28 Search Results for "Johnson, Daniel D."


Document
Anonymity-Preserving Space Partitions

Authors: Úrsula Hébert-Johnson, Chinmay Sonar, Subhash Suri, and Vaishali Surianarayanan

Published in: LIPIcs, Volume 212, 32nd International Symposium on Algorithms and Computation (ISAAC 2021)


Abstract
We consider a multidimensional space partitioning problem, which we call Anonymity-Preserving Partition. Given a set P of n points in ℝ^d and a collection H of m axis-parallel hyperplanes, the hyperplanes of H partition the space into an arrangement A(H) of rectangular cells. Given an integer parameter t > 0, we call a cell C in this arrangement deficient if 0 < |C ∩ P| < t; that is, the cell contains at least one but fewer than t data points of P. Our problem is to remove the minimum number of hyperplanes from H so that there are no deficient cells. We show that the problem is NP-complete for all dimensions d ≥ 2. We present a polynomial-time d-approximation algorithm, for any fixed d, and we also show that the problem can be solved exactly in time (2d-0.924)^k m^O(1) + O(n), where k is the solution size. The one-dimensional case of the problem, where all hyperplanes are parallel, can be solved optimally in polynomial time, but we show that a related Interval Anonymity problem is NP-complete even in one dimension.

Cite as

Úrsula Hébert-Johnson, Chinmay Sonar, Subhash Suri, and Vaishali Surianarayanan. Anonymity-Preserving Space Partitions. In 32nd International Symposium on Algorithms and Computation (ISAAC 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 212, pp. 32:1-32:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2021)


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@InProceedings{hebertjohnson_et_al:LIPIcs.ISAAC.2021.32,
  author =	{H\'{e}bert-Johnson, \'{U}rsula and Sonar, Chinmay and Suri, Subhash and Surianarayanan, Vaishali},
  title =	{{Anonymity-Preserving Space Partitions}},
  booktitle =	{32nd International Symposium on Algorithms and Computation (ISAAC 2021)},
  pages =	{32:1--32:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-214-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{212},
  editor =	{Ahn, Hee-Kap and Sadakane, Kunihiko},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2021.32},
  URN =		{urn:nbn:de:0030-drops-154654},
  doi =		{10.4230/LIPIcs.ISAAC.2021.32},
  annote =	{Keywords: Anonymity, Hitting Set, LP, Constant Approximation, Fixed-Parameter Tractable, Space Partitions, Parameterized Complexity}
}
Document
Media Exposition
How to Make a CG Video (Media Exposition)

Authors: Aaron T. Becker and Sándor P. Fekete

Published in: LIPIcs, Volume 164, 36th International Symposium on Computational Geometry (SoCG 2020)


Abstract
In this video we describe why producing a Computational Geometry video is a good idea, what it takes to make one, and how to actually do it. This includes a guide for the overall process, a number of examples, and a variety of tips and tricks.

Cite as

Aaron T. Becker and Sándor P. Fekete. How to Make a CG Video (Media Exposition). In 36th International Symposium on Computational Geometry (SoCG 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 164, pp. 74:1-74:6, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{becker_et_al:LIPIcs.SoCG.2020.74,
  author =	{Becker, Aaron T. and Fekete, S\'{a}ndor P.},
  title =	{{How to Make a CG Video}},
  booktitle =	{36th International Symposium on Computational Geometry (SoCG 2020)},
  pages =	{74:1--74:6},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-143-6},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{164},
  editor =	{Cabello, Sergio and Chen, Danny Z.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2020.74},
  URN =		{urn:nbn:de:0030-drops-122328},
  doi =		{10.4230/LIPIcs.SoCG.2020.74},
  annote =	{Keywords: Videos, animation, education, SoCG Multimedia}
}
Document
Detecting Transcriptomic Structural Variants in Heterogeneous Contexts via the Multiple Compatible Arrangements Problem

Authors: Yutong Qiu, Cong Ma, Han Xie, and Carl Kingsford

Published in: LIPIcs, Volume 143, 19th International Workshop on Algorithms in Bioinformatics (WABI 2019)


Abstract
Transcriptomic structural variants (TSVs) - large-scale transcriptome sequence change due to structural variation - are common, especially in cancer. Detecting TSVs is a challenging computational problem. Sample heterogeneity (including differences between alleles in diploid organisms) is a critical confounding factor when identifying TSVs. To improve TSV detection in heterogeneous RNA-seq samples, we introduce the Multiple Compatible Arrangement Problem (MCAP), which seeks k genome rearrangements to maximize the number of reads that are concordant with at least one rearrangement. This directly models the situation of a heterogeneous or diploid sample. We prove that MCAP is NP-hard and provide a 1/4-approximation algorithm for k=1 and a 3/4-approximation algorithm for the diploid case (k=2) assuming an oracle for k=1. Combining these, we obtain a 3/16-approximation algorithm for MCAP when k=2 (without an oracle). We also present an integer linear programming formulation for general k. We characterize the graph structures that require k>1 to satisfy all edges and show such structures are prevalent in cancer samples. We evaluate our algorithms on 381 TCGA samples and 2 cancer cell lines and show improved performance compared to the state-of-the-art TSV-calling tool, SQUID.

Cite as

Yutong Qiu, Cong Ma, Han Xie, and Carl Kingsford. Detecting Transcriptomic Structural Variants in Heterogeneous Contexts via the Multiple Compatible Arrangements Problem. In 19th International Workshop on Algorithms in Bioinformatics (WABI 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 143, pp. 18:1-18:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{qiu_et_al:LIPIcs.WABI.2019.18,
  author =	{Qiu, Yutong and Ma, Cong and Xie, Han and Kingsford, Carl},
  title =	{{Detecting Transcriptomic Structural Variants in Heterogeneous Contexts via the Multiple Compatible Arrangements Problem}},
  booktitle =	{19th International Workshop on Algorithms in Bioinformatics (WABI 2019)},
  pages =	{18:1--18:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-123-8},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{143},
  editor =	{Huber, Katharina T. and Gusfield, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2019.18},
  URN =		{urn:nbn:de:0030-drops-110483},
  doi =		{10.4230/LIPIcs.WABI.2019.18},
  annote =	{Keywords: transcriptomic structural variation, integer linear programming, heterogeneity}
}
Document
A Sub-Exponential FPT Algorithm and a Polynomial Kernel for Minimum Directed Bisection on Semicomplete Digraphs

Authors: Jayakrishnan Madathil, Roohani Sharma, and Meirav Zehavi

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


Abstract
Given an n-vertex digraph D and a non-negative integer k, the Minimum Directed Bisection problem asks if the vertices of D can be partitioned into two parts, say L and R, such that |L| and |R| differ by at most 1 and the number of arcs from R to L is at most k. This problem, in general, is W-hard as it is known to be NP-hard even when k=0. We investigate the parameterized complexity of this problem on semicomplete digraphs. We show that Minimum Directed Bisection on semicomplete digraphs is one of a handful of problems that admit sub-exponential time fixed-parameter tractable algorithms. That is, we show that the problem admits a 2^{O(sqrt{k} log k)}n^{O(1)} time algorithm on semicomplete digraphs. We also show that Minimum Directed Bisection admits a polynomial kernel on semicomplete digraphs. To design the kernel, we use (n,k,k^2)-splitters. To the best of our knowledge, this is the first time such pseudorandom objects have been used in the design of kernels. We believe that the framework of designing kernels using splitters could be applied to more problems that admit sub-exponential time algorithms via chromatic coding. To complement the above mentioned results, we prove that Minimum Directed Bisection is NP-hard on semicomplete digraphs, but polynomial time solvable on tournaments.

Cite as

Jayakrishnan Madathil, Roohani Sharma, and Meirav Zehavi. A Sub-Exponential FPT Algorithm and a Polynomial Kernel for Minimum Directed Bisection on Semicomplete Digraphs. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 28:1-28:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{madathil_et_al:LIPIcs.MFCS.2019.28,
  author =	{Madathil, Jayakrishnan and Sharma, Roohani and Zehavi, Meirav},
  title =	{{A Sub-Exponential FPT Algorithm and a Polynomial Kernel for Minimum Directed Bisection on Semicomplete Digraphs}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{28:1--28:14},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.28},
  URN =		{urn:nbn:de:0030-drops-109721},
  doi =		{10.4230/LIPIcs.MFCS.2019.28},
  annote =	{Keywords: bisection, semicomplete digraph, tournament, fpt algorithm, chromatic coding, polynomial kernel, splitters}
}
Document
Reducing the Domination Number of Graphs via Edge Contractions

Authors: Esther Galby, Paloma T. Lima, and Bernard Ries

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


Abstract
In this paper, we study the following problem: given a connected graph G, can we reduce the domination number of G by at least one using k edge contractions, for some fixed integer k >= 0? We show that for k <= 2, the problem is coNP-hard. We further prove that for k=1, the problem is W[1]-hard parameterized by the size of a minimum dominating set plus the mim-width of the input graph, and that it remains NP-hard when restricted to P_9-free graphs, bipartite graphs and {C_3,...,C_{l}}-free graphs for any l >= 3. Finally, we show that for any k >= 1, the problem is polynomial-time solvable for P_5-free graphs and that it can be solved in FPT-time and XP-time when parameterized by tree-width and mim-width, respectively.

Cite as

Esther Galby, Paloma T. Lima, and Bernard Ries. Reducing the Domination Number of Graphs via Edge Contractions. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 41:1-41:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{galby_et_al:LIPIcs.MFCS.2019.41,
  author =	{Galby, Esther and Lima, Paloma T. and Ries, Bernard},
  title =	{{Reducing the Domination Number of Graphs via Edge Contractions}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{41:1--41:13},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.41},
  URN =		{urn:nbn:de:0030-drops-109856},
  doi =		{10.4230/LIPIcs.MFCS.2019.41},
  annote =	{Keywords: domination number, blocker problem, graph classes}
}
Document
Approximate Counting CSP Seen from the Other Side

Authors: Andrei A. Bulatov and Stanislav Živný

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


Abstract
In this paper we study the complexity of counting Constraint Satisfaction Problems (CSPs) of the form #CSP(C,-), in which the goal is, given a relational structure A from a class C of structures and an arbitrary structure B, to find the number of homomorphisms from A to B. Flum and Grohe showed that #CSP(C,-) is solvable in polynomial time if C has bounded treewidth [FOCS'02]. Building on the work of Grohe [JACM'07] on decision CSPs, Dalmau and Jonsson then showed that, if C is a recursively enumerable class of relational structures of bounded arity, then assuming FPT != #W[1], there are no other cases of #CSP(C,-) solvable exactly in polynomial time (or even fixed-parameter time) [TCS'04]. We show that, assuming FPT != W[1] (under randomised parametrised reductions) and for C satisfying certain general conditions, #CSP(C,-) is not solvable even approximately for C of unbounded treewidth; that is, there is no fixed parameter tractable (and thus also not fully polynomial) randomised approximation scheme for #CSP(C,-). In particular, our condition generalises the case when C is closed under taking minors.

Cite as

Andrei A. Bulatov and Stanislav Živný. Approximate Counting CSP Seen from the Other Side. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 60:1-60:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{bulatov_et_al:LIPIcs.MFCS.2019.60,
  author =	{Bulatov, Andrei A. and \v{Z}ivn\'{y}, Stanislav},
  title =	{{Approximate Counting CSP Seen from the Other Side}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{60:1--60:14},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.60},
  URN =		{urn:nbn:de:0030-drops-110041},
  doi =		{10.4230/LIPIcs.MFCS.2019.60},
  annote =	{Keywords: constraint satisfaction, approximate counting, homomorphisms}
}
Document
On the Mortality Problem: From Multiplicative Matrix Equations to Linear Recurrence Sequences and Beyond

Authors: Paul C. Bell, Igor Potapov, and Pavel Semukhin

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


Abstract
We consider the following variant of the Mortality Problem: given k x k matrices A_1, A_2, ...,A_{t}, does there exist nonnegative integers m_1, m_2, ...,m_t such that the product A_1^{m_1} A_2^{m_2} * ... * A_{t}^{m_{t}} is equal to the zero matrix? It is known that this problem is decidable when t <= 2 for matrices over algebraic numbers but becomes undecidable for sufficiently large t and k even for integral matrices. In this paper, we prove the first decidability results for t>2. We show as one of our central results that for t=3 this problem in any dimension is Turing equivalent to the well-known Skolem problem for linear recurrence sequences. Our proof relies on the Primary Decomposition Theorem for matrices that was not used to show decidability results in matrix semigroups before. As a corollary we obtain that the above problem is decidable for t=3 and k <= 3 for matrices over algebraic numbers and for t=3 and k=4 for matrices over real algebraic numbers. Another consequence is that the set of triples (m_1,m_2,m_3) for which the equation A_1^{m_1} A_2^{m_2} A_3^{m_3} equals the zero matrix is equal to a finite union of direct products of semilinear sets. For t=4 we show that the solution set can be non-semilinear, and thus it seems unlikely that there is a direct connection to the Skolem problem. However we prove that the problem is still decidable for upper-triangular 2 x 2 rational matrices by employing powerful tools from transcendence theory such as Baker’s theorem and S-unit equations.

Cite as

Paul C. Bell, Igor Potapov, and Pavel Semukhin. On the Mortality Problem: From Multiplicative Matrix Equations to Linear Recurrence Sequences and Beyond. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 83:1-83:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{bell_et_al:LIPIcs.MFCS.2019.83,
  author =	{Bell, Paul C. and Potapov, Igor and Semukhin, Pavel},
  title =	{{On the Mortality Problem: From Multiplicative Matrix Equations to Linear Recurrence Sequences and Beyond}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{83:1--83:15},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.83},
  URN =		{urn:nbn:de:0030-drops-110279},
  doi =		{10.4230/LIPIcs.MFCS.2019.83},
  annote =	{Keywords: Linear recurrence sequences, Skolem’s problem, mortality problem, matrix equations, primary decomposition theorem, Baker’s theorem}
}
Document
Stronger Connections Between Circuit Analysis and Circuit Lower Bounds, via PCPs of Proximity

Authors: Lijie Chen and R. Ryan Williams

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


Abstract
We considerably sharpen the known connections between circuit-analysis algorithms and circuit lower bounds, show intriguing equivalences between the analysis of weak circuits and (apparently difficult) circuits, and provide strong new lower bounds for approximately computing Boolean functions with depth-two neural networks and related models. - We develop approaches to proving THR o THR lower bounds (a notorious open problem), by connecting algorithmic analysis of THR o THR to the provably weaker circuit classes THR o MAJ and MAJ o MAJ, where exponential lower bounds have long been known. More precisely, we show equivalences between algorithmic analysis of THR o THR and these weaker classes. The epsilon-error CAPP problem asks to approximate the acceptance probability of a given circuit to within additive error epsilon; it is the "canonical" derandomization problem. We show: - There is a non-trivial (2^n/n^{omega(1)} time) 1/poly(n)-error CAPP algorithm for poly(n)-size THR o THR circuits if and only if there is such an algorithm for poly(n)-size MAJ o MAJ. - There is a delta > 0 and a non-trivial SAT (delta-error CAPP) algorithm for poly(n)-size THR o THR circuits if and only if there is such an algorithm for poly(n)-size THR o MAJ. Similar results hold for depth-d linear threshold circuits and depth-d MAJORITY circuits. These equivalences are proved via new simulations of THR circuits by circuits with MAJ gates. - We strengthen the connection between non-trivial derandomization (non-trivial CAPP algorithms) for a circuit class C, and circuit lower bounds against C. Previously, [Ben-Sasson and Viola, ICALP 2014] (following [Williams, STOC 2010]) showed that for any polynomial-size class C closed under projections, non-trivial (2^{n}/n^{omega(1)} time) CAPP for OR_{poly(n)} o AND_{3} o C yields NEXP does not have C circuits. We apply Probabilistic Checkable Proofs of Proximity in a new way to show it would suffice to have a non-trivial CAPP algorithm for either XOR_2 o C, AND_2 o C or OR_2 o C. - A direct corollary of the first two bullets is that NEXP does not have THR o THR circuits would follow from either: - a non-trivial delta-error CAPP (or SAT) algorithm for poly(n)-size THR o MAJ circuits, or - a non-trivial 1/poly(n)-error CAPP algorithm for poly(n)-size MAJ o MAJ circuits. - Applying the above machinery, we extend lower bounds for depth-two neural networks and related models [R. Williams, CCC 2018] to weak approximate computations of Boolean functions. For example, for arbitrarily small epsilon > 0, we prove there are Boolean functions f computable in nondeterministic n^{log n} time such that (for infinitely many n) every polynomial-size depth-two neural network N on n inputs (with sign or ReLU activation) must satisfy max_{x in {0,1}^n}|N(x)-f(x)|>1/2-epsilon. That is, short linear combinations of ReLU gates fail miserably at computing f to within close precision. Similar results are proved for linear combinations of ACC o THR circuits, and linear combinations of low-degree F_p polynomials. These results constitute further progress towards THR o THR lower bounds.

Cite as

Lijie Chen and R. Ryan Williams. Stronger Connections Between Circuit Analysis and Circuit Lower Bounds, via PCPs of Proximity. In 34th Computational Complexity Conference (CCC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 137, pp. 19:1-19:43, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{chen_et_al:LIPIcs.CCC.2019.19,
  author =	{Chen, Lijie and Williams, R. Ryan},
  title =	{{Stronger Connections Between Circuit Analysis and Circuit Lower Bounds, via PCPs of Proximity}},
  booktitle =	{34th Computational Complexity Conference (CCC 2019)},
  pages =	{19:1--19:43},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2019.19},
  URN =		{urn:nbn:de:0030-drops-108419},
  doi =		{10.4230/LIPIcs.CCC.2019.19},
  annote =	{Keywords: PCP of Proximity, Circuit Lower Bounds, Derandomization, Threshold Circuits, ReLU}
}
Document
Pearl
Finally, a Polymorphic Linear Algebra Language (Pearl)

Authors: Amir Shaikhha and Lionel Parreaux

Published in: LIPIcs, Volume 134, 33rd European Conference on Object-Oriented Programming (ECOOP 2019)


Abstract
Many different data analytics tasks boil down to linear algebra primitives. In practice, for each different type of workload, data scientists use a particular specialised library. In this paper, we present Pilatus, a polymorphic iterative linear algebra language, applicable to various types of data analytics workloads. The design of this domain-specific language (DSL) is inspired by both mathematics and programming languages: its basic constructs are borrowed from abstract algebra, whereas the key technology behind its polymorphic design uses the tagless final approach (a.k.a. polymorphic embedding/object algebras). This design enables us to change the behaviour of arithmetic operations to express matrix algebra, graph algorithms, logical probabilistic programs, and differentiable programs. Crucially, the polymorphic design of Pilatus allows us to use multi-stage programming and rewrite-based optimisation to recover the performance of specialised code, supporting fixed sized matrices, algebraic optimisations, and fusion.

Cite as

Amir Shaikhha and Lionel Parreaux. Finally, a Polymorphic Linear Algebra Language (Pearl). In 33rd European Conference on Object-Oriented Programming (ECOOP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 134, pp. 25:1-25:29, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{shaikhha_et_al:LIPIcs.ECOOP.2019.25,
  author =	{Shaikhha, Amir and Parreaux, Lionel},
  title =	{{Finally, a Polymorphic Linear Algebra Language}},
  booktitle =	{33rd European Conference on Object-Oriented Programming (ECOOP 2019)},
  pages =	{25:1--25:29},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-111-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{134},
  editor =	{Donaldson, Alastair F.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2019.25},
  URN =		{urn:nbn:de:0030-drops-108172},
  doi =		{10.4230/LIPIcs.ECOOP.2019.25},
  annote =	{Keywords: Linear Algebra, Domain-Specific Languages, Tagless Final, Polymorphic Embedding, Object Algebra, Multi-Stage Programming, Graph Processing, Probabilistic Programming, Automatic Differentiation}
}
Document
Tool Insights Paper
MagpieBridge: A General Approach to Integrating Static Analyses into IDEs and Editors (Tool Insights Paper)

Authors: Linghui Luo, Julian Dolby, and Eric Bodden

Published in: LIPIcs, Volume 134, 33rd European Conference on Object-Oriented Programming (ECOOP 2019)


Abstract
In the past, many static analyses have been created in academia, but only a few of them have found widespread use in industry. Those analyses which are adopted by developers usually have IDE support in the form of plugins, without which developers have no convenient mechanism to use the analysis. Hence, the key to making static analyses more accessible to developers is to integrate the analyses into IDEs and editors. However, integrating static analyses into IDEs is non-trivial: different IDEs have different UI workflows and APIs, expertise in those matters is required to write such plugins, and analysis experts are not typically familiar with doing this. As a result, especially in academia, most analysis tools are headless and only have command-line interfaces. To make static analyses more usable, we propose MagpieBridge - a general approach to integrating static analyses into IDEs and editors. MagpieBridge reduces the mxn complexity problem of integrating m analyses into n IDEs to m+n complexity because each analysis and type of plugin need be done just once for MagpieBridge itself. We demonstrate our approach by integrating two existing analyses, Ariadne and CogniCrypt, into IDEs; these two analyses illustrate the generality of MagpieBridge, as they are based on different program analysis frameworks - WALA and Soot respectively - for different application areas - machine learning and security - and different programming languages - Python and Java. We show further generality of MagpieBridge by using multiple popular IDEs and editors, such as Eclipse, IntelliJ, PyCharm, Jupyter, Sublime Text and even Emacs and Vim.

Cite as

Linghui Luo, Julian Dolby, and Eric Bodden. MagpieBridge: A General Approach to Integrating Static Analyses into IDEs and Editors (Tool Insights Paper). In 33rd European Conference on Object-Oriented Programming (ECOOP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 134, pp. 21:1-21:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{luo_et_al:LIPIcs.ECOOP.2019.21,
  author =	{Luo, Linghui and Dolby, Julian and Bodden, Eric},
  title =	{{MagpieBridge: A General Approach to Integrating Static Analyses into IDEs and Editors}},
  booktitle =	{33rd European Conference on Object-Oriented Programming (ECOOP 2019)},
  pages =	{21:1--21:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-111-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{134},
  editor =	{Donaldson, Alastair F.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2019.21},
  URN =		{urn:nbn:de:0030-drops-108139},
  doi =		{10.4230/LIPIcs.ECOOP.2019.21},
  annote =	{Keywords: IDE, Tool Support, Static Analysis, Language Server Protocol}
}
Document
Garbage-Free Abstract Interpretation Through Abstract Reference Counting

Authors: Noah Van Es, Quentin Stiévenart, and Coen De Roover

Published in: LIPIcs, Volume 134, 33rd European Conference on Object-Oriented Programming (ECOOP 2019)


Abstract
Abstract garbage collection is the application of garbage collection to an abstract interpreter. Existing work has shown that abstract garbage collection can improve both the interpreter’s precision and performance. Current approaches rely on heuristics to decide when to apply abstract garbage collection. Garbage will build up and impact precision and performance when the collection is applied infrequently, while too frequent applications will bring about their own performance overhead. A balance between these tradeoffs is often difficult to strike. We propose a new approach to cope with the buildup of garbage in the results of an abstract interpreter. Our approach is able to eliminate all garbage, therefore obtaining the maximum precision and performance benefits of abstract garbage collection. At the same time, our approach does not require frequent heap traversals, and therefore adds little to the interpreters’s running time. The core of our approach uses reference counting to detect and eliminate garbage as soon as it arises. However, reference counting cannot deal with cycles, and we show that cycles are much more common in an abstract interpreter than in its concrete counterpart. To alleviate this problem, our approach detects cycles and employs reference counting at the level of strongly connected components. While this technique in general works for any system that uses reference counting, we argue that it works particularly well for an abstract interpreter. In fact, we show formally that for the continuation store, where most of the cycles occur, the cycle detection technique only requires O(1) amortized operations per continuation push. We present our approach formally, and provide a proof-of-concept implementation in the Scala-AM framework. We empirically show our approach achieves both the optimal precision and significantly better performance compared to existing approaches to abstract garbage collection.

Cite as

Noah Van Es, Quentin Stiévenart, and Coen De Roover. Garbage-Free Abstract Interpretation Through Abstract Reference Counting. In 33rd European Conference on Object-Oriented Programming (ECOOP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 134, pp. 10:1-10:33, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{vanes_et_al:LIPIcs.ECOOP.2019.10,
  author =	{Van Es, Noah and Sti\'{e}venart, Quentin and De Roover, Coen},
  title =	{{Garbage-Free Abstract Interpretation Through Abstract Reference Counting}},
  booktitle =	{33rd European Conference on Object-Oriented Programming (ECOOP 2019)},
  pages =	{10:1--10:33},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-111-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{134},
  editor =	{Donaldson, Alastair F.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2019.10},
  URN =		{urn:nbn:de:0030-drops-108022},
  doi =		{10.4230/LIPIcs.ECOOP.2019.10},
  annote =	{Keywords: abstract interpretation, abstract garbage collection, reference counting}
}
Document
Transient Typechecks Are (Almost) Free

Authors: Richard Roberts, Stefan Marr, Michael Homer, and James Noble

Published in: LIPIcs, Volume 134, 33rd European Conference on Object-Oriented Programming (ECOOP 2019)


Abstract
Transient gradual typing imposes run-time type tests that typically cause a linear slowdown. This performance impact discourages the use of type annotations because adding types to a program makes the program slower. A virtual machine can employ standard just-in-time optimizations to reduce the overhead of transient checks to near zero. These optimizations can give gradually-typed languages performance comparable to state-of-the-art dynamic languages, so programmers can add types to their code without affecting their programs' performance.

Cite as

Richard Roberts, Stefan Marr, Michael Homer, and James Noble. Transient Typechecks Are (Almost) Free. In 33rd European Conference on Object-Oriented Programming (ECOOP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 134, pp. 5:1-5:28, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{roberts_et_al:LIPIcs.ECOOP.2019.5,
  author =	{Roberts, Richard and Marr, Stefan and Homer, Michael and Noble, James},
  title =	{{Transient Typechecks Are (Almost) Free}},
  booktitle =	{33rd European Conference on Object-Oriented Programming (ECOOP 2019)},
  pages =	{5:1--5:28},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-111-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{134},
  editor =	{Donaldson, Alastair F.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ECOOP.2019.5},
  URN =		{urn:nbn:de:0030-drops-107974},
  doi =		{10.4230/LIPIcs.ECOOP.2019.5},
  annote =	{Keywords: dynamic type checking, gradual types, optional types, Grace, Moth, object-oriented programming}
}
Document
On the Qubit Routing Problem

Authors: Alexander Cowtan, Silas Dilkes, Ross Duncan, Alexandre Krajenbrink, Will Simmons, and Seyon Sivarajah

Published in: LIPIcs, Volume 135, 14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019)


Abstract
We introduce a new architecture-agnostic methodology for mapping abstract quantum circuits to realistic quantum computing devices with restricted qubit connectivity, as implemented by Cambridge Quantum Computing’s t|ket> compiler. We present empirical results showing the effectiveness of this method in terms of reducing two-qubit gate depth and two-qubit gate count, compared to other implementations.

Cite as

Alexander Cowtan, Silas Dilkes, Ross Duncan, Alexandre Krajenbrink, Will Simmons, and Seyon Sivarajah. On the Qubit Routing Problem. In 14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 135, pp. 5:1-5:32, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{cowtan_et_al:LIPIcs.TQC.2019.5,
  author =	{Cowtan, Alexander and Dilkes, Silas and Duncan, Ross and Krajenbrink, Alexandre and Simmons, Will and Sivarajah, Seyon},
  title =	{{On the Qubit Routing Problem}},
  booktitle =	{14th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2019)},
  pages =	{5:1--5:32},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-112-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{135},
  editor =	{van Dam, Wim and Man\v{c}inska, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TQC.2019.5},
  URN =		{urn:nbn:de:0030-drops-103972},
  doi =		{10.4230/LIPIcs.TQC.2019.5},
  annote =	{Keywords: Quantum Computing, Qubit routing, Compilation}
}
Document
Multimedia Exposition
Geometric Realizations of the 3D Associahedron (Multimedia Exposition)

Authors: Satyan L. Devadoss, Daniel D. Johnson, Justin Lee, and Jackson Warley

Published in: LIPIcs, Volume 99, 34th International Symposium on Computational Geometry (SoCG 2018)


Abstract
The associahedron is a convex polytope whose 1-skeleton is isomorphic to the flip graph of a convex polygon. There exists an elegant geometric realization of the associahedron, using the remarkable theory of secondary polytopes, based on the geometry of the underlying polygon. We present an interactive application that visualizes this correspondence in the 3D case.

Cite as

Satyan L. Devadoss, Daniel D. Johnson, Justin Lee, and Jackson Warley. Geometric Realizations of the 3D Associahedron (Multimedia Exposition). In 34th International Symposium on Computational Geometry (SoCG 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 99, pp. 75:1-75:4, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


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@InProceedings{devadoss_et_al:LIPIcs.SoCG.2018.75,
  author =	{Devadoss, Satyan L. and Johnson, Daniel D. and Lee, Justin and Warley, Jackson},
  title =	{{Geometric Realizations of the 3D Associahedron}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{75:1--75:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Speckmann, Bettina and T\'{o}th, Csaba D.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2018.75},
  URN =		{urn:nbn:de:0030-drops-87886},
  doi =		{10.4230/LIPIcs.SoCG.2018.75},
  annote =	{Keywords: associahedron, secondary polytope, realization}
}
Document
Recognizing Graphs Close to Bipartite Graphs

Authors: Marthe Bonamy, Konrad K. Dabrowski, Carl Feghali, Matthew Johnson, and Daniël Paulusma

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


Abstract
We continue research into a well-studied family of problems that ask if the vertices of a graph can be partitioned into sets A and B, where A is an independent set and B induces a graph from some specified graph class G. We let G be the class of k-degenerate graphs. The problem is known to be polynomial-time solvable if k=0 (bipartite graphs) and NP-complete if k=1 (near-bipartite graphs) even for graphs of diameter 4, as shown by Yang and Yuan, who also proved polynomial-time solvability for graphs of diameter 2. We show that recognizing near-bipartite graphs of diameter 3 is NP-complete resolving their open problem. To answer another open problem, we consider graphs of maximum degree D on n vertices. We show how to find A and B in O(n) time for k=1 and D=3, and in O(n^2) time for k >= 2 and D >= 4. These results also provide an algorithmic version of a result of Catlin [JCTB, 1979] and enable us to complete the complexity classification of another problem: finding a path in the vertex colouring reconfiguration graph between two given k-colourings of a graph of bounded maximum degree.

Cite as

Marthe Bonamy, Konrad K. Dabrowski, Carl Feghali, Matthew Johnson, and Daniël Paulusma. Recognizing Graphs Close to Bipartite Graphs. In 42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 83, pp. 70:1-70:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)


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@InProceedings{bonamy_et_al:LIPIcs.MFCS.2017.70,
  author =	{Bonamy, Marthe and Dabrowski, Konrad K. and Feghali, Carl and Johnson, Matthew and Paulusma, Dani\"{e}l},
  title =	{{Recognizing Graphs Close to Bipartite Graphs}},
  booktitle =	{42nd International Symposium on Mathematical Foundations of Computer Science (MFCS 2017)},
  pages =	{70:1--70:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-046-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{83},
  editor =	{Larsen, Kim G. and Bodlaender, Hans L. and Raskin, Jean-Francois},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2017.70},
  URN =		{urn:nbn:de:0030-drops-80740},
  doi =		{10.4230/LIPIcs.MFCS.2017.70},
  annote =	{Keywords: degenerate graphs, near-bipartite graphs, reconfiguration graphs}
}
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