11 Search Results for "Li, Ray"

Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2023.26
Approximating Pandora’s Box with Correlations

Authors: Shuchi Chawla, Evangelia Gergatsouli, Jeremy McMahan, and Christos Tzamos

Published in: LIPIcs, Volume 275, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)

Abstract
We revisit the classic Pandora’s Box (PB) problem under correlated distributions on the box values. Recent work of [Shuchi Chawla et al., 2020] obtained constant approximate algorithms for a restricted class of policies for the problem that visit boxes in a fixed order. In this work, we study the complexity of approximating the optimal policy which may adaptively choose which box to visit next based on the values seen so far. Our main result establishes an approximation-preserving equivalence of PB to the well studied Uniform Decision Tree (UDT) problem from stochastic optimization and a variant of the Min-Sum Set Cover (MSSC_f) problem. For distributions of support m, UDT admits a log m approximation, and while a constant factor approximation in polynomial time is a long-standing open problem, constant factor approximations are achievable in subexponential time [Ray Li et al., 2020]. Our main result implies that the same properties hold for PB and MSSC_f. We also study the case where the distribution over values is given more succinctly as a mixture of m product distributions. This problem is again related to a noisy variant of the Optimal Decision Tree which is significantly more challenging. We give a constant-factor approximation that runs in time n^Õ(m²/ε²) when the mixture components on every box are either identical or separated in TV distance by ε.
Cite as

Shuchi Chawla, Evangelia Gergatsouli, Jeremy McMahan, and Christos Tzamos. Approximating Pandora’s Box with Correlations. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 275, pp. 26:1-26:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{chawla_et_al:LIPIcs.APPROX/RANDOM.2023.26,
  author =	{Chawla, Shuchi and Gergatsouli, Evangelia and McMahan, Jeremy and Tzamos, Christos},
  title =	{{Approximating Pandora’s Box with Correlations}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2023)},
  pages =	{26:1--26:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-296-9},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{275},
  editor =	{Megow, Nicole and Smith, Adam},
  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.2023.26},
  URN =		{urn:nbn:de:0030-drops-188519},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2023.26},
  annote =	{Keywords: Pandora’s Box, Min Sum Set Cover, stochastic optimization, approximation preserving reduction}
}
Document
DOI: 10.4230/LIPIcs.ESA.2023.2
On Diameter Approximation in Directed Graphs

Authors: Amir Abboud, Mina Dalirrooyfard, Ray Li, and Virginia Vassilevska Williams

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)

Abstract
Computing the diameter of a graph, i.e. the largest distance, is a fundamental problem that is central in fine-grained complexity. In undirected graphs, the Strong Exponential Time Hypothesis (SETH) yields a lower bound on the time vs. approximation trade-off that is quite close to the upper bounds. In directed graphs, however, where only some of the upper bounds apply, much larger gaps remain. Since d(u,v) may not be the same as d(v,u), there are multiple ways to define the problem, the two most natural being the (one-way) diameter (max_(u,v) d(u,v)) and the roundtrip diameter (max_{u,v} d(u,v)+d(v,u)). In this paper we make progress on the outstanding open question for each of them. - We design the first algorithm for diameter in sparse directed graphs to achieve n^{1.5-ε} time with an approximation factor better than 2. The new upper bound trade-off makes the directed case appear more similar to the undirected case. Notably, this is the first algorithm for diameter in sparse graphs that benefits from fast matrix multiplication. - We design new hardness reductions separating roundtrip diameter from directed and undirected diameter. In particular, a 1.5-approximation in subquadratic time would refute the All-Nodes k-Cycle hypothesis, and any (2-ε)-approximation would imply a breakthrough algorithm for approximate 𝓁_∞-Closest-Pair. Notably, these are the first conditional lower bounds for diameter that are not based on SETH.
Cite as

Amir Abboud, Mina Dalirrooyfard, Ray Li, and Virginia Vassilevska Williams. On Diameter Approximation in Directed Graphs. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 2:1-2:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{abboud_et_al:LIPIcs.ESA.2023.2,
  author =	{Abboud, Amir and Dalirrooyfard, Mina and Li, Ray and Vassilevska Williams, Virginia},
  title =	{{On Diameter Approximation in Directed Graphs}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{2:1--2:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.2},
  URN =		{urn:nbn:de:0030-drops-186552},
  doi =		{10.4230/LIPIcs.ESA.2023.2},
  annote =	{Keywords: Diameter, Directed Graphs, Approximation Algorithms, Fine-grained complexity}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2021.5
Sharp Threshold Rates for Random Codes

Authors: Venkatesan Guruswami, Jonathan Mosheiff, Nicolas Resch, Shashwat Silas, and Mary Wootters

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract
Suppose that 𝒫 is a property that may be satisfied by a random code C ⊂ Σⁿ. For example, for some p ∈ (0,1), 𝒫 might be the property that there exist three elements of C that lie in some Hamming ball of radius pn. We say that R^* is the threshold rate for 𝒫 if a random code of rate R^* + ε is very likely to satisfy 𝒫, while a random code of rate R^* - ε is very unlikely to satisfy 𝒫. While random codes are well-studied in coding theory, even the threshold rates for relatively simple properties like the one above are not well understood. We characterize threshold rates for a rich class of properties. These properties, like the example above, are defined by the inclusion of specific sets of codewords which are also suitably "symmetric." For properties in this class, we show that the threshold rate is in fact equal to the lower bound that a simple first-moment calculation obtains. Our techniques not only pin down the threshold rate for the property 𝒫 above, they give sharp bounds on the threshold rate for list-recovery in several parameter regimes, as well as an efficient algorithm for estimating the threshold rates for list-recovery in general.
Cite as

Venkatesan Guruswami, Jonathan Mosheiff, Nicolas Resch, Shashwat Silas, and Mary Wootters. Sharp Threshold Rates for Random Codes. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{guruswami_et_al:LIPIcs.ITCS.2021.5,
  author =	{Guruswami, Venkatesan and Mosheiff, Jonathan and Resch, Nicolas and Silas, Shashwat and Wootters, Mary},
  title =	{{Sharp Threshold Rates for Random Codes}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{5:1--5:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.5},
  URN =		{urn:nbn:de:0030-drops-135446},
  doi =		{10.4230/LIPIcs.ITCS.2021.5},
  annote =	{Keywords: Coding theory, Random codes, Sharp thresholds}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2021.35
Algorithms and Hardness for Multidimensional Range Updates and Queries

Authors: Joshua Lau and Angus Ritossa

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)

Abstract
Traditional orthogonal range problems allow queries over a static set of points, each with some value. Dynamic variants allow points to be added or removed, one at a time. To support more powerful updates, we introduce the Grid Range class of data structure problems over arbitrarily large integer arrays in one or more dimensions. These problems allow range updates (such as filling all points in a range with a constant) and queries (such as finding the sum or maximum of values in a range). In this work, we consider these operations along with updates that replace each point in a range with the minimum, maximum, or sum of its existing value, and a constant. In one dimension, it is known that segment trees can be leveraged to facilitate any n of these operations in Õ(n) time overall. Other than a few specific cases, until now, higher dimensional variants have been largely unexplored. Despite their tightly-knit complexity in one dimension, we show that variants induced by subsets of these operations exhibit polynomial separation in two dimensions. In particular, no truly subquadratic time algorithm can support certain pairs of these updates simultaneously without falsifying several popular conjectures. On the positive side, we show that truly subquadratic algorithms can be obtained for variants induced by other subsets. We provide two general approaches to designing such algorithms that can be generalised to online and higher dimensional settings. First, we give almost-tight Õ(n^{3/2}) time algorithms for single-update variants where the update and query operations meet a set of natural conditions. Second, for other variants, we provide a general framework for reducing to instances with a special geometry. Using this, we show that O(m^{3/2-ε}) time algorithms for counting paths and walks of length 2 and 3 between vertex pairs in sparse graphs imply truly subquadratic data structures for certain variants; to this end, we give an Õ(m^{(4ω-1)/(2ω+1)}) = O(m^1.478) time algorithm for counting simple 3-paths between vertex pairs.
Cite as

Joshua Lau and Angus Ritossa. Algorithms and Hardness for Multidimensional Range Updates and Queries. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 35:1-35:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{lau_et_al:LIPIcs.ITCS.2021.35,
  author =	{Lau, Joshua and Ritossa, Angus},
  title =	{{Algorithms and Hardness for Multidimensional Range Updates and Queries}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{35:1--35:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.35},
  URN =		{urn:nbn:de:0030-drops-135742},
  doi =		{10.4230/LIPIcs.ITCS.2021.35},
  annote =	{Keywords: Orthogonal range, Range updates, Online and Dynamic Data Structures, Fine-grained complexity, Cycle counting}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.MFCS.2020.3
List-Decodability of Structured Ensembles of Codes (Invited Talk)

Authors: Mary Wootters

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

Abstract
What combinatorial properties are satisfied by a random subspace over a finite field? For example, is it likely that not too many points lie in any Hamming ball? What about any cube? In this talk, I will discuss the answer to these questions, along with a more general characterization of the properties that are likely to be satisfied by a random subspace. The motivation for this characterization comes from error correcting codes. I will discuss how to use this characterization to make progress on the questions of list-decoding and list-recovery for random linear codes, and also to establish the list-decodability of random Low Density Parity-Check (LDPC) codes. This talk is based on the works [Mosheiff et al., 2019] and [Guruswami et al., 2020], which are joint works with Venkatesan Guruswami, Ray Li, Jonathan Mosheiff, Nicolas Resch, Noga Ron-Zewi, and Shashwat Silas.
Cite as

Mary Wootters. List-Decodability of Structured Ensembles of Codes (Invited Talk). In 45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 170, pp. 3:1-3:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{wootters:LIPIcs.MFCS.2020.3,
  author =	{Wootters, Mary},
  title =	{{List-Decodability of Structured Ensembles of Codes}},
  booktitle =	{45th International Symposium on Mathematical Foundations of Computer Science (MFCS 2020)},
  pages =	{3:1--3:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-159-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{170},
  editor =	{Esparza, Javier and Kr\'{a}l', Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2020.3},
  URN =		{urn:nbn:de:0030-drops-126742},
  doi =		{10.4230/LIPIcs.MFCS.2020.3},
  annote =	{Keywords: Error Correcting Codes, List-Decoding}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2020.9
Bounds for List-Decoding and List-Recovery of Random Linear Codes

Authors: Venkatesan Guruswami, Ray Li, Jonathan Mosheiff, Nicolas Resch, Shashwat Silas, and Mary Wootters

Published in: LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)

Abstract
A family of error-correcting codes is list-decodable from error fraction p if, for every code in the family, the number of codewords in any Hamming ball of fractional radius p is less than some integer L that is independent of the code length. It is said to be list-recoverable for input list size 𝓁 if for every sufficiently large subset of codewords (of size L or more), there is a coordinate where the codewords take more than 𝓁 values. The parameter L is said to be the "list size" in either case. The capacity, i.e., the largest possible rate for these notions as the list size L → ∞, is known to be 1-h_q(p) for list-decoding, and 1-log_q 𝓁 for list-recovery, where q is the alphabet size of the code family. In this work, we study the list size of random linear codes for both list-decoding and list-recovery as the rate approaches capacity. We show the following claims hold with high probability over the choice of the code (below q is the alphabet size, and ε > 0 is the gap to capacity). - A random linear code of rate 1 - log_q(𝓁) - ε requires list size L ≥ 𝓁^{Ω(1/ε)} for list-recovery from input list size 𝓁. This is surprisingly in contrast to completely random codes, where L = O(𝓁/ε) suffices w.h.p. - A random linear code of rate 1 - h_q(p) - ε requires list size L ≥ ⌊ {h_q(p)/ε+0.99}⌋ for list-decoding from error fraction p, when ε is sufficiently small. - A random binary linear code of rate 1 - h₂(p) - ε is list-decodable from average error fraction p with list size with L ≤ ⌊ {h₂(p)/ε}⌋ + 2. (The average error version measures the average Hamming distance of the codewords from the center of the Hamming ball, instead of the maximum distance as in list-decoding.) The second and third results together precisely pin down the list sizes for binary random linear codes for both list-decoding and average-radius list-decoding to three possible values. Our lower bounds follow by exhibiting an explicit subset of codewords so that this subset - or some symbol-wise permutation of it - lies in a random linear code with high probability. This uses a recent characterization of (Mosheiff, Resch, Ron-Zewi, Silas, Wootters, 2019) of configurations of codewords that are contained in random linear codes. Our upper bound follows from a refinement of the techniques of (Guruswami, Håstad, Sudan, Zuckerman, 2002) and strengthens a previous result of (Li, Wootters, 2018), which applied to list-decoding rather than average-radius list-decoding.
Cite as

Venkatesan Guruswami, Ray Li, Jonathan Mosheiff, Nicolas Resch, Shashwat Silas, and Mary Wootters. Bounds for List-Decoding and List-Recovery of Random Linear Codes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{guruswami_et_al:LIPIcs.APPROX/RANDOM.2020.9,
  author =	{Guruswami, Venkatesan and Li, Ray and Mosheiff, Jonathan and Resch, Nicolas and Silas, Shashwat and Wootters, Mary},
  title =	{{Bounds for List-Decoding and List-Recovery of Random Linear Codes}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)},
  pages =	{9:1--9:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-164-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{176},
  editor =	{Byrka, Jaros{\l}aw and Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.9},
  URN =		{urn:nbn:de:0030-drops-126126},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2020.9},
  annote =	{Keywords: list-decoding, list-recovery, random linear codes, coding theory}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2019.59
Minimizing and Computing the Inverse Geodesic Length on Trees

Authors: Serge Gaspers and Joshua Lau

Published in: LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

Abstract
For any fixed measure H that maps graphs to real numbers, the MinH problem is defined as follows: given a graph G, an integer k, and a target tau, is there a set S of k vertices that can be deleted, so that H(G - S) is at most tau? In this paper, we consider the MinH problem on trees. We call H balanced on trees if, whenever G is a tree, there is an optimal choice of S such that the components of G - S have sizes bounded by a polynomial in n / k. We show that MinH on trees is Fixed-Parameter Tractable (FPT) for parameter n / k, and furthermore, can be solved in subexponential time, and polynomial space, whenever H is additive, balanced on trees, and computable in polynomial time. A particular measure of interest is the Inverse Geodesic Length (IGL), which is used to gauge the efficiency and connectedness of a graph. It is defined as the sum of inverse distances between every two vertices: IGL(G) = sum_{{u,v} subseteq V} 1/d_G(u,v). While MinIGL is W[1]-hard for parameter treewidth, and cannot be solved in 2^{o(k + n + m)} time, even on bipartite graphs with n vertices and m edges, the complexity status of the problem remains open in the case where G is a tree. We show that IGL is balanced on trees, to give a 2^O((n log n)^(5/6)) time, polynomial space algorithm. The distance distribution of G is the sequence {a_i} describing the number of vertex pairs distance i apart in G: a_i = |{{u, v}: d_G(u, v) = i}|. Given only the distance distribution, one can easily determine graph parameters such as diameter, Wiener index, and particularly, the IGL. We show that the distance distribution of a tree can be computed in O(n log^2 n) time by reduction to polynomial multiplication. We also extend the result to graphs with small treewidth by showing that the first p values of the distance distribution can be computed in 2^(O(tw(G))) n^(1 + epsilon) sqrt(p) time, and the entire distance distribution can be computed in 2^(O(tw(G))) n^{1 + epsilon} time, when the diameter of G is O(n^epsilon') for every epsilon' > 0.
Cite as

Serge Gaspers and Joshua Lau. Minimizing and Computing the Inverse Geodesic Length on Trees. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 59:1-59:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{gaspers_et_al:LIPIcs.ISAAC.2019.59,
  author =	{Gaspers, Serge and Lau, Joshua},
  title =	{{Minimizing and Computing the Inverse Geodesic Length on Trees}},
  booktitle =	{30th International Symposium on Algorithms and Computation (ISAAC 2019)},
  pages =	{59:1--59:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-130-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{149},
  editor =	{Lu, Pinyan and Zhang, Guochuan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.59},
  URN =		{urn:nbn:de:0030-drops-115555},
  doi =		{10.4230/LIPIcs.ISAAC.2019.59},
  annote =	{Keywords: Trees, Treewidth, Fixed-Parameter Tractability, Inverse Geodesic Length, Vertex deletion, Polynomial multiplication, Distance distribution}
}
Document
RANDOM
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.38
Lifted Multiplicity Codes and the Disjoint Repair Group Property

Authors: Ray Li and Mary Wootters

Published in: LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)

Abstract
Lifted Reed Solomon Codes (Guo, Kopparty, Sudan 2013) were introduced in the context of locally correctable and testable codes. They are multivariate polynomials whose restriction to any line is a codeword of a Reed-Solomon code. We consider a generalization of their construction, which we call lifted multiplicity codes. These are multivariate polynomial codes whose restriction to any line is a codeword of a multiplicity code (Kopparty, Saraf, Yekhanin 2014). We show that lifted multiplicity codes have a better trade-off between redundancy and a notion of locality called the t-disjoint-repair-group property than previously known constructions. More precisely, we show that, for t <=sqrt{N}, lifted multiplicity codes with length N and redundancy O(t^{0.585} sqrt{N}) have the property that any symbol of a codeword can be reconstructed in t different ways, each using a disjoint subset of the other coordinates. This gives the best known trade-off for this problem for any super-constant t < sqrt{N}. We also give an alternative analysis of lifted Reed Solomon codes using dual codes, which may be of independent interest.
Cite as

Ray Li and Mary Wootters. Lifted Multiplicity Codes and the Disjoint Repair Group Property. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 38:1-38:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{li_et_al:LIPIcs.APPROX-RANDOM.2019.38,
  author =	{Li, Ray and Wootters, Mary},
  title =	{{Lifted Multiplicity Codes and the Disjoint Repair Group Property}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{38:1--38:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.},
  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.2019.38},
  URN =		{urn:nbn:de:0030-drops-112539},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.38},
  annote =	{Keywords: Lifted codes, Multiplicity codes, Disjoint repair group property, PIR code, Coding theory}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2019.74
Enumeration of Preferred Extensions in Almost Oriented Digraphs

Authors: Serge Gaspers and Ray Li

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract
In this paper, we present enumeration algorithms to list all preferred extensions of an argumentation framework. This task is equivalent to enumerating all maximal semikernels of a directed graph. For directed graphs on n vertices, all preferred extensions can be enumerated in O^*(3^{n/3}) time and there are directed graphs with Omega(3^{n/3}) preferred extensions. We give faster enumeration algorithms for directed graphs with at most 0.8004 * n vertices occurring in 2-cycles. In particular, for oriented graphs (digraphs with no 2-cycles) one of our algorithms runs in time O(1.2321^n), and we show that there are oriented graphs with Omega(3^{n/6}) > Omega(1.2009^n) preferred extensions. A combination of three algorithms leads to the fastest enumeration times for various proportions of the number of vertices in 2-cycles. The most innovative one is a new 2-stage sampling algorithm, combined with a new parameterized enumeration algorithm, analyzed with a combination of the recent monotone local search technique (STOC 2016) and an extension thereof (ICALP 2017).
Cite as

Serge Gaspers and Ray Li. Enumeration of Preferred Extensions in Almost Oriented Digraphs. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 74:1-74:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{gaspers_et_al:LIPIcs.MFCS.2019.74,
  author =	{Gaspers, Serge and Li, Ray},
  title =	{{Enumeration of Preferred Extensions in Almost Oriented Digraphs}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{74:1--74:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.74},
  URN =		{urn:nbn:de:0030-drops-110188},
  doi =		{10.4230/LIPIcs.MFCS.2019.74},
  annote =	{Keywords: abstract argumentation, exact algorithms, exponential time algorithms, parameterized algorithms, enumeration algorithms, semikernels in digraphs}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.50
Improved List-Decodability of Random Linear Binary Codes

Authors: Ray Li and Mary Wootters

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

Abstract
There has been a great deal of work establishing that random linear codes are as list-decodable as uniformly random codes, in the sense that a random linear binary code of rate 1 - H(p) - epsilon is (p,O(1/epsilon))-list-decodable with high probability. In this work, we show that such codes are (p, H(p)/epsilon + 2)-list-decodable with high probability, for any p in (0, 1/2) and epsilon > 0. In addition to improving the constant in known list-size bounds, our argument - which is quite simple - works simultaneously for all values of p, while previous works obtaining L = O(1/epsilon) patched together different arguments to cover different parameter regimes. Our approach is to strengthen an existential argument of (Guruswami, Håstad, Sudan and Zuckerman, IEEE Trans. IT, 2002) to hold with high probability. To complement our upper bound for random linear binary codes, we also improve an argument of (Guruswami, Narayanan, IEEE Trans. IT, 2014) to obtain a tight lower bound of 1/epsilon on the list size of uniformly random binary codes; this implies that random linear binary codes are in fact more list-decodable than uniformly random binary codes, in the sense that the list sizes are strictly smaller. To demonstrate the applicability of these techniques, we use them to (a) obtain more information about the distribution of list sizes of random linear binary codes and (b) to prove a similar result for random linear rank-metric codes.
Cite as

Ray Li and Mary Wootters. Improved List-Decodability of Random Linear Binary Codes. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 50:1-50:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{li_et_al:LIPIcs.APPROX-RANDOM.2018.50,
  author =	{Li, Ray and Wootters, Mary},
  title =	{{Improved List-Decodability of Random Linear Binary Codes}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{50:1--50:19},
  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.2018.50},
  URN =		{urn:nbn:de:0030-drops-94547},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.50},
  annote =	{Keywords: List-decoding, Random linear codes, Rank-metric codes}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2017.47
Efficiently Decodable Codes for the Binary Deletion Channel

Authors: Venkatesan Guruswami and Ray Li

Published in: LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)

Abstract
In the random deletion channel, each bit is deleted independently with probability p. For the random deletion channel, the existence of codes of rate (1-p)/9, and thus bounded away from 0 for any p < 1, has been known. We give an explicit construction with polynomial time encoding and deletion correction algorithms with rate c_0 (1-p) for an absolute constant c_0 > 0.
Cite as

Venkatesan Guruswami and Ray Li. Efficiently Decodable Codes for the Binary Deletion Channel. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 47:1-47:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{guruswami_et_al:LIPIcs.APPROX-RANDOM.2017.47,
  author =	{Guruswami, Venkatesan and Li, Ray},
  title =	{{Efficiently Decodable Codes for the Binary Deletion Channel}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{47:1--47:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.},
  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.2017.47},
  URN =		{urn:nbn:de:0030-drops-75964},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.47},
  annote =	{Keywords: Coding theory, Combinatorics, Synchronization errors, Channel capacity}
}
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