12 Search Results for "Wu, Hongxun"

Document
DOI: 10.4230/LIPIcs.CCC.2024.18
Pseudorandomness, Symmetry, Smoothing: I

Authors: Harm Derksen, Peter Ivanov, Chin Ho Lee, and Emanuele Viola

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract
We prove several new results about bounded uniform and small-bias distributions. A main message is that, small-bias, even perturbed with noise, does not fool several classes of tests better than bounded uniformity. We prove this for threshold tests, small-space algorithms, and small-depth circuits. In particular, we obtain small-bias distributions that - achieve an optimal lower bound on their statistical distance to any bounded-uniform distribution. This closes a line of research initiated by Alon, Goldreich, and Mansour in 2003, and improves on a result by O'Donnell and Zhao. - have heavier tail mass than the uniform distribution. This answers a question posed by several researchers including Bun and Steinke. - rule out a popular paradigm for constructing pseudorandom generators, originating in a 1989 work by Ajtai and Wigderson. This again answers a question raised by several researchers. For branching programs, our result matches a bound by Forbes and Kelley. Our small-bias distributions above are symmetric. We show that the xor of any two symmetric small-bias distributions fools any bounded function. Hence our examples cannot be extended to the xor of two small-bias distributions, another popular paradigm whose power remains unknown. We also generalize and simplify the proof of a result of Bazzi.
Cite as

Harm Derksen, Peter Ivanov, Chin Ho Lee, and Emanuele Viola. Pseudorandomness, Symmetry, Smoothing: I. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 18:1-18:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{derksen_et_al:LIPIcs.CCC.2024.18,
  author =	{Derksen, Harm and Ivanov, Peter and Lee, Chin Ho and Viola, Emanuele},
  title =	{{Pseudorandomness, Symmetry, Smoothing: I}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{18:1--18:27},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.18},
  URN =		{urn:nbn:de:0030-drops-204144},
  doi =		{10.4230/LIPIcs.CCC.2024.18},
  annote =	{Keywords: pseudorandomness, k-wise uniform distributions, small-bias distributions, noise, symmetric tests, thresholds, Krawtchouk polynomials}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.32
BPL ⊆ L-AC¹

Authors: Kuan Cheng and Yichuan Wang

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)

Abstract
Whether BPL = 𝖫 (which is conjectured to be equal) or even whether BPL ⊆ NL, is a big open problem in theoretical computer science. It is well known that 𝖫 ⊆ NL ⊆ L-AC¹. In this work we show that BPL ⊆ L-AC¹ also holds. Our proof is based on a new iteration method for boosting precision in approximating matrix powering, which is inspired by the Richardson Iteration method developed in a recent line of work [AmirMahdi Ahmadinejad et al., 2020; Edward Pyne and Salil P. Vadhan, 2021; Gil Cohen et al., 2021; William M. Hoza, 2021; Gil Cohen et al., 2023; Aaron (Louie) Putterman and Edward Pyne, 2023; Lijie Chen et al., 2023]. We also improve the algorithm for approximate counting in low-depth L-AC circuits from an additive error setting to a multiplicative error setting.
Cite as

Kuan Cheng and Yichuan Wang. BPL ⊆ L-AC¹. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 32:1-32:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{cheng_et_al:LIPIcs.CCC.2024.32,
  author =	{Cheng, Kuan and Wang, Yichuan},
  title =	{{BPL ⊆ L-AC¹}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{32:1--32:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.32},
  URN =		{urn:nbn:de:0030-drops-204282},
  doi =		{10.4230/LIPIcs.CCC.2024.32},
  annote =	{Keywords: Randomized Space Complexity, Circuit Complexity, Derandomization}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.41
Faster Algorithms for Dual-Failure Replacement Paths

Authors: Shiri Chechik and Tianyi Zhang

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
Given a simple weighted directed graph G = (V, E, ω) on n vertices as well as two designated terminals s, t ∈ V, our goal is to compute the shortest path from s to t avoiding any pair of presumably failed edges f₁, f₂ ∈ E, which is a natural generalization of the classical replacement path problem which considers single edge failures only. This dual failure replacement paths problem was recently studied by Vassilevska Williams, Woldeghebriel and Xu [FOCS 2022] who designed a cubic time algorithm for general weighted digraphs which is conditionally optimal; in the same paper, for unweighted graphs where ω ≡ 1, the authors presented an algebraic algorithm with runtime Õ(n^{2.9146}), as well as a conditional lower bound of n^{8/3-o(1)} against combinatorial algorithms. However, it was unknown in their work whether fast matrix multiplication is necessary for a subcubic runtime in unweighted digraphs. As our primary result, we present the first truly subcubic combinatorial algorithm for dual failure replacement paths in unweighted digraphs. Our runtime is Õ(n^{3-1/18}). Besides, we also study algebraic algorithms for digraphs with small integer edge weights from {-M, -M+1, ⋯, M-1, M}. As our secondary result, we obtained a runtime of Õ(Mn^{2.8716}), which is faster than the previous bound of Õ(M^{2/3}n^{2.9144} + Mn^{2.8716}) from [Vassilevska Williams, Woldeghebriela and Xu, 2022].
Cite as

Shiri Chechik and Tianyi Zhang. Faster Algorithms for Dual-Failure Replacement Paths. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 41:1-41:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{chechik_et_al:LIPIcs.ICALP.2024.41,
  author =	{Chechik, Shiri and Zhang, Tianyi},
  title =	{{Faster Algorithms for Dual-Failure Replacement Paths}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{41:1--41:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.41},
  URN =		{urn:nbn:de:0030-drops-201849},
  doi =		{10.4230/LIPIcs.ICALP.2024.41},
  annote =	{Keywords: graph algorithms, shortest paths, replacement paths}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.64
Minimizing Tardy Processing Time on a Single Machine in Near-Linear Time

Authors: Nick Fischer and Leo Wennmann

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
In this work we revisit the elementary scheduling problem 1||∑ p_j U_j. The goal is to select, among n jobs with processing times and due dates, a subset of jobs with maximum total processing time that can be scheduled in sequence without violating their due dates. This problem is NP-hard, but a classical algorithm by Lawler and Moore from the 60s solves this problem in pseudo-polynomial time O(nP), where P is the total processing time of all jobs. With the aim to develop best-possible pseudo-polynomial-time algorithms, a recent wave of results has improved Lawler and Moore’s algorithm for 1||∑ p_j U_j: First to time Õ(P^{7/4}) [Bringmann, Fischer, Hermelin, Shabtay, Wellnitz; ICALP'20], then to time Õ(P^{5/3}) [Klein, Polak, Rohwedder; SODA'23], and finally to time Õ(P^{7/5}) [Schieber, Sitaraman; WADS'23]. It remained an exciting open question whether these works can be improved further. In this work we develop an algorithm in near-linear time Õ(P) for the 1||∑ p_j U_j problem. This running time not only significantly improves upon the previous results, but also matches conditional lower bounds based on the Strong Exponential Time Hypothesis or the Set Cover Hypothesis and is therefore likely optimal (up to subpolynomial factors). Our new algorithm also extends to the case of m machines in time Õ(P^m). In contrast to the previous improvements, we take a different, more direct approach inspired by the recent reductions from Modular Subset Sum to dynamic string problems. We thereby arrive at a satisfyingly simple algorithm.
Cite as

Nick Fischer and Leo Wennmann. Minimizing Tardy Processing Time on a Single Machine in Near-Linear Time. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 64:1-64:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{fischer_et_al:LIPIcs.ICALP.2024.64,
  author =	{Fischer, Nick and Wennmann, Leo},
  title =	{{Minimizing Tardy Processing Time on a Single Machine in Near-Linear Time}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{64:1--64:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.64},
  URN =		{urn:nbn:de:0030-drops-202079},
  doi =		{10.4230/LIPIcs.ICALP.2024.64},
  annote =	{Keywords: Scheduling, Fine-Grained Complexity, Dynamic Strings}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.94
A Faster Algorithm for Pigeonhole Equal Sums

Authors: Ce Jin and Hongxun Wu

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
An important area of research in exact algorithms is to solve Subset-Sum-type problems faster than meet-in-middle. In this paper we study Pigeonhole Equal Sums, a total search problem proposed by Papadimitriou (1994): given n positive integers w₁,… ,w_n of total sum ∑_{i = 1}ⁿ w_i < 2ⁿ-1, the task is to find two distinct subsets A, B ⊆ [n] such that ∑_{i ∈ A}w_i = ∑_{i ∈ B}w_i. Similar to the status of the Subset Sum problem, the best known algorithm for Pigeonhole Equal Sums runs in O^*(2^{n/2}) time, via either meet-in-middle or dynamic programming (Allcock, Hamoudi, Joux, Klingelhöfer, and Santha, 2022). Our main result is an improved algorithm for Pigeonhole Equal Sums in O^*(2^{0.4n}) time. We also give a polynomial-space algorithm in O^*(2^{0.75n}) time. Unlike many previous works in this area, our approach does not use the representation method, but rather exploits a simple structural characterization of input instances with few solutions.
Cite as

Ce Jin and Hongxun Wu. A Faster Algorithm for Pigeonhole Equal Sums. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 94:1-94:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{jin_et_al:LIPIcs.ICALP.2024.94,
  author =	{Jin, Ce and Wu, Hongxun},
  title =	{{A Faster Algorithm for Pigeonhole Equal Sums}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{94:1--94:11},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.94},
  URN =		{urn:nbn:de:0030-drops-202375},
  doi =		{10.4230/LIPIcs.ICALP.2024.94},
  annote =	{Keywords: Subset Sum, Pigeonhole, PPP}
}
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.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
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.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.2021.68
Random Order Vertex Arrival Contention Resolution Schemes for Matching, with Applications

Authors: Hu Fu, Zhihao Gavin Tang, Hongxun Wu, Jinzhao Wu, and Qianfan Zhang

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
With a wide range of applications, stochastic matching problems have been studied in different models, including prophet inequality, Query-Commit, and Price-of-Information. While there have been recent breakthroughs in all these settings for bipartite graphs, few non-trivial results are known for general graphs. In this paper, we study the random order vertex arrival contention resolution scheme for matching in general graphs, which is inspired by the recent work of Ezra et al. (EC 2020). We design an 8/15-selectable batched RCRS for matching and apply it to achieve 8/15-competitive/approximate algorithms for all the three models. Our results are the first non-trivial results for random order prophet matching and Price-of-Information matching in general graphs. For the Query-Commit model, our result substantially improves upon the 0.501 approximation ratio by Tang et al. (STOC 2020). We also show that no batched RCRS for matching can be better than 1/2+1/(2e²) ≈ 0.567-selectable.
Cite as

Hu Fu, Zhihao Gavin Tang, Hongxun Wu, Jinzhao Wu, and Qianfan Zhang. Random Order Vertex Arrival Contention Resolution Schemes for Matching, with Applications. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 68:1-68:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{fu_et_al:LIPIcs.ICALP.2021.68,
  author =	{Fu, Hu and Tang, Zhihao Gavin and Wu, Hongxun and Wu, Jinzhao and Zhang, Qianfan},
  title =	{{Random Order Vertex Arrival Contention Resolution Schemes for Matching, with Applications}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{68:1--68:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.68},
  URN =		{urn:nbn:de:0030-drops-141376},
  doi =		{10.4230/LIPIcs.ICALP.2021.68},
  annote =	{Keywords: Matching, Contention Resolution Scheme, Price of Information, Query-Commit}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.79
Improved Distance Sensitivity Oracles with Subcubic Preprocessing Time

Authors: Hanlin Ren

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
We consider the problem of building Distance Sensitivity Oracles (DSOs). Given a directed graph G = (V, E) with edge weights in {1, 2, … , M}, we need to preprocess it into a data structure, and answer the following queries: given vertices u,v,x ∈ V, output the length of the shortest path from u to v that does not go through x. Our main result is a simple DSO with Õ(n^2.7233 M²) preprocessing time and O(1) query time. Moreover, if the input graph is undirected, the preprocessing time can be improved to Õ(n^2.6865 M²). Our algorithms are randomized with correct probability ≥ 1-1/n^c, for a constant c that can be made arbitrarily large. Previously, there is a DSO with Õ(n^2.8729 M) preprocessing time and polylog(n) query time [Chechik and Cohen, STOC'20]. At the core of our DSO is the following observation from [Bernstein and Karger, STOC'09]: if there is a DSO with preprocessing time P and query time Q, then we can construct a DSO with preprocessing time P+Õ(Mn²)⋅ Q and query time O(1). (Here Õ(⋅) hides polylog(n) factors.)
Cite as

Hanlin Ren. Improved Distance Sensitivity Oracles with Subcubic Preprocessing Time. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 79:1-79:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{ren:LIPIcs.ESA.2020.79,
  author =	{Ren, Hanlin},
  title =	{{Improved Distance Sensitivity Oracles with Subcubic Preprocessing Time}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{79:1--79:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.79},
  URN =		{urn:nbn:de:0030-drops-129450},
  doi =		{10.4230/LIPIcs.ESA.2020.79},
  annote =	{Keywords: Graph theory, Failure-prone structures}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2020.105
Near-Optimal Algorithm for Constructing Greedy Consensus Tree

Authors: Hongxun Wu

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

Abstract
In biology, phylogenetic trees are important tools for describing evolutionary relations, but various data sources may result in conflicting phylogenetic trees. To summarize these conflicting phylogenetic trees, consensus tree methods take k conflicting phylogenetic trees (each with n leaves) as input and output a single phylogenetic tree as consensus. Among the consensus tree methods, a widely used method is the greedy consensus tree. The previous fastest algorithms for constructing a greedy consensus tree have time complexity Õ(kn^1.5) [Gawrychowski, Landau, Sung, Weimann 2018] and Õ(k²n) [Sung 2019] respectively. In this paper, we improve the running time to Õ(kn). Since k input trees have Θ(kn) nodes in total, our algorithm is optimal up to polylogarithmic factors.
Cite as

Hongxun Wu. Near-Optimal Algorithm for Constructing Greedy Consensus Tree. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 105:1-105:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{wu:LIPIcs.ICALP.2020.105,
  author =	{Wu, Hongxun},
  title =	{{Near-Optimal Algorithm for Constructing Greedy Consensus Tree}},
  booktitle =	{47th International Colloquium on Automata, Languages, and Programming (ICALP 2020)},
  pages =	{105:1--105:14},
  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.2020.105},
  URN =		{urn:nbn:de:0030-drops-125122},
  doi =		{10.4230/LIPIcs.ICALP.2020.105},
  annote =	{Keywords: phylogenetic trees, greedy consensus trees, splay tree}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.48
Faster Algorithms for All Pairs Non-Decreasing Paths Problem

Authors: Ran Duan, Ce Jin, and Hongxun Wu

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
In this paper, we present an improved algorithm for the All Pairs Non-decreasing Paths (APNP) problem on weighted simple digraphs, which has running time O~(n^{{3 + omega}/{2}}) = O~(n^{2.686}). Here n is the number of vertices, and omega < 2.373 is the exponent of time complexity of fast matrix multiplication [Williams 2012, Le Gall 2014]. This matches the current best upper bound for (max, min)-matrix product [Duan, Pettie 2009] which is reducible to APNP. Thus, further improvement for APNP will imply a faster algorithm for (max, min)-matrix product. The previous best upper bound for APNP on weighted digraphs was O~(n^{1/2(3 + {3 - omega}/{omega + 1} + omega)}) = O~(n^{2.78}) [Duan, Gu, Zhang 2018]. We also show an O~(n^2) time algorithm for APNP in undirected simple graphs which also reaches optimal within logarithmic factors.
Cite as

Ran Duan, Ce Jin, and Hongxun Wu. Faster Algorithms for All Pairs Non-Decreasing Paths Problem. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 48:1-48:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{duan_et_al:LIPIcs.ICALP.2019.48,
  author =	{Duan, Ran and Jin, Ce and Wu, Hongxun},
  title =	{{Faster Algorithms for All Pairs Non-Decreasing Paths Problem}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{48:1--48:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.48},
  URN =		{urn:nbn:de:0030-drops-106241},
  doi =		{10.4230/LIPIcs.ICALP.2019.48},
  annote =	{Keywords: graph optimization, matrix multiplication, non-decreasing paths}
}
Document
DOI: 10.4230/OASIcs.SOSA.2019.17
A Simple Near-Linear Pseudopolynomial Time Randomized Algorithm for Subset Sum

Authors: Ce Jin and Hongxun Wu

Published in: OASIcs, Volume 69, 2nd Symposium on Simplicity in Algorithms (SOSA 2019)

Abstract
Given a multiset S of n positive integers and a target integer t, the Subset Sum problem asks to determine whether there exists a subset of S that sums up to t. The current best deterministic algorithm, by Koiliaris and Xu [SODA'17], runs in O~(sqrt{n}t) time, where O~ hides poly-logarithm factors. Bringmann [SODA'17] later gave a randomized O~(n + t) time algorithm using two-stage color-coding. The O~(n+t) running time is believed to be near-optimal. In this paper, we present a simple and elegant randomized algorithm for Subset Sum in O~(n + t) time. Our new algorithm actually solves its counting version modulo prime p>t, by manipulating generating functions using FFT.
Cite as

Ce Jin and Hongxun Wu. A Simple Near-Linear Pseudopolynomial Time Randomized Algorithm for Subset Sum. In 2nd Symposium on Simplicity in Algorithms (SOSA 2019). Open Access Series in Informatics (OASIcs), Volume 69, pp. 17:1-17:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{jin_et_al:OASIcs.SOSA.2019.17,
  author =	{Jin, Ce and Wu, Hongxun},
  title =	{{A Simple Near-Linear Pseudopolynomial Time Randomized Algorithm for Subset Sum}},
  booktitle =	{2nd Symposium on Simplicity in Algorithms (SOSA 2019)},
  pages =	{17:1--17:6},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-099-6},
  ISSN =	{2190-6807},
  year =	{2019},
  volume =	{69},
  editor =	{Fineman, Jeremy T. and Mitzenmacher, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/OASIcs.SOSA.2019.17},
  URN =		{urn:nbn:de:0030-drops-100436},
  doi =		{10.4230/OASIcs.SOSA.2019.17},
  annote =	{Keywords: subset sum, formal power series, FFT}
}
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