10 Search Results for "Cheng, Yu"


Document
On Min-Max Graph Balancing with Strict Negative Correlation Constraints

Authors: Ting-Yu Kuo, Yu-Han Chen, Andrea Frosini, Sun-Yuan Hsieh, Shi-Chun Tsai, and Mong-Jen Kao

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


Abstract
We consider the min-max graph balancing problem with strict negative correlation (SNC) constraints. The graph balancing problem arises as an equivalent formulation of the classic unrelated machine scheduling problem, where we are given a hypergraph G = (V,E) with vertex-dependent edge weight function p: E×V ↦ ℤ^{≥0} that represents the processing time of the edges (jobs). The SNC constraints, which are given as edge subsets C_1,C_2,…,C_k, require that the edges in the same subset cannot be assigned to the same vertex at the same time. Under these constraints, the goal is to compute an edge orientation (assignment) that minimizes the maximum workload of the vertices. In this paper, we conduct a general study on the approximability of this problem. First, we show that, in the presence of SNC constraints, the case with max_{e ∈ E} |e| = max_i |C_i| = 2 is the only case for which approximation solutions can be obtained. Further generalization on either direction, e.g., max_{e ∈ E} |e| or max_i |C_i|, will directly make computing a feasible solution an NP-complete problem to solve. Then, we present a 2-approximation algorithm for the case with max_{e ∈ E} |e| = max_i |C_i| = 2, based on a set of structural simplifications and a tailored assignment LP for this problem. We note that our approach is general and can be applied to similar settings, e.g., scheduling with SNC constraints to minimize the weighted completion time, to obtain similar approximation guarantees. Further cases are discussed to describe the landscape of the approximability of this prbolem. For the case with |V| ≤ 2, which is already known to be NP-hard, we present a fully-polynomial time approximation scheme (FPTAS). On the other hand, we show that the problem is at least as hard as vertex cover to approximate when |V| ≥ 3.

Cite as

Ting-Yu Kuo, Yu-Han Chen, Andrea Frosini, Sun-Yuan Hsieh, Shi-Chun Tsai, and Mong-Jen Kao. On Min-Max Graph Balancing with Strict Negative Correlation Constraints. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 50:1-50:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{kuo_et_al:LIPIcs.ISAAC.2023.50,
  author =	{Kuo, Ting-Yu and Chen, Yu-Han and Frosini, Andrea and Hsieh, Sun-Yuan and Tsai, Shi-Chun and Kao, Mong-Jen},
  title =	{{On Min-Max Graph Balancing with Strict Negative Correlation Constraints}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{50:1--50:15},
  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.2023.50},
  URN =		{urn:nbn:de:0030-drops-193524},
  doi =		{10.4230/LIPIcs.ISAAC.2023.50},
  annote =	{Keywords: Unrelated Scheduling, Graph Balancing, Strict Correlation Constraints}
}
Document
On Relaxed Locally Decodable Codes for Hamming and Insertion-Deletion Errors

Authors: Alexander R. Block, Jeremiah Blocki, Kuan Cheng, Elena Grigorescu, Xin Li, Yu Zheng, and Minshen Zhu

Published in: LIPIcs, Volume 264, 38th Computational Complexity Conference (CCC 2023)


Abstract
Locally Decodable Codes (LDCs) are error-correcting codes C:Σⁿ → Σ^m, encoding messages in Σⁿ to codewords in Σ^m, with super-fast decoding algorithms. They are important mathematical objects in many areas of theoretical computer science, yet the best constructions so far have codeword length m that is super-polynomial in n, for codes with constant query complexity and constant alphabet size. In a very surprising result, Ben-Sasson, Goldreich, Harsha, Sudan, and Vadhan (SICOMP 2006) show how to construct a relaxed version of LDCs (RLDCs) with constant query complexity and almost linear codeword length over the binary alphabet, and used them to obtain significantly-improved constructions of Probabilistically Checkable Proofs. In this work, we study RLDCs in the standard Hamming-error setting, and introduce their variants in the insertion and deletion (Insdel) error setting. Standard LDCs for Insdel errors were first studied by Ostrovsky and Paskin-Cherniavsky (Information Theoretic Security, 2015), and are further motivated by recent advances in DNA random access bio-technologies. Our first result is an exponential lower bound on the length of Hamming RLDCs making 2 queries (even adaptively), over the binary alphabet. This answers a question explicitly raised by Gur and Lachish (SICOMP 2021) and is the first exponential lower bound for RLDCs. Combined with the results of Ben-Sasson et al., our result exhibits a "phase-transition"-type behavior on the codeword length for some constant-query complexity. We achieve these lower bounds via a transformation of RLDCs to standard Hamming LDCs, using a careful analysis of restrictions of message bits that fix codeword bits. We further define two variants of RLDCs in the Insdel-error setting, a weak and a strong version. On the one hand, we construct weak Insdel RLDCs with almost linear codeword length and constant query complexity, matching the parameters of the Hamming variants. On the other hand, we prove exponential lower bounds for strong Insdel RLDCs. These results demonstrate that, while these variants are equivalent in the Hamming setting, they are significantly different in the insdel setting. Our results also prove a strict separation between Hamming RLDCs and Insdel RLDCs.

Cite as

Alexander R. Block, Jeremiah Blocki, Kuan Cheng, Elena Grigorescu, Xin Li, Yu Zheng, and Minshen Zhu. On Relaxed Locally Decodable Codes for Hamming and Insertion-Deletion Errors. In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 14:1-14:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{block_et_al:LIPIcs.CCC.2023.14,
  author =	{Block, Alexander R. and Blocki, Jeremiah and Cheng, Kuan and Grigorescu, Elena and Li, Xin and Zheng, Yu and Zhu, Minshen},
  title =	{{On Relaxed Locally Decodable Codes for Hamming and Insertion-Deletion Errors}},
  booktitle =	{38th Computational Complexity Conference (CCC 2023)},
  pages =	{14:1--14:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-282-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{264},
  editor =	{Ta-Shma, Amnon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.14},
  URN =		{urn:nbn:de:0030-drops-182847},
  doi =		{10.4230/LIPIcs.CCC.2023.14},
  annote =	{Keywords: Relaxed Locally Decodable Codes, Hamming Errors, Insdel Errors, Lower Bounds}
}
Document
Track A: Algorithms, Complexity and Games
Linear Insertion Deletion Codes in the High-Noise and High-Rate Regimes

Authors: Kuan Cheng, Zhengzhong Jin, Xin Li, Zhide Wei, and Yu Zheng

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


Abstract
This work continues the study of linear error correcting codes against adversarial insertion deletion errors (insdel errors). Previously, the work of Cheng, Guruswami, Haeupler, and Li [Kuan Cheng et al., 2021] showed the existence of asymptotically good linear insdel codes that can correct arbitrarily close to 1 fraction of errors over some constant size alphabet, or achieve rate arbitrarily close to 1/2 even over the binary alphabet. As shown in [Kuan Cheng et al., 2021], these bounds are also the best possible. However, known explicit constructions in [Kuan Cheng et al., 2021], and subsequent improved constructions by Con, Shpilka, and Tamo [Con et al., 2022] all fall short of meeting these bounds. Over any constant size alphabet, they can only achieve rate < 1/8 or correct < 1/4 fraction of errors; over the binary alphabet, they can only achieve rate < 1/1216 or correct < 1/54 fraction of errors. Apparently, previous techniques face inherent barriers to achieve rate better than 1/4 or correct more than 1/2 fraction of errors. In this work we give new constructions of such codes that meet these bounds, namely, asymptotically good linear insdel codes that can correct arbitrarily close to 1 fraction of errors over some constant size alphabet, and binary asymptotically good linear insdel codes that can achieve rate arbitrarily close to 1/2. All our constructions are efficiently encodable and decodable. Our constructions are based on a novel approach of code concatenation, which embeds the index information implicitly into codewords. This significantly differs from previous techniques and may be of independent interest. Finally, we also prove the existence of linear concatenated insdel codes with parameters that match random linear codes, and propose a conjecture about linear insdel codes.

Cite as

Kuan Cheng, Zhengzhong Jin, Xin Li, Zhide Wei, and Yu Zheng. Linear Insertion Deletion Codes in the High-Noise and High-Rate Regimes. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 41:1-41:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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@InProceedings{cheng_et_al:LIPIcs.ICALP.2023.41,
  author =	{Cheng, Kuan and Jin, Zhengzhong and Li, Xin and Wei, Zhide and Zheng, Yu},
  title =	{{Linear Insertion Deletion Codes in the High-Noise and High-Rate Regimes}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{41:1--41:17},
  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.2023.41},
  URN =		{urn:nbn:de:0030-drops-180931},
  doi =		{10.4230/LIPIcs.ICALP.2023.41},
  annote =	{Keywords: Error correcting code, Edit distance, Pseudorandomness, Derandomization}
}
Document
Lower Bounds and Improved Algorithms for Asymmetric Streaming Edit Distance and Longest Common Subsequence

Authors: Xin Li and Yu Zheng

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)


Abstract
In this paper, we study edit distance (ED) and longest common subsequence (LCS) in the asymmetric streaming model, introduced by Saks and Seshadhri [Saks and Seshadhri, 2013]. As an intermediate model between the random access model and the streaming model, this model allows one to have streaming access to one string and random access to the other string. Meanwhile, ED and LCS are both fundamental problems that are often studied on large strings, thus the (asymmetric) streaming model is ideal for studying these problems. Our first main contribution is a systematic study of space lower bounds for ED and LCS in the asymmetric streaming model. Previously, there are no explicitly stated results in this context, although some lower bounds about LCS can be inferred from the lower bounds for longest increasing subsequence (LIS) in [Sun and Woodruff, 2007; Gál and Gopalan, 2010; Ergun and Jowhari, 2008]. Yet these bounds only work for large alphabet size. In this paper, we develop several new techniques to handle ED in general and LCS for small alphabet size, thus establishing strong lower bounds for both problems. In particular, our lower bound for ED provides an exponential separation between edit distance and Hamming distance in the asymmetric streaming model. Our lower bounds also extend to LIS and longest non-decreasing subsequence (LNS) in the standard streaming model. Together with previous results, our bounds provide an almost complete picture for these two problems. As our second main contribution, we give improved algorithms for ED and LCS in the asymmetric streaming model. For ED, we improve the space complexity of the constant factor approximation algorithms in [Farhadi et al., 2020; Cheng et al., 2020] from Õ({n^δ}/δ) to O({d^δ}/δ polylog(n)), where n is the length of each string and d is the edit distance between the two strings. For LCS, we give the first 1/2+ε approximation algorithm with space n^δ for any constant δ > 0, over a binary alphabet. Our work leaves a plethora of intriguing open questions, including establishing lower bounds and designing algorithms for a natural generalization of LIS and LNS, which we call longest non-decreasing subsequence with threshold (LNST).

Cite as

Xin Li and Yu Zheng. Lower Bounds and Improved Algorithms for Asymmetric Streaming Edit Distance and Longest Common Subsequence. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 27:1-27:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{li_et_al:LIPIcs.FSTTCS.2021.27,
  author =	{Li, Xin and Zheng, Yu},
  title =	{{Lower Bounds and Improved Algorithms for Asymmetric Streaming Edit Distance and Longest Common Subsequence}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{27:1--27:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.27},
  URN =		{urn:nbn:de:0030-drops-155381},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.27},
  annote =	{Keywords: Asymmetric Streaming Model, Edit Distance, Longest Common Subsequence, Space Lower Bound}
}
Document
Track A: Algorithms, Complexity and Games
Sparsification of Directed Graphs via Cut Balance

Authors: Ruoxu Cen, Yu Cheng, Debmalya Panigrahi, and Kevin Sun

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


Abstract
In this paper, we consider the problem of designing cut sparsifiers and sketches for directed graphs. To bypass known lower bounds, we allow the sparsifier/sketch to depend on the balance of the input graph, which smoothly interpolates between undirected and directed graphs. We give nearly matching upper and lower bounds for both for-all (cf. Benczúr and Karger, STOC 1996) and for-each (Andoni et al., ITCS 2016) cut sparsifiers/sketches as a function of cut balance, defined the maximum ratio of the cut value in the two directions of a directed graph (Ene et al., STOC 2016). We also show an interesting application of digraph sparsification via cut balance by using it to give a very short proof of a celebrated maximum flow result of Karger and Levine (STOC 2002).

Cite as

Ruoxu Cen, Yu Cheng, Debmalya Panigrahi, and Kevin Sun. Sparsification of Directed Graphs via Cut Balance. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 45:1-45:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{cen_et_al:LIPIcs.ICALP.2021.45,
  author =	{Cen, Ruoxu and Cheng, Yu and Panigrahi, Debmalya and Sun, Kevin},
  title =	{{Sparsification of Directed Graphs via Cut Balance}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{45:1--45:21},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.45},
  URN =		{urn:nbn:de:0030-drops-141143},
  doi =		{10.4230/LIPIcs.ICALP.2021.45},
  annote =	{Keywords: Graph sparsification, directed graphs, cut sketches, space complexity}
}
Document
Track A: Algorithms, Complexity and Games
Streaming and Small Space Approximation Algorithms for Edit Distance and Longest Common Subsequence

Authors: Kuan Cheng, Alireza Farhadi, MohammadTaghi Hajiaghayi, Zhengzhong Jin, Xin Li, Aviad Rubinstein, Saeed Seddighin, and Yu Zheng

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


Abstract
The edit distance (ED) and longest common subsequence (LCS) are two fundamental problems which quantify how similar two strings are to one another. In this paper, we first consider these problems in the asymmetric streaming model introduced by Andoni, Krauthgamer and Onak [Andoni et al., 2010] (FOCS'10) and Saks and Seshadhri [Saks and Seshadhri, 2013] (SODA'13). In this model we have random access to one string and streaming access the other one. Our main contribution is a constant factor approximation algorithm for ED with memory Õ(n^δ) for any constant δ > 0. In addition to this, we present an upper bound of Õ _ε(√n) on the memory needed to approximate ED or LCS within a factor 1±ε. All our algorithms are deterministic and run in polynomial time in a single pass. We further study small-space approximation algorithms for ED, LCS, and longest increasing sequence (LIS) in the non-streaming setting. Here, we design algorithms that achieve 1 ± ε approximation for all three problems, where ε > 0 can be any constant and even slightly sub-constant. Our algorithms only use poly-logarithmic space while maintaining a polynomial running time. This significantly improves previous results in terms of space complexity, where all known results need to use space at least Ω(√n). Our algorithms make novel use of triangle inequality and carefully designed recursions to save space, which can be of independent interest.

Cite as

Kuan Cheng, Alireza Farhadi, MohammadTaghi Hajiaghayi, Zhengzhong Jin, Xin Li, Aviad Rubinstein, Saeed Seddighin, and Yu Zheng. Streaming and Small Space Approximation Algorithms for Edit Distance and Longest Common Subsequence. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 54:1-54:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{cheng_et_al:LIPIcs.ICALP.2021.54,
  author =	{Cheng, Kuan and Farhadi, Alireza and Hajiaghayi, MohammadTaghi and Jin, Zhengzhong and Li, Xin and Rubinstein, Aviad and Seddighin, Saeed and Zheng, Yu},
  title =	{{Streaming and Small Space Approximation Algorithms for Edit Distance and Longest Common Subsequence}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{54:1--54:20},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.54},
  URN =		{urn:nbn:de:0030-drops-141236},
  doi =		{10.4230/LIPIcs.ICALP.2021.54},
  annote =	{Keywords: Edit Distance, Longest Common Subsequence, Longest Increasing Subsequence, Space Efficient Algorithm, Approximation Algorithm}
}
Document
On Deterministic Linearizable Set Agreement Objects

Authors: Felipe de Azevedo Piovezan, Vassos Hadzilacos, and Sam Toueg

Published in: LIPIcs, Volume 153, 23rd International Conference on Principles of Distributed Systems (OPODIS 2019)


Abstract
A recent work showed that, for all n and k, there is a linearizable (n,k)-set agreement object O_L that is equivalent to the (n,k)-set agreement task [David Yu Cheng Chan et al., 2017]: given O_L, it is possible to solve the (n,k)-set agreement task, and given any algorithm that solves the (n,k)-set agreement task (and registers), it is possible to implement O_L. This linearizable object O_L, however, is not deterministic. It turns out that there is also a deterministic (n,k)-set agreement object O_D that is equivalent to the (n,k)-set agreement task, but this deterministic object O_D is not linearizable. This raises the question whether there exists a deterministic and linearizable (n,k)-set agreement object that is equivalent to the (n,k)-set agreement task. Here we show that in general the answer is no: specifically, we prove that for all n ≥ 4, every deterministic linearizable (n,2)-set agreement object is strictly stronger than the (n,2)-set agreement task. We prove this by showing that, for all n ≥ 4, every deterministic and linearizable (n,2)-set agreement object (together with registers) can be used to solve 2-consensus, whereas it is known that the (n,2)-set agreement task cannot do so. For a natural subset of (n,2)-set agreement objects, we prove that this result holds even for n = 3.

Cite as

Felipe de Azevedo Piovezan, Vassos Hadzilacos, and Sam Toueg. On Deterministic Linearizable Set Agreement Objects. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 16:1-16:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{deazevedopiovezan_et_al:LIPIcs.OPODIS.2019.16,
  author =	{de Azevedo Piovezan, Felipe and Hadzilacos, Vassos and Toueg, Sam},
  title =	{{On Deterministic Linearizable Set Agreement Objects}},
  booktitle =	{23rd International Conference on Principles of Distributed Systems (OPODIS 2019)},
  pages =	{16:1--16:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-133-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{153},
  editor =	{Felber, Pascal and Friedman, Roy and Gilbert, Seth and Miller, Avery},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2019.16},
  URN =		{urn:nbn:de:0030-drops-118026},
  doi =		{10.4230/LIPIcs.OPODIS.2019.16},
  annote =	{Keywords: Asynchronous shared-memory systems, consensus, set agreement, deterministic objects}
}
Document
Well-Supported vs. Approximate Nash Equilibria: Query Complexity of Large Games

Authors: Xi Chen, Yu Cheng, and Bo Tang

Published in: LIPIcs, Volume 67, 8th Innovations in Theoretical Computer Science Conference (ITCS 2017)


Abstract
In this paper we present a generic reduction from the problem of finding an \epsilon-well-supported Nash equilibrium (WSNE) to that of finding an \Theta(\epsilon)-approximate Nash equilibrium (ANE), in large games with n players and a bounded number of strategies for each player. Our reduction complements the existing literature on relations between WSNE and ANE, and can be applied to extend hardness results on WSNE to similar results on ANE. This allows one to focus on WSNE first, which is in general easier to analyze and control in hardness constructions. As an application we prove a 2^{\Omega(n/\log n)} lower bound on the randomized query complexity of finding an \epsilon-ANE in binary-action n-player games, for some constant \epsilon>0. This answers an open problem posed by Hart and Nisan and Babichenko, and is very close to the trivial upper bound of 2^n. Previously for WSNE, Babichenko showed a 2^{\Omega(n)} lower bound on the randomized query complexity of finding an \epsilon-WSNE for some constant epsilon>0. Our result follows directly from combining Babichenko's result and our new reduction from WSNE to ANE.

Cite as

Xi Chen, Yu Cheng, and Bo Tang. Well-Supported vs. Approximate Nash Equilibria: Query Complexity of Large Games. In 8th Innovations in Theoretical Computer Science Conference (ITCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 67, pp. 57:1-57:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{chen_et_al:LIPIcs.ITCS.2017.57,
  author =	{Chen, Xi and Cheng, Yu and Tang, Bo},
  title =	{{Well-Supported vs. Approximate Nash Equilibria: Query Complexity of Large Games}},
  booktitle =	{8th Innovations in Theoretical Computer Science Conference (ITCS 2017)},
  pages =	{57:1--57:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-029-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{67},
  editor =	{Papadimitriou, Christos H.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2017.57},
  URN =		{urn:nbn:de:0030-drops-81636},
  doi =		{10.4230/LIPIcs.ITCS.2017.57},
  annote =	{Keywords: Equilibrium Computation, Query Complexity, Large Games}
}
Document
On the Number of Objects with Distinct Power and the Linearizability of Set Agreement Objects

Authors: David Yu Cheng Chan, Vassos Hadzilacos, and Sam Toueg

Published in: LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)


Abstract
We first prove that there are uncountably many objects with distinct computational powers. More precisely, we show that there is an uncountable set of objects such that for any two of them, at least one cannot be implemented from the other (and registers) in a wait-free manner. We then strengthen this result by showing that there are uncountably many linearizable objects with distinct computational powers. To do so, we prove that for all positive integers n and k, there is a linearizable object that is computationally equivalent to the k-set agreement task among n processes. To the best of our knowledge, these are the first linearizable objects proven to be computationally equivalent to set agreement tasks.

Cite as

David Yu Cheng Chan, Vassos Hadzilacos, and Sam Toueg. On the Number of Objects with Distinct Power and the Linearizability of Set Agreement Objects. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 12:1-12:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{chan_et_al:LIPIcs.DISC.2017.12,
  author =	{Chan, David Yu Cheng and Hadzilacos, Vassos and Toueg, Sam},
  title =	{{On the Number of Objects with Distinct Power and the Linearizability of Set Agreement Objects}},
  booktitle =	{31st International Symposium on Distributed Computing (DISC 2017)},
  pages =	{12:1--12:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-053-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{91},
  editor =	{Richa, Andr\'{e}a},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.12},
  URN =		{urn:nbn:de:0030-drops-79973},
  doi =		{10.4230/LIPIcs.DISC.2017.12},
  annote =	{Keywords: Set Agreement, Asynchronous System, Shared Memory}
}
Document
Bounded Disagreement

Authors: David Yu Cheng Chan, Vassos Hadzilacos, and Sam Toueg

Published in: LIPIcs, Volume 70, 20th International Conference on Principles of Distributed Systems (OPODIS 2016)


Abstract
A well-known generalization of the consensus problem, namely, set agreement (SA), limits the number of distinct decision values that processes decide. In some settings, it may be more important to limit the number of "disagreers". Thus, we introduce another natural generalization of the consensus problem, namely, bounded disagreement (BD), which limits the number of processes that decide differently from the plurality. More precisely, in a system with n processes, the (n, l)-BD task has the following requirement: there is a value v such that at most l processes (the disagreers) decide a value other than v. Despite their apparent similarities, the results described below show that bounded disagreement, consensus, and set agreement are in fact fundamentally different problems. We investigate the relationship between bounded disagreement, consensus, and set agreement. In particular, we determine the consensus number for every instance of the BD task. We also determine values of n, l, m, and k such that the (n, l)-BD task can solve the (m, k)-SA task (where m processes can decide at most k distinct values). Using our results and a previously known impossibility result for set agreement, we prove that for all n >= 2, there is a BD task (and a corresponding BD object) that has consensus number n but can not be solved using n-consensus and registers. Prior to our paper, the only objects known to have this unusual characteristic for n >= 2 (which shows that the consensus number of an object is not sufficient to fully capture its power) were artificial objects crafted solely for the purpose of exhibiting this behaviour.

Cite as

David Yu Cheng Chan, Vassos Hadzilacos, and Sam Toueg. Bounded Disagreement. In 20th International Conference on Principles of Distributed Systems (OPODIS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 70, pp. 5:1-5:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


Copy BibTex To Clipboard

@InProceedings{yuchengchan_et_al:LIPIcs.OPODIS.2016.5,
  author =	{Yu Cheng Chan, David and Hadzilacos, Vassos and Toueg, Sam},
  title =	{{Bounded Disagreement}},
  booktitle =	{20th International Conference on Principles of Distributed Systems (OPODIS 2016)},
  pages =	{5:1--5:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-031-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{70},
  editor =	{Fatourou, Panagiota and Jim\'{e}nez, Ernesto and Pedone, Fernando},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2016.5},
  URN =		{urn:nbn:de:0030-drops-70742},
  doi =		{10.4230/LIPIcs.OPODIS.2016.5},
  annote =	{Keywords: Consensus, Set Agreement, Asynchronous System, Distributed Algorithms, Shared Memory}
}
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