =	{{Improving Local Search for Structured SAT Formulas via Unit Propagation Based Construct and Cut Initialization}},
  booktitle =	{27th International Conference on Principles and Practice of Constraint Programming (CP 2021)},
  pages =	{5:1--5:10},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CP.2021.5},
  URN =		{urn:nbn:de:0030-drops-152969},
  doi =		{10.4230/LIPIcs.CP.2021.5},
  annote =	{Keywords: Satisfiability, Local Search, Unit Propagation, Mathematical Problems}
}
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