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Invited Talk

DOI: 10.4230/LIPIcs.ICDT.2024.2

How Database Theory Helps Teach Relational Queries in Database Education (Invited Talk)

Authors: Sudeepa Roy, Amir Gilad, Yihao Hu, Hanze Meng, Zhengjie Miao, Kristin Stephens-Martinez, and Jun Yang

Published in: LIPIcs, Volume 290, 27th International Conference on Database Theory (ICDT 2024)

Abstract

Data analytics skills have become an indispensable part of any education that seeks to prepare its students for the modern workforce. Essential in this skill set is the ability to work with structured relational data. Relational queries are based on logic and may be declarative in nature, posing new challenges to novices and students. Manual teaching resources being limited and enrollment growing rapidly, automated tools that help students debug queries and explain errors are potential game-changers in database education. We present a suite of tools built on the foundations of database theory that has been used by over 1600 students in database classes at Duke University, showcasing a high-impact application of database theory in database education.

Cite as

Sudeepa Roy, Amir Gilad, Yihao Hu, Hanze Meng, Zhengjie Miao, Kristin Stephens-Martinez, and Jun Yang. How Database Theory Helps Teach Relational Queries in Database Education (Invited Talk). In 27th International Conference on Database Theory (ICDT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 290, pp. 2:1-2:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{roy_et_al:LIPIcs.ICDT.2024.2,
  author =	{Roy, Sudeepa and Gilad, Amir and Hu, Yihao and Meng, Hanze and Miao, Zhengjie and Stephens-Martinez, Kristin and Yang, Jun},
  title =	{{How Database Theory Helps Teach Relational Queries in Database Education}},
  booktitle =	{27th International Conference on Database Theory (ICDT 2024)},
  pages =	{2:1--2:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-312-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{290},
  editor =	{Cormode, Graham and Shekelyan, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2024.2},
  URN =		{urn:nbn:de:0030-drops-197841},
  doi =		{10.4230/LIPIcs.ICDT.2024.2},
  annote =	{Keywords: Query Debugging, SQL, Relational Algebra, Relational Calculus, Database Education, Boolean Provenance}
}

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Track A: Algorithms, Complexity and Games

DOI: 10.4230/LIPIcs.ICALP.2022.51

One-Pass Additive-Error Subset Selection for 𝓁_p Subspace Approximation

Authors: Amit Deshpande and Rameshwar Pratap

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

Abstract

We consider the problem of subset selection for 𝓁_p subspace approximation, that is, to efficiently find a small subset of data points such that solving the problem optimally for this subset gives a good approximation to solving the problem optimally for the original input. Previously known subset selection algorithms based on volume sampling and adaptive sampling [Deshpande and Varadarajan, 2007], for the general case of p ∈ [1, ∞), require multiple passes over the data. In this paper, we give a one-pass subset selection with an additive approximation guarantee for 𝓁_p subspace approximation, for any p ∈ [1, ∞). Earlier subset selection algorithms that give a one-pass multiplicative (1+ε) approximation work under the special cases. Cohen et al. [Michael B. Cohen et al., 2017] gives a one-pass subset section that offers multiplicative (1+ε) approximation guarantee for the special case of 𝓁₂ subspace approximation. Mahabadi et al. [Sepideh Mahabadi et al., 2020] gives a one-pass noisy subset selection with (1+ε) approximation guarantee for 𝓁_p subspace approximation when p ∈ {1, 2}. Our subset selection algorithm gives a weaker, additive approximation guarantee, but it works for any p ∈ [1, ∞).

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Amit Deshpande and Rameshwar Pratap. One-Pass Additive-Error Subset Selection for 𝓁_p Subspace Approximation. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 51:1-51:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{deshpande_et_al:LIPIcs.ICALP.2022.51,
  author =	{Deshpande, Amit and Pratap, Rameshwar},
  title =	{{One-Pass Additive-Error Subset Selection for 𝓁\underlinep Subspace Approximation}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{51:1--51:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.51},
  URN =		{urn:nbn:de:0030-drops-163924},
  doi =		{10.4230/LIPIcs.ICALP.2022.51},
  annote =	{Keywords: Subspace approximation, streaming algorithms, low-rank approximation, adaptive sampling, volume sampling, subset selection}
}

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DOI: 10.4230/LIPIcs.SWAT.2022.23

Almost Shortest Paths with Near-Additive Error in Weighted Graphs

Authors: Michael Elkin, Yuval Gitlitz, and Ofer Neiman

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

Abstract

Let G = (V,E,w) be a weighted undirected graph with n vertices and m edges, and fix a set of s sources S ⊆ V. We study the problem of computing almost shortest paths (ASP) for all pairs in S × V in both classical centralized and parallel (PRAM) models of computation. Consider the regime of multiplicative approximation of 1+ε, for an arbitrarily small constant ε > 0 (henceforth (1+ε)-ASP for S × V). In this regime existing centralized algorithms require Ω(min{|E|s,n^ω}) time, where ω < 2.372 is the matrix multiplication exponent. Existing PRAM algorithms with polylogarithmic depth (aka time) require work Ω(min{|E|s,n^ω}). In a bold attempt to achieve centralized time close to the lower bound of m + n s, Cohen [Edith Cohen, 2000] devised an algorithm which, in addition to the multiplicative stretch of 1+ε, allows also additive error of β ⋅ W_{max}, where W_{max} is the maximum edge weight in G (assuming that the minimum edge weight is 1), and β = (log n)^{O((log 1/ρ)/ρ)} is polylogarithmic in n. It also depends on the (possibly) arbitrarily small parameter ρ > 0 that determines the running time O((m + ns)n^ρ) of the algorithm. The tradeoff of [Edith Cohen, 2000] was improved in [M. Elkin, 2001], whose algorithm has similar approximation guarantee and running time, but its β is (1/ρ)^{O((log 1/ρ)/ρ)}. However, the latter algorithm produces distance estimates rather than actual approximate shortest paths. Also, the additive terms in [Edith Cohen, 2000; M. Elkin, 2001] depend linearly on a possibly quite large global maximum edge weight W_{max}. In the current paper we significantly improve this state of affairs. Our centralized algorithm has running time O((m+ ns)n^ρ), and its PRAM counterpart has polylogarithmic depth and work O((m + ns)n^ρ), for an arbitrarily small constant ρ > 0. For a pair (s,v) ∈ S× V, it provides a path of length d̂(s,v) that satisfies d̂(s,v) ≤ (1+ε)d_G(s,v) + β ⋅ W(s,v), where W(s,v) is the weight of the heaviest edge on some shortest s-v path. Hence our additive term depends linearly on a local maximum edge weight, as opposed to the global maximum edge weight in [Edith Cohen, 2000; M. Elkin, 2001]. Finally, our β = (1/ρ)^{O(1/ρ)}, i.e., it is significantly smaller than in [Edith Cohen, 2000; M. Elkin, 2001]. We also extend a centralized algorithm of Dor et al. [D. Dor et al., 2000]. For a parameter κ = 1,2,…, this algorithm provides for unweighted graphs a purely additive approximation of 2(κ -1) for all pairs shortest paths (APASP) in time Õ(n^{2+1/κ}). Within the same running time, our algorithm for weighted graphs provides a purely additive error of 2(κ - 1) W(u,v), for every vertex pair (u,v) ∈ binom(V,2), with W(u,v) defined as above. On the way to these results we devise a suite of novel constructions of spanners, emulators and hopsets.

Cite as

Michael Elkin, Yuval Gitlitz, and Ofer Neiman. Almost Shortest Paths with Near-Additive Error in Weighted Graphs. In 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 227, pp. 23:1-23:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{elkin_et_al:LIPIcs.SWAT.2022.23,
  author =	{Elkin, Michael and Gitlitz, Yuval and Neiman, Ofer},
  title =	{{Almost Shortest Paths with Near-Additive Error in Weighted Graphs}},
  booktitle =	{18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022)},
  pages =	{23:1--23:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-236-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{227},
  editor =	{Czumaj, Artur and Xin, Qin},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SWAT.2022.23},
  URN =		{urn:nbn:de:0030-drops-161833},
  doi =		{10.4230/LIPIcs.SWAT.2022.23},
  annote =	{Keywords: spanners, hopset, shortest paths, PRAM, distance oracles}
}

Document

DOI: 10.4230/LIPIcs.CCC.2021.13

Barriers for Recent Methods in Geodesic Optimization

Authors: W. Cole Franks and Philipp Reichenbach

Published in: LIPIcs, Volume 200, 36th Computational Complexity Conference (CCC 2021)

Abstract

We study a class of optimization problems including matrix scaling, matrix balancing, multidimensional array scaling, operator scaling, and tensor scaling that arise frequently in theory and in practice. Some of these problems, such as matrix and array scaling, are convex in the Euclidean sense, but others such as operator scaling and tensor scaling are geodesically convex on a different Riemannian manifold. Trust region methods, which include box-constrained Newton’s method, are known to produce high precision solutions very quickly for matrix scaling and matrix balancing (Cohen et. al., FOCS 2017, Allen-Zhu et. al. FOCS 2017), and result in polynomial time algorithms for some geodesically convex problems like operator scaling (Garg et. al. STOC 2018, Bürgisser et. al. FOCS 2019). One is led to ask whether these guarantees also hold for multidimensional array scaling and tensor scaling. We show that this is not the case by exhibiting instances with exponential diameter bound: we construct polynomial-size instances of 3-dimensional array scaling and 3-tensor scaling whose approximate solutions all have doubly exponential condition number. Moreover, we study convex-geometric notions of complexity known as margin and gap, which are used to bound the running times of all existing optimization algorithms for such problems. We show that margin and gap are exponentially small for several problems including array scaling, tensor scaling and polynomial scaling. Our results suggest that it is impossible to prove polynomial running time bounds for tensor scaling based on diameter bounds alone. Therefore, our work motivates the search for analogues of more sophisticated algorithms, such as interior point methods, for geodesically convex optimization that do not rely on polynomial diameter bounds.

Cite as

W. Cole Franks and Philipp Reichenbach. Barriers for Recent Methods in Geodesic Optimization. In 36th Computational Complexity Conference (CCC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 200, pp. 13:1-13:54, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{franks_et_al:LIPIcs.CCC.2021.13,
  author =	{Franks, W. Cole and Reichenbach, Philipp},
  title =	{{Barriers for Recent Methods in Geodesic Optimization}},
  booktitle =	{36th Computational Complexity Conference (CCC 2021)},
  pages =	{13:1--13:54},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-193-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{200},
  editor =	{Kabanets, Valentine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2021.13},
  URN =		{urn:nbn:de:0030-drops-142879},
  doi =		{10.4230/LIPIcs.CCC.2021.13},
  annote =	{Keywords: Geodesically Convex Optimization, Weight Margin, Moment Polytope, Diameter Bounds, Tensor Scaling, Matrix Scaling}
}

Document

Invited Paper

DOI: 10.4230/LIPIcs.ITP.2021.1

The CakeML Project’s Quest for Ever Stronger Correctness Theorems (Invited Paper)

Authors: Magnus O. Myreen

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

Abstract

The CakeML project has developed a proof-producing code generation mechanism for the HOL4 theorem prover, a verified compiler for ML and, using these, a number of verified application programs that are proved correct down to the machine code that runs them (in some cases, even down to the underlying hardware). The purpose of this extended abstract is to tell the story of the project and to point curious readers to publications where they can read more about specific contributions.

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Magnus O. Myreen. The CakeML Project’s Quest for Ever Stronger Correctness Theorems (Invited Paper). In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 1:1-1:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{myreen:LIPIcs.ITP.2021.1,
  author =	{Myreen, Magnus O.},
  title =	{{The CakeML Project’s Quest for Ever Stronger Correctness Theorems}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{1:1--1:10},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.1},
  URN =		{urn:nbn:de:0030-drops-138963},
  doi =		{10.4230/LIPIcs.ITP.2021.1},
  annote =	{Keywords: Program verification, interactive theorem proving}
}

Document

DOI: 10.4230/LIPIcs.ITP.2021.21

Proving Quantum Programs Correct

Authors: Kesha Hietala, Robert Rand, Shih-Han Hung, Liyi Li, and Michael Hicks

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

Abstract

As quantum computing progresses steadily from theory into practice, programmers will face a common problem: How can they be sure that their code does what they intend it to do? This paper presents encouraging results in the application of mechanized proof to the domain of quantum programming in the context of the SQIR development. It verifies the correctness of a range of a quantum algorithms including Grover’s algorithm and quantum phase estimation, a key component of Shor’s algorithm. In doing so, it aims to highlight both the successes and challenges of formal verification in the quantum context and motivate the theorem proving community to target quantum computing as an application domain.

Cite as

Kesha Hietala, Robert Rand, Shih-Han Hung, Liyi Li, and Michael Hicks. Proving Quantum Programs Correct. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 21:1-21:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{hietala_et_al:LIPIcs.ITP.2021.21,
  author =	{Hietala, Kesha and Rand, Robert and Hung, Shih-Han and Li, Liyi and Hicks, Michael},
  title =	{{Proving Quantum Programs Correct}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{21:1--21:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.21},
  URN =		{urn:nbn:de:0030-drops-139160},
  doi =		{10.4230/LIPIcs.ITP.2021.21},
  annote =	{Keywords: Formal Verification, Quantum Computing, Proof Engineering}
}

Document

DOI: 10.4230/LIPIcs.ITP.2021.30

Specifying Message Formats with Contiguity Types

Authors: Konrad Slind

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

Abstract

We introduce Contiguity Types, a formalism for network message formats, aimed especially at self-describing formats. Contiguity types provide an intermediate layer between programming language data structures and messages, offering a helpful setting from which to automatically generate decoders, filters, and message generators. The syntax and semantics of contiguity types are defined and used to prove the correctness of a matching algorithm which has the flavour of a parser generator. The matcher has been used to enforce semantic well-formedness conditions on complex message formats for an autonomous unmanned avionics system.

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Konrad Slind. Specifying Message Formats with Contiguity Types. In 12th International Conference on Interactive Theorem Proving (ITP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 193, pp. 30:1-30:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{slind:LIPIcs.ITP.2021.30,
  author =	{Slind, Konrad},
  title =	{{Specifying Message Formats with Contiguity Types}},
  booktitle =	{12th International Conference on Interactive Theorem Proving (ITP 2021)},
  pages =	{30:1--30:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-188-7},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{193},
  editor =	{Cohen, Liron and Kaliszyk, Cezary},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2021.30},
  URN =		{urn:nbn:de:0030-drops-139252},
  doi =		{10.4230/LIPIcs.ITP.2021.30},
  annote =	{Keywords: Logic, verification, formal language theory, message format languages}
}

Document

DOI: 10.4230/LIPIcs.ITCS.2021.62

Relative Lipschitzness in Extragradient Methods and a Direct Recipe for Acceleration

Authors: Michael B. Cohen, Aaron Sidford, and Kevin Tian

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

Abstract

We show that standard extragradient methods (i.e. mirror prox [Arkadi Nemirovski, 2004] and dual extrapolation [Yurii Nesterov, 2007]) recover optimal accelerated rates for first-order minimization of smooth convex functions. To obtain this result we provide fine-grained characterization of the convergence rates of extragradient methods for solving monotone variational inequalities in terms of a natural condition we call relative Lipschitzness. We further generalize this framework to handle local and randomized notions of relative Lipschitzness and thereby recover rates for box-constrained 𝓁_∞ regression based on area convexity [Jonah Sherman, 2017] and complexity bounds achieved by accelerated (randomized) coordinate descent [Zeyuan {Allen Zhu} et al., 2016; Yurii Nesterov and Sebastian U. Stich, 2017] for smooth convex function minimization.

Cite as

Michael B. Cohen, Aaron Sidford, and Kevin Tian. Relative Lipschitzness in Extragradient Methods and a Direct Recipe for Acceleration. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 62:1-62:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{cohen_et_al:LIPIcs.ITCS.2021.62,
  author =	{Cohen, Michael B. and Sidford, Aaron and Tian, Kevin},
  title =	{{Relative Lipschitzness in Extragradient Methods and a Direct Recipe for Acceleration}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{62:1--62:18},
  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.2021.62},
  URN =		{urn:nbn:de:0030-drops-136011},
  doi =		{10.4230/LIPIcs.ITCS.2021.62},
  annote =	{Keywords: Variational inequalities, minimax optimization, acceleration, 𝓁\underline∞ regression}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.FSTTCS.2020.3

Convex Optimization and Dynamic Data Structure (Invited Talk)

Authors: Yin Tat Lee

Published in: LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)

Abstract

In the last three years, there are many breakthroughs in optimization such as nearly quadratic time algorithms for bipartite matching, linear programming algorithms that are as fast as Ax = b. All of these algorithms are based on a careful combination of optimization techniques and dynamic data structures. In this talk, we will explain the framework underlying all the recent breakthroughs. Joint work with Jan van den Brand, Michael B. Cohen, Sally Dong, Haotian Jiang, Tarun Kathuria, Danupon Nanongkai, Swati Padmanabhan, Richard Peng, Thatchaphol Saranurak, Aaron Sidford, Zhao Song, Di Wang, Sam Chiu-wai Wong, Guanghao Ye, Qiuyi Zhang.

Cite as

Yin Tat Lee. Convex Optimization and Dynamic Data Structure (Invited Talk). In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{lee:LIPIcs.FSTTCS.2020.3,
  author =	{Lee, Yin Tat},
  title =	{{Convex Optimization and Dynamic Data Structure}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{3:1--3:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Saxena, Nitin and Simon, Sunil},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.3},
  URN =		{urn:nbn:de:0030-drops-132440},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.3},
  annote =	{Keywords: Convex Optimization, Dynamic Data Structure}
}

Document

DOI: 10.4230/LIPIcs.IPEC.2019.9

C-Planarity Testing of Embedded Clustered Graphs with Bounded Dual Carving-Width

Authors: Giordano Da Lozzo, David Eppstein, Michael T. Goodrich, and Siddharth Gupta

Published in: LIPIcs, Volume 148, 14th International Symposium on Parameterized and Exact Computation (IPEC 2019)

Abstract

For a clustered graph, i.e, a graph whose vertex set is recursively partitioned into clusters, the C-Planarity Testing problem asks whether it is possible to find a planar embedding of the graph and a representation of each cluster as a region homeomorphic to a closed disk such that 1. the subgraph induced by each cluster is drawn in the interior of the corresponding disk, 2. each edge intersects any disk at most once, and 3. the nesting between clusters is reflected by the representation, i.e., child clusters are properly contained in their parent cluster. The computational complexity of this problem, whose study has been central to the theory of graph visualization since its introduction in 1995 [Feng, Cohen, and Eades, Planarity for clustered graphs, ESA'95], has only been recently settled [Fulek and Tóth, Atomic Embeddability, Clustered Planarity, and Thickenability, to appear at SODA'20]. Before such a breakthrough, the complexity question was still unsolved even when the graph has a prescribed planar embedding, i.e, for embedded clustered graphs. We show that the C-Planarity Testing problem admits a single-exponential single-parameter FPT algorithm for embedded clustered graphs, when parameterized by the carving-width of the dual graph of the input. This is the first FPT algorithm for this long-standing open problem with respect to a single notable graph-width parameter. Moreover, in the general case, the polynomial dependency of our FPT algorithm is smaller than the one of the algorithm by Fulek and Tóth. To further strengthen the relevance of this result, we show that the C-Planarity Testing problem retains its computational complexity when parameterized by several other graph-width parameters, which may potentially lead to faster algorithms.

Cite as

Giordano Da Lozzo, David Eppstein, Michael T. Goodrich, and Siddharth Gupta. C-Planarity Testing of Embedded Clustered Graphs with Bounded Dual Carving-Width. In 14th International Symposium on Parameterized and Exact Computation (IPEC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 148, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{dalozzo_et_al:LIPIcs.IPEC.2019.9,
  author =	{Da Lozzo, Giordano and Eppstein, David and Goodrich, Michael T. and Gupta, Siddharth},
  title =	{{C-Planarity Testing of Embedded Clustered Graphs with Bounded Dual Carving-Width}},
  booktitle =	{14th International Symposium on Parameterized and Exact Computation (IPEC 2019)},
  pages =	{9:1--9:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-129-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{148},
  editor =	{Jansen, Bart M. P. and Telle, Jan Arne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.IPEC.2019.9},
  URN =		{urn:nbn:de:0030-drops-114705},
  doi =		{10.4230/LIPIcs.IPEC.2019.9},
  annote =	{Keywords: Clustered planarity, carving-width, non-crossing partitions, FPT}
}

Document

DOI: 10.4230/LIPIcs.ESA.2019.33

Efficient Approximation Schemes for Uniform-Cost Clustering Problems in Planar Graphs

Authors: Vincent Cohen-Addad, Marcin Pilipczuk, and Michał Pilipczuk

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract

We consider the k-Median problem on planar graphs: given an edge-weighted planar graph G, a set of clients C subseteq V(G), a set of facilities F subseteq V(G), and an integer parameter k, the task is to find a set of at most k facilities whose opening minimizes the total connection cost of clients, where each client contributes to the cost with the distance to the closest open facility. We give two new approximation schemes for this problem: - FPT Approximation Scheme: for any epsilon>0, in time 2^{O(k epsilon^{-3} log (k epsilon^{-1}))}* n^O(1) we can compute a solution that has connection cost at most (1+epsilon) times the optimum, with high probability. - Efficient Bicriteria Approximation Scheme: for any epsilon>0, in time 2^{O(epsilon^{-5} log (epsilon^{-1}))}* n^O(1) we can compute a set of at most (1+epsilon)k facilities whose opening yields connection cost at most (1+epsilon) times the optimum connection cost for opening at most k facilities, with high probability. As a direct corollary of the second result we obtain an EPTAS for Uniform Facility Location on planar graphs, with same running time. Our main technical tool is a new construction of a "coreset for facilities" for k-Median in planar graphs: we show that in polynomial time one can compute a subset of facilities F_0 subseteq F of size k * (log n/epsilon)^O(epsilon^{-3}) with a guarantee that there is a (1+epsilon)-approximate solution contained in F_0.

Cite as

Vincent Cohen-Addad, Marcin Pilipczuk, and Michał Pilipczuk. Efficient Approximation Schemes for Uniform-Cost Clustering Problems in Planar Graphs. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 33:1-33:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{cohenaddad_et_al:LIPIcs.ESA.2019.33,
  author =	{Cohen-Addad, Vincent and Pilipczuk, Marcin and Pilipczuk, Micha{\l}},
  title =	{{Efficient Approximation Schemes for Uniform-Cost Clustering Problems in Planar Graphs}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{33:1--33:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019.33},
  URN =		{urn:nbn:de:0030-drops-111543},
  doi =		{10.4230/LIPIcs.ESA.2019.33},
  annote =	{Keywords: k-Median, Facility Location, Planar Graphs, Approximation Scheme}
}

Document

DOI: 10.4230/LIPIcs.ESA.2019.66

Min-Cost Flow in Unit-Capacity Planar Graphs

Authors: Adam Karczmarz and Piotr Sankowski

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract

In this paper we give an O~((nm)^(2/3) log C) time algorithm for computing min-cost flow (or min-cost circulation) in unit capacity planar multigraphs where edge costs are integers bounded by C. For planar multigraphs, this improves upon the best known algorithms for general graphs: the O~(m^(10/7) log C) time algorithm of Cohen et al. [SODA 2017], the O(m^(3/2) log(nC)) time algorithm of Gabow and Tarjan [SIAM J. Comput. 1989] and the O~(sqrt(n) m log C) time algorithm of Lee and Sidford [FOCS 2014]. In particular, our result constitutes the first known fully combinatorial algorithm that breaks the Omega(m^(3/2)) time barrier for min-cost flow problem in planar graphs. To obtain our result we first give a very simple successive shortest paths based scaling algorithm for unit-capacity min-cost flow problem that does not explicitly operate on dual variables. This algorithm also runs in O~(m^(3/2) log C) time for general graphs, and, to the best of our knowledge, it has not been described before. We subsequently show how to implement this algorithm faster on planar graphs using well-established tools: r-divisions and efficient algorithms for computing (shortest) paths in so-called dense distance graphs.

Cite as

Adam Karczmarz and Piotr Sankowski. Min-Cost Flow in Unit-Capacity Planar Graphs. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 66:1-66:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{karczmarz_et_al:LIPIcs.ESA.2019.66,
  author =	{Karczmarz, Adam and Sankowski, Piotr},
  title =	{{Min-Cost Flow in Unit-Capacity Planar Graphs}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{66:1--66:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola 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.2019.66},
  URN =		{urn:nbn:de:0030-drops-111878},
  doi =		{10.4230/LIPIcs.ESA.2019.66},
  annote =	{Keywords: minimum-cost flow, minimum-cost circulation, planar graphs}
}

Document

DOI: 10.4230/LIPIcs.CCC.2019.9

Typically-Correct Derandomization for Small Time and Space

Authors: William M. Hoza

Published in: LIPIcs, Volume 137, 34th Computational Complexity Conference (CCC 2019)

Abstract

Suppose a language L can be decided by a bounded-error randomized algorithm that runs in space S and time n * poly(S). We give a randomized algorithm for L that still runs in space O(S) and time n * poly(S) that uses only O(S) random bits; our algorithm has a low failure probability on all but a negligible fraction of inputs of each length. As an immediate corollary, there is a deterministic algorithm for L that runs in space O(S) and succeeds on all but a negligible fraction of inputs of each length. We also give several other complexity-theoretic applications of our technique.

Cite as

William M. Hoza. Typically-Correct Derandomization for Small Time and Space. In 34th Computational Complexity Conference (CCC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 137, pp. 9:1-9:39, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{hoza:LIPIcs.CCC.2019.9,
  author =	{Hoza, William M.},
  title =	{{Typically-Correct Derandomization for Small Time and Space}},
  booktitle =	{34th Computational Complexity Conference (CCC 2019)},
  pages =	{9:1--9:39},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-116-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{137},
  editor =	{Shpilka, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2019.9},
  URN =		{urn:nbn:de:0030-drops-108317},
  doi =		{10.4230/LIPIcs.CCC.2019.9},
  annote =	{Keywords: Derandomization, pseudorandomness, space complexity}
}

Document

DOI: 10.4230/LIPIcs.CCC.2019.16

Near-Optimal Pseudorandom Generators for Constant-Depth Read-Once Formulas

Authors: Dean Doron, Pooya Hatami, and William M. Hoza

Published in: LIPIcs, Volume 137, 34th Computational Complexity Conference (CCC 2019)

Abstract

We give an explicit pseudorandom generator (PRG) for read-once AC^0, i.e., constant-depth read-once formulas over the basis {wedge, vee, neg} with unbounded fan-in. The seed length of our PRG is O~(log(n/epsilon)). Previously, PRGs with near-optimal seed length were known only for the depth-2 case [Gopalan et al., 2012]. For a constant depth d > 2, the best prior PRG is a recent construction by Forbes and Kelley with seed length O~(log^2 n + log n log(1/epsilon)) for the more general model of constant-width read-once branching programs with arbitrary variable order [Michael A. Forbes and Zander Kelley, 2018]. Looking beyond read-once AC^0, we also show that our PRG fools read-once AC^0[oplus] with seed length O~(t + log(n/epsilon)), where t is the number of parity gates in the formula. Our construction follows Ajtai and Wigderson’s approach of iterated pseudorandom restrictions [Ajtai and Wigderson, 1989]. We assume by recursion that we already have a PRG for depth-d AC^0 formulas. To fool depth-(d + 1) AC^0 formulas, we use the given PRG, combined with a small-bias distribution and almost k-wise independence, to sample a pseudorandom restriction. The analysis of Forbes and Kelley [Michael A. Forbes and Zander Kelley, 2018] shows that our restriction approximately preserves the expectation of the formula. The crux of our work is showing that after poly(log log n) independent applications of our pseudorandom restriction, the formula simplifies in the sense that every gate other than the output has only polylog n remaining children. Finally, as the last step, we use a recent PRG by Meka, Reingold, and Tal [Meka et al., 2019] to fool this simpler formula.

Cite as

Dean Doron, Pooya Hatami, and William M. Hoza. Near-Optimal Pseudorandom Generators for Constant-Depth Read-Once Formulas. In 34th Computational Complexity Conference (CCC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 137, pp. 16:1-16:34, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{doron_et_al:LIPIcs.CCC.2019.16,
  author =	{Doron, Dean and Hatami, Pooya and Hoza, William M.},
  title =	{{Near-Optimal Pseudorandom Generators for Constant-Depth Read-Once Formulas}},
  booktitle =	{34th Computational Complexity Conference (CCC 2019)},
  pages =	{16:1--16:34},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-116-0},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{137},
  editor =	{Shpilka, Amir},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2019.16},
  URN =		{urn:nbn:de:0030-drops-108382},
  doi =		{10.4230/LIPIcs.CCC.2019.16},
  annote =	{Keywords: Pseudorandom generators, Constant-depth formulas, Explicit constructions}
}

Document

DOI: 10.4230/OASIcs.SOSA.2018.15

Simple Analyses of the Sparse Johnson-Lindenstrauss Transform

Authors: Michael B. Cohen, T.S. Jayram, and Jelani Nelson

Published in: OASIcs, Volume 61, 1st Symposium on Simplicity in Algorithms (SOSA 2018)

Abstract

For every n-point subset X of Euclidean space and target distortion 1+eps for 0<eps<1, the Sparse Johnson Lindenstrauss Transform (SJLT) of (Kane, Nelson, J. ACM 2014) provides a linear dimensionality-reducing map f:X-->l_2^m where f(x) = Ax for A a matrix with m rows where (1) m = O((log n)/eps^2), and (2) each column of A is sparse, having only O(eps m) non-zero entries. Though the constructions given for such A in (Kane, Nelson, J. ACM 2014) are simple, the analyses are not, employing intricate combinatorial arguments. We here give two simple alternative proofs of their main result, involving no delicate combinatorics. One of these proofs has already been tested pedagogically, requiring slightly under forty minutes by the third author at a casual pace to cover all details in a blackboard course lecture.

Cite as

Michael B. Cohen, T.S. Jayram, and Jelani Nelson. Simple Analyses of the Sparse Johnson-Lindenstrauss Transform. In 1st Symposium on Simplicity in Algorithms (SOSA 2018). Open Access Series in Informatics (OASIcs), Volume 61, pp. 15:1-15:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{cohen_et_al:OASIcs.SOSA.2018.15,
  author =	{Cohen, Michael B. and Jayram, T.S. and Nelson, Jelani},
  title =	{{Simple Analyses of the Sparse Johnson-Lindenstrauss Transform}},
  booktitle =	{1st Symposium on Simplicity in Algorithms (SOSA 2018)},
  pages =	{15:1--15:9},
  series =	{Open Access Series in Informatics (OASIcs)},
  ISBN =	{978-3-95977-064-4},
  ISSN =	{2190-6807},
  year =	{2018},
  volume =	{61},
  editor =	{Seidel, Raimund},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/OASIcs.SOSA.2018.15},
  URN =		{urn:nbn:de:0030-drops-83056},
  doi =		{10.4230/OASIcs.SOSA.2018.15},
  annote =	{Keywords: dimensionality reduction, Johnson-Lindenstrauss, Sparse Johnson-Lindenstrauss Transform}
}

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