TY - CONF AB - The minimum cut problem for an undirected edge-weighted graph asks us to divide its set of nodes into two blocks while minimizing the weighted sum of the cut edges. In this paper, we engineer the fastest known exact algorithm for the problem. State-of-the-art algorithms like the algorithm of Padberg and Rinaldi or the algorithm of Nagamochi, Ono and Ibaraki identify edges that can be contracted to reduce the graph size such that at least one minimum cut is maintained in the contracted graph. Our algorithm achieves improvements in running time over these algorithms by a multitude of techniques. First, we use a recently developed fast and parallel inexact minimum cut algorithm to obtain a better bound for the problem. Afterwards, we use reductions that depend on this bound to reduce the size of the graph much faster than previously possible. We use improved data structures to further lower the running time of our algorithm. Additionally, we parallelize the contraction routines of Nagamochi et al. . Overall, we arrive at a system that significantly outperforms the fastest state-of-the-art solvers for the exact minimum cut problem. AU - Henzinger, Monika H AU - Noe, Alexander AU - Schulz, Christian ID - 11851 SN - 978-1-7281-1247-3 T2 - 33rd International Parallel and Distributed Processing Symposium TI - Shared-memory exact minimum cuts ER - TY - CONF AB - We present the first sublinear-time algorithm that can compute the edge connectivity λ of a network exactly on distributed message-passing networks (the CONGEST model), as long as the network contains no multi-edge. We present the first sublinear-time algorithm for a distributed message-passing network sto compute its edge connectivity λ exactly in the CONGEST model, as long as there are no parallel edges. Our algorithm takes Õ(n1−1/353D1/353+n1−1/706) time to compute λ and a cut of cardinality λ with high probability, where n and D are the number of nodes and the diameter of the network, respectively, and Õ hides polylogarithmic factors. This running time is sublinear in n (i.e. Õ(n1−є)) whenever D is. Previous sublinear-time distributed algorithms can solve this problem either (i) exactly only when λ=O(n1/8−є) [Thurimella PODC’95; Pritchard, Thurimella, ACM Trans. Algorithms’11; Nanongkai, Su, DISC’14] or (ii) approximately [Ghaffari, Kuhn, DISC’13; Nanongkai, Su, DISC’14]. To achieve this we develop and combine several new techniques. First, we design the first distributed algorithm that can compute a k-edge connectivity certificate for any k=O(n1−є) in time Õ(√nk+D). The previous sublinear-time algorithm can do so only when k=o(√n) [Thurimella PODC’95]. In fact, our algorithm can be turned into the first parallel algorithm with polylogarithmic depth and near-linear work. Previous near-linear work algorithms are essentially sequential and previous polylogarithmic-depth algorithms require Ω(mk) work in the worst case (e.g. [Karger, Motwani, STOC’93]). Second, we show that by combining the recent distributed expander decomposition technique of [Chang, Pettie, Zhang, SODA’19] with techniques from the sequential deterministic edge connectivity algorithm of [Kawarabayashi, Thorup, STOC’15], we can decompose the network into a sublinear number of clusters with small average diameter and without any mincut separating a cluster (except the “trivial” ones). This leads to a simplification of the Kawarabayashi-Thorup framework (except that we are randomized while they are deterministic). This might make this framework more useful in other models of computation. Finally, by extending the tree packing technique from [Karger STOC’96], we can find the minimum cut in time proportional to the number of components. As a byproduct of this technique, we obtain an Õ(n)-time algorithm for computing exact minimum cut for weighted graphs. AU - Daga, Mohit AU - Henzinger, Monika H AU - Nanongkai, Danupon AU - Saranurak, Thatchaphol ID - 11865 SN - 0737-8017 T2 - Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing TI - Distributed edge connectivity in sublinear time ER - TY - CONF AB - Many dynamic graph algorithms have an amortized update time, rather than a stronger worst-case guarantee. But amortized data structures are not suitable for real-time systems, where each individual operation has to be executed quickly. For this reason, there exist many recent randomized results that aim to provide a guarantee stronger than amortized expected. The strongest possible guarantee for a randomized algorithm is that it is always correct (Las Vegas), and has high-probability worst-case update time, which gives a bound on the time for each individual operation that holds with high probability. In this paper we present the first polylogarithmic high-probability worst-case time bounds for the dynamic spanner and the dynamic maximal matching problem. 1. For dynamic spanner, the only known o(n) worst-case bounds were O(n3/4) high-probability worst-case update time for maintaining a 3-spanner, and O(n5/9) for maintaining a 5-spanner. We give a O(1)k log3(n) high-probability worst-case time bound for maintaining a (2k – 1)-spanner, which yields the first worst-case polylog update time for all constant k. (All the results above maintain the optimal tradeoff of stretch 2k – 1 and Õ(n1+1/k) edges.) 2. For dynamic maximal matching, or dynamic 2-approximate maximum matching, no algorithm with o(n) worst-case time bound was known and we present an algorithm with O(log5 (n)) high-probability worst-case time; similar worst-case bounds existed only for maintaining a matching that was (2 + ∊)-approximate, and hence not maximal. Our results are achieved using a new approach for converting amortized guarantees to worst-case ones for randomized data structures by going through a third type of guarantee, which is a middle ground between the two above: an algorithm is said to have worst-case expected update time α if for every update σ, the expected time to process σ is at most α. Although stronger than amortized expected, the worst-case expected guarantee does not resolve the fundamental problem of amortization: a worst-case expected update time of O(1) still allows for the possibility that every 1/f(n) updates requires Θ(f(n)) time to process, for arbitrarily high f(n). In this paper we present a black-box reduction that converts any data structure with worst-case expected update time into one with a high-probability worst-case update time: the query time remains the same, while the update time increases by a factor of O(log2(n)). Thus we achieve our results in two steps: (1) First we show how to convert existing dynamic graph algorithms with amortized expected polylogarithmic running times into algorithms with worst-case expected polylogarithmic running times. (2) Then we use our black-box reduction to achieve the polylogarithmic high-probability worst-case time bound. All our algorithms are Las-Vegas-type algorithms. AU - Bernstein, Aaron AU - Forster, Sebastian AU - Henzinger, Monika H ID - 11871 T2 - 30th Annual ACM-SIAM Symposium on Discrete Algorithms TI - A deamortization approach for dynamic spanner and dynamic maximal matching ER - TY - JOUR AB - We build upon the recent papers by Weinstein and Yu (FOCS'16), Larsen (FOCS'12), and Clifford et al. (FOCS'15) to present a general framework that gives amortized lower bounds on the update and query times of dynamic data structures. Using our framework, we present two concrete results. (1) For the dynamic polynomial evaluation problem, where the polynomial is defined over a finite field of size n1+Ω(1) and has degree n, any dynamic data structure must either have an amortized update time of Ω((lgn/lglgn)2) or an amortized query time of Ω((lgn/lglgn)2). (2) For the dynamic online matrix vector multiplication problem, where we get an n×n matrix whose entires are drawn from a finite field of size nΘ(1), any dynamic data structure must either have an amortized update time of Ω((lgn/lglgn)2) or an amortized query time of Ω(n⋅(lgn/lglgn)2). For these two problems, the previous works by Larsen (FOCS'12) and Clifford et al. (FOCS'15) gave the same lower bounds, but only for worst case update and query times. Our bounds match the highest unconditional lower bounds known till date for any dynamic problem in the cell-probe model. AU - Bhattacharya, Sayan AU - Henzinger, Monika H AU - Neumann, Stefan ID - 11898 JF - Theoretical Computer Science SN - 0304-3975 TI - New amortized cell-probe lower bounds for dynamic problems VL - 779 ER - TY - JOUR AB - Cross-coupling reactions mediated by dual nickel/photocatalysis are synthetically attractive but rely mainly on expensive, non-recyclable noble-metal complexes as photocatalysts. Heterogeneous semiconductors, which are commonly used for artificial photosynthesis and wastewater treatment, are a sustainable alternative. Graphitic carbon nitrides, a class of metal-free polymers that can be easily prepared from bulk chemicals, are heterogeneous semiconductors with high potential for photocatalytic organic transformations. Here, we demonstrate that graphitic carbon nitrides in combination with nickel catalysis can induce selective C−O cross-couplings of carboxylic acids with aryl halides, yielding the respective aryl esters in excellent yield and selectivity. The heterogeneous organic photocatalyst exhibits a broad substrate scope, is able to harvest green light, and can be recycled multiple times. In situ FTIR was used to track the reaction progress to study this transformation at different irradiation wavelengths and reaction scales. AU - Pieber, Bartholomäus AU - Malik, Jamal A. AU - Cavedon, Cristian AU - Gisbertz, Sebastian AU - Savateev, Aleksandr AU - Cruz, Daniel AU - Heil, Tobias AU - Zhang, Guigang AU - Seeberger, Peter H. ID - 11957 IS - 28 JF - Angewandte Chemie International Edition SN - 1433-7851 TI - Semi‐heterogeneous dual nickel/photocatalysis using carbon nitrides: Esterification of carboxylic acids with aryl halides VL - 58 ER - TY - JOUR AB - Differentially protected galactosamine building blocks are key components for the synthesis of human and bacterial oligosaccharides. The azidophenylselenylation of 3,4,6-tri-O-acetyl-d-galactal provides straightforward access to the corresponding 2-nitrogenated glycoside. Poor reproducibility and the use of azides that lead to the formation of potentially explosive and toxic species limit the scalability of this reaction and render it a bottleneck for carbohydrate synthesis. Here, we present a method for the safe, efficient, and reliable azidophenylselenylation of 3,4,6-tri-O-acetyl-d-galactal at room temperature, using continuous flow chemistry. Careful analysis of the transformation resulted in reaction conditions that produce minimal side products while the reaction time was reduced drastically when compared to batch reactions. The flow setup is readily scalable to process 5 mmol of galactal in 3 h, producing 1.2 mmol/h of product. AU - Guberman, Mónica AU - Pieber, Bartholomäus AU - Seeberger, Peter H. ID - 11984 IS - 12 JF - Organic Process Research and Development SN - 1083-6160 TI - Safe and scalable continuous flow azidophenylselenylation of galactal to prepare galactosamine building blocks VL - 23 ER - TY - JOUR AB - A carbon nitride material can be combined with homogeneous nickel catalysts for light-mediated cross-couplings of aryl bromides with alcohols under mild conditions. The metal-free heterogeneous semiconductor is fully recyclable and couples a broad range of electron-poor aryl bromides with primary and secondary alcohols as well as water. The application for intramolecular reactions and the synthesis of active pharmaceutical ingredients was demonstrated. The catalytic protocol is applicable for the coupling of aryl iodides with thiols as well. AU - Cavedon, Cristian AU - Madani, Amiera AU - Seeberger, Peter H. AU - Pieber, Bartholomäus ID - 11982 IS - 13 JF - Organic Letters SN - 1523-7060 TI - Semiheterogeneous dual nickel/photocatalytic (thio)etherification using carbon nitrides VL - 21 ER - TY - JOUR AB - Upper and lower bounds, of the expected order of magnitude, are obtained for the number of rational points of bounded height on any quartic del Pezzo surface over ℚ that contains a conic defined over ℚ . AU - Browning, Timothy D AU - Sofos, Efthymios ID - 170 IS - 3-4 JF - Mathematische Annalen TI - Counting rational points on quartic del Pezzo surfaces with a rational conic VL - 373 ER - TY - JOUR AU - Kalinin, Nikita AU - Shkolnikov, Mikhail ID - 441 IS - 3 JF - European Journal of Mathematics SN - 2199-675X TI - Tropical formulae for summation over a part of SL(2,Z) VL - 5 ER - TY - CHAP AB - The transcription coactivator, Yes-associated protein (YAP), which is a nuclear effector of the Hippo signaling pathway, has been shown to be a mechano-transducer. By using mutant fish and human 3D spheroids, we have recently demonstrated that YAP is also a mechano-effector. YAP functions in three-dimensional (3D) morphogenesis of organ and global body shape by controlling actomyosin-mediated tissue tension. In this chapter, we present a platform that links the findings in fish embryos with human cells. The protocols for analyzing tissue tension-mediated global body shape/organ morphogenesis in vivo and ex vivo using medaka fish embryos and in vitro using human cell spheroids represent useful tools for unraveling the molecular mechanisms by which YAP functions in regulating global body/organ morphogenesis. AU - Asaoka, Yoichi AU - Morita, Hitoshi AU - Furumoto, Hiroko AU - Heisenberg, Carl-Philipp J AU - Furutani-Seiki, Makoto ED - Hergovich, Alexander ID - 5793 SN - 978-1-4939-8909-6 T2 - The hippo pathway TI - Studying YAP-mediated 3D morphogenesis using fish embryos and human spheroids VL - 1893 ER - TY - JOUR AB - Cryptographic security is usually defined as a guarantee that holds except when a bad event with negligible probability occurs, and nothing is guaranteed in that bad case. However, in settings where such failure can happen with substantial probability, one needs to provide guarantees even for the bad case. A typical example is where a (possibly weak) password is used instead of a secure cryptographic key to protect a session, the bad event being that the adversary correctly guesses the password. In a situation with multiple such sessions, a per-session guarantee is desired: any session for which the password has not been guessed remains secure, independently of whether other sessions have been compromised. A new formalism for stating such gracefully degrading security guarantees is introduced and applied to analyze the examples of password-based message authentication and password-based encryption. While a natural per-message guarantee is achieved for authentication, the situation of password-based encryption is more delicate: a per-session confidentiality guarantee only holds against attackers for which the distribution of password-guessing effort over the sessions is known in advance. In contrast, for more general attackers without such a restriction, a strong, composable notion of security cannot be achieved. AU - Demay, Gregory AU - Gazi, Peter AU - Maurer, Ueli AU - Tackmann, Bjorn ID - 5887 IS - 1 JF - Journal of Computer Security SN - 0926227X TI - Per-session security: Password-based cryptography revisited VL - 27 ER - TY - CONF AB - We propose a new non-orthogonal basis to express the 3D Euclidean space in terms of a regular grid. Every grid point, each represented by integer 3-coordinates, corresponds to rhombic dodecahedron centroid. Rhombic dodecahedron is a space filling polyhedron which represents the close packing of spheres in 3D space and the Voronoi structures of the face centered cubic (FCC) lattice. In order to illustrate the interest of the new coordinate system, we propose the characterization of 3D digital plane with its topological features, such as the interrelation between the thickness of the digital plane and the separability constraint we aim to obtain. A characterization of a 3D digital sphere with relevant topological features is proposed as well with the help of a 48 symmetry that comes with the new coordinate system. AU - Biswas, Ranita AU - Largeteau-Skapin, Gaëlle AU - Zrour, Rita AU - Andres, Eric ID - 6163 SN - 0302-9743 T2 - 21st IAPR International Conference on Discrete Geometry for Computer Imagery TI - Rhombic dodecahedron grid—coordinate system and 3D digital object definitions VL - 11414 ER - TY - JOUR AB - We give non-degeneracy criteria for Riemannian simplices based on simplices in spaces of constant sectional curvature. It extends previous work on Riemannian simplices, where we developed Riemannian simplices with respect to Euclidean reference simplices. The criteria we give in this article are in terms of quality measures for spaces of constant curvature that we develop here. We see that simplices in spaces that have nearly constant curvature, are already non-degenerate under very weak quality demands. This is of importance because it allows for sampling of Riemannian manifolds based on anisotropy of the manifold and not (absolute) curvature. AU - Dyer, Ramsay AU - Vegter, Gert AU - Wintraecken, Mathijs ID - 6515 IS - 1 JF - Journal of Computational Geometry SN - 1920-180X TI - Simplices modelled on spaces of constant curvature VL - 10 ER - TY - CONF AB - We construct a verifiable delay function (VDF) by showing how the Rivest-Shamir-Wagner time-lock puzzle can be made publicly verifiable. Concretely, we give a statistically sound public-coin protocol to prove that a tuple (N,x,T,y) satisfies y=x2T (mod N) where the prover doesn’t know the factorization of N and its running time is dominated by solving the puzzle, that is, compute x2T, which is conjectured to require T sequential squarings. To get a VDF we make this protocol non-interactive using the Fiat-Shamir heuristic.The motivation for this work comes from the Chia blockchain design, which uses a VDF as akey ingredient. For typical parameters (T≤2 40, N= 2048), our proofs are of size around 10K B, verification cost around three RSA exponentiations and computing the proof is 8000 times faster than solving the puzzle even without any parallelism. AU - Pietrzak, Krzysztof Z ID - 6528 SN - 1868-8969 T2 - 10th Innovations in Theoretical Computer Science Conference TI - Simple verifiable delay functions VL - 124 ER - TY - CONF AB - In this paper, we address the problem of synthesizing periodic switching controllers for stabilizing a family of linear systems. Our broad approach consists of constructing a finite game graph based on the family of linear systems such that every winning strategy on the game graph corresponds to a stabilizing switching controller for the family of linear systems. The construction of a (finite) game graph, the synthesis of a winning strategy and the extraction of a stabilizing controller are all computationally feasible. We illustrate our method on an example. AU - Kundu, Atreyee AU - Garcia Soto, Miriam AU - Prabhakar, Pavithra ID - 6565 SN - 978-153866246-5 T2 - 5th Indian Control Conference Proceedings TI - Formal synthesis of stabilizing controllers for periodically controlled linear switched systems ER - TY - CONF AB - Fejes Tóth [5] and Schneider [9] studied approximations of smooth convex hypersurfaces in Euclidean space by piecewise flat triangular meshes with a given number of vertices on the hypersurface that are optimal with respect to Hausdorff distance. They proved that this Hausdorff distance decreases inversely proportional with m 2/(d−1), where m is the number of vertices and d is the dimension of Euclidean space. Moreover the pro-portionality constant can be expressed in terms of the Gaussian curvature, an intrinsic quantity. In this short note, we prove the extrinsic nature of this constant for manifolds of sufficiently high codimension. We do so by constructing an family of isometric embeddings of the flat torus in Euclidean space. AU - Vegter, Gert AU - Wintraecken, Mathijs ID - 6628 T2 - The 31st Canadian Conference in Computational Geometry TI - The extrinsic nature of the Hausdorff distance of optimal triangulations of manifolds ER - TY - CONF AB - Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a discrete probability distribution as a point in the standard simplex of the appropriate dimension, we can understand collections of such objects in geometric and topological terms. Importantly, instead of using the standard Euclidean distance, we look into dissimilarity measures with information-theoretic justification, and we develop the theory needed for applying topological data analysis in this setting. In doing so, we emphasize constructions that enable the usage of existing computational topology software in this context. AU - Edelsbrunner, Herbert AU - Virk, Ziga AU - Wagner, Hubert ID - 6648 SN - 9783959771047 T2 - 35th International Symposium on Computational Geometry TI - Topological data analysis in information space VL - 129 ER - TY - JOUR AB - Chemical labeling of proteins with synthetic molecular probes offers the possibility to probe the functions of proteins of interest in living cells. However, the methods for covalently labeling targeted proteins using complementary peptide tag-probe pairs are still limited, irrespective of the versatility of such pairs in biological research. Herein, we report the new CysHis tag-Ni(II) probe pair for the specific covalent labeling of proteins. A broad-range evaluation of the reactivity profiles of the probe and the CysHis peptide tag afforded a tag-probe pair with an optimized and high labeling selectivity and reactivity. In particular, the labeling specificity of this pair was notably improved compared to the previously reported one. This pair was successfully utilized for the fluorescence imaging of membrane proteins on the surfaces of living cells, demonstrating its potential utility in biological research. AU - Zenmyo, Naoki AU - Tokumaru, Hiroki AU - Uchinomiya, Shohei AU - Fuchida, Hirokazu AU - Tabata, Shigekazu AU - Hamachi, Itaru AU - Shigemoto, Ryuichi AU - Ojida, Akio ID - 6659 IS - 5 JF - Bulletin of the Chemical Society of Japan SN - 00092673 TI - Optimized reaction pair of the CysHis tag and Ni(II)-NTA probe for highly selective chemical labeling of membrane proteins VL - 92 ER - TY - JOUR AB - In phase retrieval, we want to recover an unknown signal 𝑥∈ℂ𝑑 from n quadratic measurements of the form 𝑦𝑖=|⟨𝑎𝑖,𝑥⟩|2+𝑤𝑖, where 𝑎𝑖∈ℂ𝑑 are known sensing vectors and 𝑤𝑖 is measurement noise. We ask the following weak recovery question: What is the minimum number of measurements n needed to produce an estimator 𝑥^(𝑦) that is positively correlated with the signal 𝑥? We consider the case of Gaussian vectors 𝑎𝑎𝑖. We prove that—in the high-dimensional limit—a sharp phase transition takes place, and we locate the threshold in the regime of vanishingly small noise. For 𝑛≤𝑑−𝑜(𝑑), no estimator can do significantly better than random and achieve a strictly positive correlation. For 𝑛≥𝑑+𝑜(𝑑), a simple spectral estimator achieves a positive correlation. Surprisingly, numerical simulations with the same spectral estimator demonstrate promising performance with realistic sensing matrices. Spectral methods are used to initialize non-convex optimization algorithms in phase retrieval, and our approach can boost the performance in this setting as well. Our impossibility result is based on classical information-theoretic arguments. The spectral algorithm computes the leading eigenvector of a weighted empirical covariance matrix. We obtain a sharp characterization of the spectral properties of this random matrix using tools from free probability and generalizing a recent result by Lu and Li. Both the upper bound and lower bound generalize beyond phase retrieval to measurements 𝑦𝑖 produced according to a generalized linear model. As a by-product of our analysis, we compare the threshold of the proposed spectral method with that of a message passing algorithm. AU - Mondelli, Marco AU - Montanari, Andrea ID - 6662 IS - 3 JF - Foundations of Computational Mathematics TI - Fundamental limits of weak recovery with applications to phase retrieval VL - 19 ER - TY - JOUR AB - The construction of anisotropic triangulations is desirable for various applications, such as the numerical solving of partial differential equations and the representation of surfaces in graphics. To solve this notoriously difficult problem in a practical way, we introduce the discrete Riemannian Voronoi diagram, a discrete structure that approximates the Riemannian Voronoi diagram. This structure has been implemented and was shown to lead to good triangulations in $\mathbb{R}^2$ and on surfaces embedded in $\mathbb{R}^3$ as detailed in our experimental companion paper. In this paper, we study theoretical aspects of our structure. Given a finite set of points $\mathcal{P}$ in a domain $\Omega$ equipped with a Riemannian metric, we compare the discrete Riemannian Voronoi diagram of $\mathcal{P}$ to its Riemannian Voronoi diagram. Both diagrams have dual structures called the discrete Riemannian Delaunay and the Riemannian Delaunay complex. We provide conditions that guarantee that these dual structures are identical. It then follows from previous results that the discrete Riemannian Delaunay complex can be embedded in $\Omega$ under sufficient conditions, leading to an anisotropic triangulation with curved simplices. Furthermore, we show that, under similar conditions, the simplices of this triangulation can be straightened. AU - Boissonnat, Jean-Daniel AU - Rouxel-Labbé, Mael AU - Wintraecken, Mathijs ID - 6672 IS - 3 JF - SIAM Journal on Computing SN - 0097-5397 TI - Anisotropic triangulations via discrete Riemannian Voronoi diagrams VL - 48 ER -