14 Search Results for "Wu, Chen"

Document
DOI: 10.4230/LIPIcs.ITCS.2024.29
Recursive Error Reduction for Regular Branching Programs

Authors: Eshan Chattopadhyay and Jyun-Jie Liao

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
In a recent work, Chen, Hoza, Lyu, Tal and Wu (FOCS 2023) showed an improved error reduction framework for the derandomization of regular read-once branching programs (ROBPs). Their result is based on a clever modification to the inverse Laplacian perspective of space-bounded derandomization, which was originally introduced by Ahmadinejad, Kelner, Murtagh, Peebles, Sidford and Vadhan (FOCS 2020). In this work, we give an alternative error reduction framework for regular ROBPs. Our new framework is based on a binary recursive formula from the work of Chattopadhyay and Liao (CCC 2020), that they used to construct weighted pseudorandom generators (WPRGs) for general ROBPs. Based on our new error reduction framework, we give alternative proofs to the following results for regular ROBPs of length n and width w, both of which were proved in the work of Chen et al. using their error reduction: - There is a WPRG with error ε that has seed length Õ(log(n)(√{log(1/ε)}+log(w))+log(1/ε)). - There is a (non-black-box) deterministic algorithm which estimates the expectation of any such program within error ±ε with space complexity Õ(log(nw)⋅log log(1/ε)). This was first proved in the work of Ahmadinejad et al., but the proof by Chen et al. is simpler. Because of the binary recursive nature of our new framework, both of our proofs are based on a straightforward induction that is arguably simpler than the Laplacian-based proof in the work of Chen et al. In fact, because of its simplicity, our proof of the second result directly gives a slightly stronger claim: our algorithm computes a ε-singular value approximation (a notion of approximation introduced in a recent work by Ahmadinejad, Peebles, Pyne, Sidford and Vadhan (FOCS 2023)) of the random walk matrix of the given ROBP in space Õ(log(nw)⋅log log(1/ε)). It is not clear how to get this stronger result from the previous proofs.
Cite as

Eshan Chattopadhyay and Jyun-Jie Liao. Recursive Error Reduction for Regular Branching Programs. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 29:1-29:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chattopadhyay_et_al:LIPIcs.ITCS.2024.29,
  author =	{Chattopadhyay, Eshan and Liao, Jyun-Jie},
  title =	{{Recursive Error Reduction for Regular Branching Programs}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{29:1--29:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.29},
  URN =		{urn:nbn:de:0030-drops-195571},
  doi =		{10.4230/LIPIcs.ITCS.2024.29},
  annote =	{Keywords: read-once branching program, regular branching program, weighted pseudorandom generator, derandomization}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2023.18
Distance Queries over Dynamic Interval Graphs

Authors: Jingbang Chen, Meng He, J. Ian Munro, Richard Peng, Kaiyu Wu, and Daniel J. Zhang

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

Abstract
We design the first dynamic distance oracles for interval graphs, which are intersection graphs of a set of intervals on the real line, and for proper interval graphs, which are intersection graphs of a set of intervals in which no interval is properly contained in another. For proper interval graphs, we design a linear space data structure which supports distance queries (computing the distance between two query vertices) and vertex insertion or deletion in O(lg n) worst-case time, where n is the number of vertices currently in G. Under incremental (insertion only) or decremental (deletion only) settings, we design linear space data structures that support distance queries in O(lg n) worst-case time and vertex insertion or deletion in O(lg n) amortized time, where n is the maximum number of vertices in the graph. Under fully dynamic settings, we design a data structure that represents an interval graph G in O(n) words of space to support distance queries in O(n lg n/S(n)) worst-case time and vertex insertion or deletion in O(S(n)+lg n) worst-case time, where n is the number of vertices currently in G and S(n) is an arbitrary function that satisfies S(n) = Ω(1) and S(n) = O(n). This implies an O(n)-word solution with O(√{nlg n})-time support for both distance queries and updates. All four data structures can answer shortest path queries by reporting the vertices in the shortest path between two query vertices in O(lg n) worst-case time per vertex. We also study the hardness of supporting distance queries under updates over an intersection graph of 3D axis-aligned line segments, which generalizes our problem to 3D. Finally, we solve the problem of computing the diameter of a dynamic connected interval graph.
Cite as

Jingbang Chen, Meng He, J. Ian Munro, Richard Peng, Kaiyu Wu, and Daniel J. Zhang. Distance Queries over Dynamic Interval Graphs. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 18:1-18:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chen_et_al:LIPIcs.ISAAC.2023.18,
  author =	{Chen, Jingbang and He, Meng and Munro, J. Ian and Peng, Richard and Wu, Kaiyu and Zhang, Daniel J.},
  title =	{{Distance Queries over Dynamic Interval Graphs}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{18:1--18:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.18},
  URN =		{urn:nbn:de:0030-drops-193207},
  doi =		{10.4230/LIPIcs.ISAAC.2023.18},
  annote =	{Keywords: interval graph, proper interval graph, intersection graph, geometric intersection graph, distance oracle, distance query, shortest path query, dynamic graph}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.38
Quantum Algorithms and Lower Bounds for Linear Regression with Norm Constraints

Authors: Yanlin Chen and Ronald de Wolf

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
Lasso and Ridge are important minimization problems in machine learning and statistics. They are versions of linear regression with squared loss where the vector θ ∈ ℝ^d of coefficients is constrained in either 𝓁₁-norm (for Lasso) or in 𝓁₂-norm (for Ridge). We study the complexity of quantum algorithms for finding ε-minimizers for these minimization problems. We show that for Lasso we can get a quadratic quantum speedup in terms of d by speeding up the cost-per-iteration of the Frank-Wolfe algorithm, while for Ridge the best quantum algorithms are linear in d, as are the best classical algorithms. As a byproduct of our quantum lower bound for Lasso, we also prove the first classical lower bound for Lasso that is tight up to polylog-factors.
Cite as

Yanlin Chen and Ronald de Wolf. Quantum Algorithms and Lower Bounds for Linear Regression with Norm Constraints. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 38:1-38:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2023.38,
  author =	{Chen, Yanlin and de Wolf, Ronald},
  title =	{{Quantum Algorithms and Lower Bounds for Linear Regression with Norm Constraints}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{38:1--38:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.38},
  URN =		{urn:nbn:de:0030-drops-180907},
  doi =		{10.4230/LIPIcs.ICALP.2023.38},
  annote =	{Keywords: Quantum algorithms, Regularized linear regression, Lasso, Ridge, Lower bounds}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.39
New PRGs for Unbounded-Width/Adaptive-Order Read-Once Branching Programs

Authors: Lijie Chen, Xin Lyu, Avishay Tal, and Hongxun Wu

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
We give the first pseudorandom generators with sub-linear seed length for the following variants of read-once branching programs (roBPs): 1) First, we show there is an explicit PRG of seed length O(log²(n/ε)log(n)) fooling unbounded-width unordered permutation branching programs with a single accept state, where n is the length of the program. Previously, [Lee-Pyne-Vadhan RANDOM 2022] gave a PRG with seed length Ω(n) for this class. For the ordered case, [Hoza-Pyne-Vadhan ITCS 2021] gave a PRG with seed length Õ(log n ⋅ log 1/ε). 2) Second, we show there is an explicit PRG fooling unbounded-width unordered regular branching programs with a single accept state with seed length Õ(√{n ⋅ log 1/ε} + log 1/ε). Previously, no non-trivial PRG (with seed length less than n) was known for this class (even in the ordered setting). For the ordered case, [Bogdanov-Hoza-Prakriya-Pyne CCC 2022] gave an HSG with seed length Õ(log n ⋅ log 1/ε). 3) Third, we show there is an explicit PRG fooling width w adaptive branching programs with seed length O(log n ⋅ log² (nw/ε)). Here, the branching program can choose an input bit to read depending on its current state, while it is guaranteed that on any input x ∈ {0,1}ⁿ, the branching program reads each input bit exactly once. Previously, no PRG with a non-trivial seed length is known for this class. We remark that there are some functions computable by constant-width adaptive branching programs but not by sub-exponential-width unordered branching programs. In terms of techniques, we indeed show that the Forbes-Kelly PRG (with the right parameters) from [Forbes-Kelly FOCS 2018] already fools all variants of roBPs above. Our proof adds several new ideas to the original analysis of Forbes-Kelly, and we believe it further demonstrates the versatility of the Forbes-Kelly PRG.
Cite as

Lijie Chen, Xin Lyu, Avishay Tal, and Hongxun Wu. New PRGs for Unbounded-Width/Adaptive-Order Read-Once Branching Programs. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 39:1-39:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2023.39,
  author =	{Chen, Lijie and Lyu, Xin and Tal, Avishay and Wu, Hongxun},
  title =	{{New PRGs for Unbounded-Width/Adaptive-Order Read-Once Branching Programs}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{39:1--39:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.39},
  URN =		{urn:nbn:de:0030-drops-180916},
  doi =		{10.4230/LIPIcs.ICALP.2023.39},
  annote =	{Keywords: pseudorandom generators, derandomization, read-once branching programs}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2023.99
Zero-Rate Thresholds and New Capacity Bounds for List-Decoding and List-Recovery

Authors: Nicolas Resch, Chen Yuan, and Yihan Zhang

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)

Abstract
In this work we consider the list-decodability and list-recoverability of arbitrary q-ary codes, for all integer values of q ≥ 2. A code is called (p,L)_q-list-decodable if every radius pn Hamming ball contains less than L codewords; (p,𝓁,L)_q-list-recoverability is a generalization where we place radius pn Hamming balls on every point of a combinatorial rectangle with side length 𝓁 and again stipulate that there be less than L codewords. Our main contribution is to precisely calculate the maximum value of p for which there exist infinite families of positive rate (p,𝓁,L)_q-list-recoverable codes, the quantity we call the zero-rate threshold. Denoting this value by p_*, we in fact show that codes correcting a p_*+ε fraction of errors must have size O_ε(1), i.e., independent of n. Such a result is typically referred to as a "Plotkin bound." To complement this, a standard random code with expurgation construction shows that there exist positive rate codes correcting a p_*-ε fraction of errors. We also follow a classical proof template (typically attributed to Elias and Bassalygo) to derive from the zero-rate threshold other tradeoffs between rate and decoding radius for list-decoding and list-recovery. Technically, proving the Plotkin bound boils down to demonstrating the Schur convexity of a certain function defined on the q-simplex as well as the convexity of a univariate function derived from it. We remark that an earlier argument claimed similar results for q-ary list-decoding; however, we point out that this earlier proof is flawed.
Cite as

Nicolas Resch, Chen Yuan, and Yihan Zhang. Zero-Rate Thresholds and New Capacity Bounds for List-Decoding and List-Recovery. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 99:1-99:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{resch_et_al:LIPIcs.ICALP.2023.99,
  author =	{Resch, Nicolas and Yuan, Chen and Zhang, Yihan},
  title =	{{Zero-Rate Thresholds and New Capacity Bounds for List-Decoding and List-Recovery}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{99:1--99:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.99},
  URN =		{urn:nbn:de:0030-drops-181518},
  doi =		{10.4230/LIPIcs.ICALP.2023.99},
  annote =	{Keywords: Coding theory, List-decoding, List-recovery, Zero-rate thresholds}
}
Document
PACE Solver Description
DOI: 10.4230/LIPIcs.IPEC.2022.29
PACE Solver Description: Hust-Solver - A Heuristic Algorithm of Directed Feedback Vertex Set Problem

Authors: YuMing Du, QingYun Zhang, JunZhou Xu, ShunGen Zhang, Chao Liao, ZhiHuai Chen, ZhiBo Sun, ZhouXing Su, JunWen Ding, Chen Wu, PinYan Lu, and ZhiPeng Lv

Published in: LIPIcs, Volume 249, 17th International Symposium on Parameterized and Exact Computation (IPEC 2022)

Abstract
A directed graph is formed by vertices and arcs from one vertex to another. The feedback vertex set problem (FVSP) consists in making a given directed graph acyclic by removing as few vertices as possible. In this write-up, we outline the core techniques used in the heuristic feedback vertex set algorithm, submitted to the heuristic track of the 2022 PACE challenge.
Cite as

YuMing Du, QingYun Zhang, JunZhou Xu, ShunGen Zhang, Chao Liao, ZhiHuai Chen, ZhiBo Sun, ZhouXing Su, JunWen Ding, Chen Wu, PinYan Lu, and ZhiPeng Lv. PACE Solver Description: Hust-Solver - A Heuristic Algorithm of Directed Feedback Vertex Set Problem. In 17th International Symposium on Parameterized and Exact Computation (IPEC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 249, pp. 29:1-29:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{du_et_al:LIPIcs.IPEC.2022.29,
  author =	{Du, YuMing and Zhang, QingYun and Xu, JunZhou and Zhang, ShunGen and Liao, Chao and Chen, ZhiHuai and Sun, ZhiBo and Su, ZhouXing and Ding, JunWen and Wu, Chen and Lu, PinYan and Lv, ZhiPeng},
  title =	{{PACE Solver Description: Hust-Solver - A Heuristic Algorithm of Directed Feedback Vertex Set Problem}},
  booktitle =	{17th International Symposium on Parameterized and Exact Computation (IPEC 2022)},
  pages =	{29:1--29:3},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-260-0},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{249},
  editor =	{Dell, Holger and Nederlof, Jesper},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2022.29},
  URN =		{urn:nbn:de:0030-drops-173855},
  doi =		{10.4230/LIPIcs.IPEC.2022.29},
  annote =	{Keywords: directed feedback vertex set, local search, simulated annealing, set covering}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.39
Approximation Algorithms for Interdiction Problem with Packing Constraints

Authors: Lin Chen, Xiaoyu Wu, and Guochuan Zhang

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
We study a bilevel optimization problem which is a zero-sum Stackelberg game. In this problem, there are two players, a leader and a follower, who pick items from a common set. Both the leader and the follower have their own (multi-dimensional) budgets, respectively. Each item is associated with a profit, which is the same to the leader and the follower, and will consume the leader’s (follower’s) budget if it is selected by the leader (follower). The leader and the follower will select items in a sequential way: First, the leader selects items within the leader’s budget. Then the follower selects items from the remaining items within the follower’s budget. The goal of the leader is to minimize the maximum profit that the follower can obtain. Let s_A and s_B be the dimension of the leader’s and follower’s budget, respectively. A special case of our problem is the bilevel knapsack problem studied by Caprara et al. [SIAM Journal on Optimization, 2014], where s_A = s_B = 1. We consider the general problem and obtain an (s_B+ε)-approximation algorithm when s_A and s_B are both constant. In particular, if s_B = 1, our algorithm implies a PTAS for the bilevel knapsack problem, which is the first 𝒪(1)-approximation algorithm. We also complement our result by showing that there does not exist any (4/3-ε)-approximation algorithm even if s_A = 1 and s_B = 2. We also consider a variant of our problem with resource augmentation when s_A and s_B are both part of the input. We obtain an 𝒪(1)-approximation algorithm with 𝒪(1)-resource augmentation, that is, we give an algorithm that returns a solution which exceeds the given leader’s budget by 𝒪(1) times, and the objective value achieved by the solution is 𝒪(1) times the optimal objective value that respects the leader’s budget.
Cite as

Lin Chen, Xiaoyu Wu, and Guochuan Zhang. Approximation Algorithms for Interdiction Problem with Packing Constraints. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 39:1-39:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{chen_et_al:LIPIcs.ICALP.2022.39,
  author =	{Chen, Lin and Wu, Xiaoyu and Zhang, Guochuan},
  title =	{{Approximation Algorithms for Interdiction Problem with Packing Constraints}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{39:1--39:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.39},
  URN =		{urn:nbn:de:0030-drops-163806},
  doi =		{10.4230/LIPIcs.ICALP.2022.39},
  annote =	{Keywords: Bilevel Integer Programming, Interdiction Constraints, Knapsack}
}
Document
DOI: 10.4230/LIPIcs.ITP.2021.4
A Graphical User Interface Framework for Formal Verification

Authors: Edward W. Ayers, Mateja Jamnik, and W. T. Gowers

Published in: LIPIcs, Volume 193, 12th International Conference on Interactive Theorem Proving (ITP 2021)

Abstract
We present the "ProofWidgets" framework for implementing general user interfaces (UIs) within an interactive theorem prover. The framework uses web technology and functional reactive programming, as well as metaprogramming features of advanced interactive theorem proving (ITP) systems to allow users to create arbitrary interactive UIs for representing the goal state. Users of the framework can create GUIs declaratively within the ITP’s metaprogramming language, without having to develop in multiple languages and without coordinated changes across multiple projects, which improves development time for new designs of UI. The ProofWidgets framework also allows UIs to make use of the full context of the theorem prover and the specialised libraries that ITPs offer, such as methods for dealing with expressions and tactics. The framework includes an extensible structured pretty-printing engine that enables advanced interaction with expressions such as interactive term rewriting. We exemplify the framework with an implementation for the https://leanprover-community.github.io. The framework is already in use by hundreds of contributors to the Lean mathematical library.
Cite as

Edward W. Ayers, Mateja Jamnik, and W. T. Gowers. A Graphical User Interface Framework for Formal Verification. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 4:1-4:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{ayers_et_al:LIPIcs.ITP.2021.4,
  author =	{Ayers, Edward W. and Jamnik, Mateja and Gowers, W. T.},
  title =	{{A Graphical User Interface Framework for Formal Verification}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{4:1--4:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.4},
  URN =		{urn:nbn:de:0030-drops-138996},
  doi =		{10.4230/LIPIcs.ITP.2021.4},
  annote =	{Keywords: User Interfaces, ITP}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.14
Online Makespan Minimization: The Power of Restart

Authors: Zhiyi Huang, Ning Kang, Zhihao Gavin Tang, Xiaowei Wu, and Yuhao Zhang

Published in: LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)

Abstract
We consider the online makespan minimization problem on identical machines. Chen and Vestjens (ORL 1997) show that the largest processing time first (LPT) algorithm is 1.5-competitive. For the special case of two machines, Noga and Seiden (TCS 2001) introduce the SLEEPY algorithm that achieves a competitive ratio of (5 - sqrt{5})/2 ~~ 1.382, matching the lower bound by Chen and Vestjens (ORL 1997). Furthermore, Noga and Seiden note that in many applications one can kill a job and restart it later, and they leave an open problem whether algorithms with restart can obtain better competitive ratios. We resolve this long-standing open problem on the positive end. Our algorithm has a natural rule for killing a processing job: a newly-arrived job replaces the smallest processing job if 1) the new job is larger than other pending jobs, 2) the new job is much larger than the processing one, and 3) the processed portion is small relative to the size of the new job. With appropriate choice of parameters, we show that our algorithm improves the 1.5 competitive ratio for the general case, and the 1.382 competitive ratio for the two-machine case.
Cite as

Zhiyi Huang, Ning Kang, Zhihao Gavin Tang, Xiaowei Wu, and Yuhao Zhang. Online Makespan Minimization: The Power of Restart. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 14:1-14:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{huang_et_al:LIPIcs.APPROX-RANDOM.2018.14,
  author =	{Huang, Zhiyi and Kang, Ning and Tang, Zhihao Gavin and Wu, Xiaowei and Zhang, Yuhao},
  title =	{{Online Makespan Minimization: The Power of Restart}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{14:1--14:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.14},
  URN =		{urn:nbn:de:0030-drops-94182},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.14},
  annote =	{Keywords: Online Scheduling, Makespan Minimization, Identical Machines}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2017.22
The Complexity of SORE-definability Problems

Authors: Ping Lu, Zhilin Wu, and Haiming Chen

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

Abstract
Single occurrence regular expressions (SORE) are a special kind of deterministic regular expressions, which are extensively used in the schema languages DTD and XSD for XML documents. In this paper, with motivations from the simplification of XML schemas, we consider the SORE-definability problem: Given a regular expression, decide whether it has an equivalent SORE. We investigate extensively the complexity of the SORE-definability problem: We consider both (standard) regular expressions and regular expressions with counting, and distinguish between the alphabets of size at least two and unary alphabets. In all cases, we obtain tight complexity bounds. In addition, we consider another variant of this problem, the bounded SORE-definability problem, which is to decide, given a regular expression E and a number M (encoded in unary or binary), whether there is an SORE, which is equivalent to E on the set of words of length at most M. We show that in several cases, there is an exponential decrease in the complexity when switching from the SORE-definability problem to its bounded variant.
Cite as

Ping Lu, Zhilin Wu, and Haiming Chen. The Complexity of SORE-definability Problems. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 22:1-22:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{lu_et_al:LIPIcs.MFCS.2017.22,
  author =	{Lu, Ping and Wu, Zhilin and Chen, Haiming},
  title =	{{The Complexity of SORE-definability Problems}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{22:1--22:15},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.22},
  URN =		{urn:nbn:de:0030-drops-80822},
  doi =		{10.4230/LIPIcs.MFCS.2017.22},
  annote =	{Keywords: Single occurrence regular expressions, Definability, Complexity}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2017.37
Tractability of Separation Logic with Inductive Definitions: Beyond Lists

Authors: Taolue Chen, Fu Song, and Zhilin Wu

Published in: LIPIcs, Volume 85, 28th International Conference on Concurrency Theory (CONCUR 2017)

Abstract
In 2011, Cook et al. showed that the satisfiability and entailment can be checked in polynomial time for a fragment of separation logic that allows for reasoning about programs with pointers and linked lists. In this paper, we investigate whether the tractability results can be extended to more expressive fragments of separation logic that allow defining data structures beyond linked lists. To this end, we introduce separation logic with a simply-nonlinear compositional inductive predicate where source, destination, and static parameters are identified explicitly (SLID[snc]). We show that if the inductive predicate has more than one source (destination) parameter, the satisfiability problem for SLID[snc] becomes intractable in general. This is exemplified by an inductive predicate for doubly linked list segments. By contrast, if the inductive predicate has only one source (destination) parameter, the satisfiability and entailment problems for SLID[snc] are tractable. In particular, the tractability results hold for inductive predicates that define list segments with tail pointers and trees with one hole.
Cite as

Taolue Chen, Fu Song, and Zhilin Wu. Tractability of Separation Logic with Inductive Definitions: Beyond Lists. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 37:1-37:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chen_et_al:LIPIcs.CONCUR.2017.37,
  author =	{Chen, Taolue and Song, Fu and Wu, Zhilin},
  title =	{{Tractability of Separation Logic with Inductive Definitions: Beyond Lists}},
  booktitle =	{28th International Conference on Concurrency Theory (CONCUR 2017)},
  pages =	{37:1--37:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-048-4},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{85},
  editor =	{Meyer, Roland and Nestmann, Uwe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2017.37},
  URN =		{urn:nbn:de:0030-drops-77826},
  doi =		{10.4230/LIPIcs.CONCUR.2017.37},
  annote =	{Keywords: Separation logic, Inductive definitions, Satisfiability, Entailment}
}
Document
Multimedia Contribution
DOI: 10.4230/LIPIcs.SoCG.2017.65
Cardiac Trabeculae Segmentation: an Application of Computational Topology (Multimedia Contribution)

Authors: Chao Chen, Dimitris Metaxas, Yusu Wang, and Pengxiang Wu

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

Abstract
In this video, we present a research project on cardiac trabeculae segmentation. Trabeculae are fine muscle columns within human ventricles whose both ends are attached to the wall. Extracting these structures are very challenging even with state-of-the-art image segmentation techniques. We observed that these structures form natural topological handles. Based on such observation, we developed a topological approach, which employs advanced computational topology methods and achieve high quality segmentation results.
Cite as

Chao Chen, Dimitris Metaxas, Yusu Wang, and Pengxiang Wu. Cardiac Trabeculae Segmentation: an Application of Computational Topology (Multimedia Contribution). In 33rd International Symposium on Computational Geometry (SoCG 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 77, pp. 65:1-65:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{chen_et_al:LIPIcs.SoCG.2017.65,
  author =	{Chen, Chao and Metaxas, Dimitris and Wang, Yusu and Wu, Pengxiang},
  title =	{{Cardiac Trabeculae Segmentation: an Application of Computational Topology}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{65:1--65:4},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2017.65},
  URN =		{urn:nbn:de:0030-drops-72429},
  doi =		{10.4230/LIPIcs.SoCG.2017.65},
  annote =	{Keywords: image segmentation, trabeculae, persistent homology, homology localization}
}
Document
DOI: 10.4230/LIPIcs.ESA.2016.3
Beating Ratio 0.5 for Weighted Oblivious Matching Problems

Authors: Melika Abolhassani, T.-H. Hubert Chan, Fei Chen, Hossein Esfandiari, MohammadTaghi Hajiaghayi, Mahini Hamid, and Xiaowei Wu

Published in: LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)

Abstract
We prove the first non-trivial performance ratios strictly above 0.5 for weighted versions of the oblivious matching problem. Even for the unweighted version, since Aronson, Dyer, Frieze, and Suen first proved a non-trivial ratio above 0.5 in the mid-1990s, during the next twenty years several attempts have been made to improve this ratio, until Chan, Chen, Wu and Zhao successfully achieved a significant ratio of 0.523 very recently (SODA 2014). To the best of our knowledge, our work is the first in the literature that considers the node-weighted and edge-weighted versions of the problem in arbitrary graphs (as opposed to bipartite graphs). (1) For arbitrary node weights, we prove that a weighted version of the Ranking algorithm has ratio strictly above 0.5. We have discovered a new structural property of the ranking algorithm: if a node has two unmatched neighbors at the end of algorithm, then it will still be matched even when its rank is demoted to the bottom. This property allows us to form LP constraints for both the node-weighted and the unweighted oblivious matching problems. As a result, we prove that the ratio for the node-weighted case is at least 0.501512. Interestingly via the structural property, we can also improve slightly the ratio for the unweighted case to 0.526823 (from the previous best 0.523166 in SODA 2014). (2) For a bounded number of distinct edge weights, we show that ratio strictly above 0.5 can be achieved by partitioning edges carefully according to the weights, and running the (unweighted) Ranking algorithm on each part. Our analysis is based on a new primal-dual framework known as \emph{matching coverage}, in which dual feasibility is bypassed. Instead, only dual constraints corresponding to edges in an optimal matching are satisfied. Using this framework we also design and analyze an algorithm for the edge-weighted online bipartite matching problem with free disposal. We prove that for the case of bounded online degrees, the ratio is strictly above 0.5.
Cite as

Melika Abolhassani, T.-H. Hubert Chan, Fei Chen, Hossein Esfandiari, MohammadTaghi Hajiaghayi, Mahini Hamid, and Xiaowei Wu. Beating Ratio 0.5 for Weighted Oblivious Matching Problems. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 3:1-3:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{abolhassani_et_al:LIPIcs.ESA.2016.3,
  author =	{Abolhassani, Melika and Chan, T.-H. Hubert and Chen, Fei and Esfandiari, Hossein and Hajiaghayi, MohammadTaghi and Hamid, Mahini and Wu, Xiaowei},
  title =	{{Beating Ratio 0.5 for Weighted Oblivious Matching Problems}},
  booktitle =	{24th Annual European Symposium on Algorithms (ESA 2016)},
  pages =	{3:1--3:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-015-6},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{57},
  editor =	{Sankowski, Piotr and Zaroliagis, Christos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.3},
  URN =		{urn:nbn:de:0030-drops-63443},
  doi =		{10.4230/LIPIcs.ESA.2016.3},
  annote =	{Keywords: Weighted matching, oblivious algorithms, Ranking, linear programming}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2015.254
On the Satisfiability of Indexed Linear Temporal Logics

Authors: Taolue Chen, Fu Song, and Zhilin Wu

Published in: LIPIcs, Volume 42, 26th International Conference on Concurrency Theory (CONCUR 2015)

Abstract
Indexed Linear Temporal Logics (ILTL) are an extension of standard Linear Temporal Logics (LTL) with quantifications over index variables which range over a set of process identifiers. ILTL has been widely used in specifying and verifying properties of parameterised systems, e.g., in parameterised model checking of concurrent processes. However there is still a lack of theoretical investigations on properties of ILTL, compared to the well-studied LTL. In this paper, we start to narrow this gap, focusing on the satisfiability problem, i.e., to decide whether a model exists for a given formula. This problem is in general undecidable. Various fragments of ILTL have been considered in the literature typically in parameterised model checking, e.g., ILTL formulae in prenex normal form, or containing only non-nested quantifiers, or admitting limited temporal operators. We carry out a thorough study on the decidability and complexity of the satisfiability problem for these fragments. Namely, for each fragment, we either show that it is undecidable, or otherwise provide tight complexity bounds.
Cite as

Taolue Chen, Fu Song, and Zhilin Wu. On the Satisfiability of Indexed Linear Temporal Logics. In 26th International Conference on Concurrency Theory (CONCUR 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 42, pp. 254-267, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{chen_et_al:LIPIcs.CONCUR.2015.254,
  author =	{Chen, Taolue and Song, Fu and Wu, Zhilin},
  title =	{{On the Satisfiability of Indexed Linear Temporal Logics}},
  booktitle =	{26th International Conference on Concurrency Theory (CONCUR 2015)},
  pages =	{254--267},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-91-0},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{42},
  editor =	{Aceto, Luca and de Frutos Escrig, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2015.254},
  URN =		{urn:nbn:de:0030-drops-53767},
  doi =		{10.4230/LIPIcs.CONCUR.2015.254},
  annote =	{Keywords: Satisfiability, Indexed linear temporal logic, Parameterised systems}
}
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