@article{11605, abstract = {Context. The discovery of moderate differential rotation between the core and the envelope of evolved solar-like stars could be the signature of a strong magnetic field trapped inside the radiative interior. The population of intermediate-mass red giants presenting surprisingly low-amplitude mixed modes (i.e. oscillation modes that behave as acoustic modes in their external envelope and as gravity modes in their core) could also arise from the effect of an internal magnetic field. Indeed, stars more massive than about 1.1 solar masses are known to develop a convective core during their main sequence. The field generated by the dynamo triggered by this convection could be the progenitor of a strong fossil magnetic field trapped inside the core of the star for the remainder of its evolution. Aims. Observations of mixed modes can constitute an excellent probe of the deepest layers of evolved solar-like stars, and magnetic fields in those regions can impact their propagation. The magnetic perturbation on mixed modes may therefore be visible in asteroseismic data. To unravel which constraints can be obtained from observations, we theoretically investigate the effects of a plausible mixed axisymmetric magnetic field with various amplitudes on the mixed-mode frequencies of evolved solar-like stars. Methods. First-order frequency perturbations due to an axisymmetric magnetic field were computed for dipolar and quadrupolar mixed modes. These computations were carried out for a range of stellar ages, masses, and metallicities. Conclusions. We show that typical fossil-field strengths of 0.1 − 1 MG, consistent with the presence of a dynamo in the convective core during the main sequence, provoke significant asymmetries on mixed-mode frequency multiplets during the red giant branch. We provide constraints and methods for the detectability of such magnetic signatures. We show that these signatures may be detectable in asteroseismic data for field amplitudes small enough for the amplitude of the modes not to be affected by the conversion of gravity into Alfvén waves inside the magnetised interior. Finally, we infer an upper limit for the strength of the field and the associated lower limit for the timescale of its action in order to redistribute angular momentum in stellar interiors.}, author = {Bugnet, Lisa Annabelle and Prat, V. and Mathis, S. and Astoul, A. and Augustson, K. and García, R. A. and Mathur, S. and Amard, L. and Neiner, C.}, issn = {1432-0746}, journal = {Astronomy & Astrophysics}, keywords = {Space and Planetary Science, Astronomy and Astrophysics, stars, oscillations / stars, magnetic field / stars, interiors / stars, evolution / stars, rotation}, publisher = {EDP Sciences}, title = {{Magnetic signatures on mixed-mode frequencies: I. An axisymmetric fossil field inside the core of red giants}}, doi = {10.1051/0004-6361/202039159}, volume = {650}, year = {2021}, } @article{11606, abstract = {Context. Our knowledge of the dynamics of stars has undergone a revolution through the simultaneous large amount of high-quality photometric observations collected by space-based asteroseismology and ground-based high-precision spectropolarimetry. They allowed us to probe the internal rotation of stars and their surface magnetism in the whole Hertzsprung-Russell diagram. However, new methods should still be developed to probe the deep magnetic fields in these stars. Aims. Our goal is to provide seismic diagnoses that allow us to probe the internal magnetism of stars. Methods. We focused on asymptotic low-frequency gravity modes and high-frequency acoustic modes. Using a first-order perturbative theory, we derived magnetic splittings of their frequencies as explicit functions of stellar parameters. Results. As in the case of rotation, we show that asymptotic gravity and acoustic modes can allow us to probe the different components of the magnetic field in the cavities in which they propagate. This again demonstrates the high potential of using mixed-modes when this is possible.}, author = {Mathis, S. and Bugnet, Lisa Annabelle and Prat, V. and Augustson, K. and Mathur, S. and Garcia, R. A.}, issn = {1432-0746}, journal = {Astronomy & Astrophysics}, keywords = {Space and Planetary Science, Astronomy and Astrophysics, asteroseismology / waves / stars, magnetic field / stars, oscillations / methods, analytical}, publisher = {EDP Sciences}, title = {{Probing the internal magnetism of stars using asymptotic magneto-asteroseismology}}, doi = {10.1051/0004-6361/202039180}, volume = {647}, year = {2021}, } @article{11608, abstract = {In order to understand stellar evolution, it is crucial to efficiently determine stellar surface rotation periods. Indeed, while they are of great importance in stellar models, angular momentum transport processes inside stars are still poorly understood today. Surface rotation, which is linked to the age of the star, is one of the constraints needed to improve the way those processes are modelled. Statistics of the surface rotation periods for a large sample of stars of different spectral types are thus necessary. An efficient tool to automatically determine reliable rotation periods is needed when dealing with large samples of stellar photometric datasets. The objective of this work is to develop such a tool. For this purpose, machine learning classifiers constitute relevant bases to build our new methodology. Random forest learning abilities are exploited to automate the extraction of rotation periods in Kepler light curves. Rotation periods and complementary parameters are obtained via three different methods: a wavelet analysis, the autocorrelation function of the light curve, and the composite spectrum. We trained three different classifiers: one to detect if rotational modulations are present in the light curve, one to flag close binary or classical pulsators candidates that can bias our rotation period determination, and finally one classifier to provide the final rotation period. We tested our machine learning pipeline on 23 431 stars of the Kepler K and M dwarf reference rotation catalogue for which 60% of the stars have been visually inspected. For the sample of 21 707 stars where all the input parameters are provided to the algorithm, 94.2% of them are correctly classified (as rotating or not). Among the stars that have a rotation period in the reference catalogue, the machine learning provides a period that agrees within 10% of the reference value for 95.3% of the stars. Moreover, the yield of correct rotation periods is raised to 99.5% after visually inspecting 25.2% of the stars. Over the two main analysis steps, rotation classification and period selection, the pipeline yields a global agreement with the reference values of 92.1% and 96.9% before and after visual inspection. Random forest classifiers are efficient tools to determine reliable rotation periods in large samples of stars. The methodology presented here could be easily adapted to extract surface rotation periods for stars with different spectral types or observed by other instruments such as K2, TESS or by PLATO in the near future.}, author = {Breton, S. N. and Santos, A. R. G. and Bugnet, Lisa Annabelle and Mathur, S. and García, R. A. and Pallé, P. L.}, issn = {1432-0746}, journal = {Astronomy & Astrophysics}, keywords = {Space and Planetary Science, Astronomy and Astrophysics, methods: data analysis / stars: solar-type / stars: activity / stars: rotation / starspots}, publisher = {EDP Sciences}, title = {{ROOSTER: A machine-learning analysis tool for Kepler stellar rotation periods}}, doi = {10.1051/0004-6361/202039947}, volume = {647}, year = {2021}, } @article{11609, abstract = {Context. Stellar interiors are the seat of efficient transport of angular momentum all along their evolution. In this context, understanding the dependence of the turbulent transport triggered by the instabilities of the vertical and horizontal shears of the differential rotation in stellar radiation zones as a function of their rotation, stratification, and thermal diffusivity is mandatory. Indeed, it constitutes one of the cornerstones of the rotational transport and mixing theory, which is implemented in stellar evolution codes to predict the rotational and chemical evolutions of stars. Aims. We investigate horizontal shear instabilities in rotating stellar radiation zones by considering the full Coriolis acceleration with both the dimensionless horizontal Coriolis component f̃ and the vertical component f. Methods. We performed a linear stability analysis using linearized equations derived from the Navier-Stokes and heat transport equations in the rotating nontraditional f-plane. We considered a horizontal shear flow with a hyperbolic tangent profile as the base flow. The linear stability was analyzed numerically in wide ranges of parameters, and we performed an asymptotic analysis for large vertical wavenumbers using the Wentzel-Kramers-Brillouin-Jeffreys (WKBJ) approximation for nondiffusive and highly-diffusive fluids. Results. As in the traditional f-plane approximation, we identify two types of instabilities: the inflectional and inertial instabilities. The inflectional instability is destabilized as f̃ increases and its maximum growth rate increases significantly, while the thermal diffusivity stabilizes the inflectional instability similarly to the traditional case. The inertial instability is also strongly affected; for instance, the inertially unstable regime is also extended in the nondiffusive limit as 0 < f < 1 + f̃ 2/N2, where N is the dimensionless Brunt-Väisälä frequency. More strikingly, in the high thermal diffusivity limit, it is always inertially unstable at any colatitude θ except at the poles (i.e., 0° < θ <  180°). We also derived the critical Reynolds numbers for the inertial instability using the asymptotic dispersion relations obtained from the WKBJ analysis. Using the asymptotic and numerical results, we propose a prescription for the effective turbulent viscosities induced by the inertial and inflectional instabilities that can be possibly used in stellar evolution models. The characteristic time of this turbulence is short enough so that it is efficient to redistribute angular momentum and to mix chemicals in stellar radiation zones.}, author = {Park, J. and Prat, V. and Mathis, S. and Bugnet, Lisa Annabelle}, issn = {1432-0746}, journal = {Astronomy & Astrophysics}, keywords = {Space and Planetary Science, Astronomy and Astrophysics, hydrodynamics / turbulence / stars, rotation / stars, evolution}, publisher = {EDP Sciences}, title = {{Horizontal shear instabilities in rotating stellar radiation zones: II. Effects of the full Coriolis acceleration}}, doi = {10.1051/0004-6361/202038654}, volume = {646}, year = {2021}, } @inproceedings{11649, abstract = {While operating communication networks adaptively may improve utilization and performance, frequent adjustments also introduce an algorithmic challenge: the re-optimization of traffic engineering solutions is time-consuming and may limit the granularity at which a network can be adjusted. This paper is motivated by question whether the reactivity of a network can be improved by re-optimizing solutions dynamically rather than from scratch, especially if inputs such as link weights do not change significantly. This paper explores to what extent dynamic algorithms can be used to speed up fundamental tasks in network operations. We specifically investigate optimizations related to traffic engineering (namely shortest paths and maximum flow computations), but also consider spanning tree and matching applications. While prior work on dynamic graph algorithms focusses on link insertions and deletions, we are interested in the practical problem of link weight changes. We revisit existing upper bounds in the weight-dynamic model, and present several novel lower bounds on the amortized runtime for recomputing solutions. In general, we find that the potential performance gains depend on the application, and there are also strict limitations on what can be achieved, even if link weights change only slightly.}, author = {Henzinger, Monika H and Paz, Ami and Schmid, Stefan}, booktitle = {IFIP Networking Conference}, issn = {1861-2288}, location = { Espoo and Helsinki, Finland}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{On the complexity of weight-dynamic network algorithms}}, doi = {10.23919/ifipnetworking52078.2021.9472803}, year = {2021}, } @article{11663, abstract = {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 article, 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(log 5 (n)) high-probability worst-case time; similar worst-case bounds existed only for maintaining a matching that was (2+ϵ)-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 ɑ if for every update σ, the expected time to process σ is at most ɑ. 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 article, 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(log 2(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.}, author = {Bernstein, Aaron and Forster, Sebastian and Henzinger, Monika H}, issn = {1549-6333}, journal = {ACM Transactions on Algorithms}, number = {4}, publisher = {Association for Computing Machinery}, title = {{A deamortization approach for dynamic spanner and dynamic maximal matching}}, doi = {10.1145/3469833}, volume = {17}, year = {2021}, } @article{11756, abstract = {We give two fully dynamic algorithms that maintain a (1 + ε)-approximation of the weight M of a minimum spanning forest (MSF) of an n-node graph G with edges weights in [1, W ], for any ε > 0. (1) Our deterministic algorithm takes O (W 2 log W /ε3) worst-case update time, which is O (1) if both W and ε are constants. (2) Our randomized (Monte-Carlo style) algorithm works with high probability and runs in worst-case O (log W /ε4) update time if W = O ((m∗)1/6/log2/3 n), where m∗ is the minimum number of edges in the graph throughout all the updates. It works even against an adaptive adversary. We complement our algorithmic results with two cell-probe lower bounds for dynamically maintaining an approximation of the weight of an MSF of a graph.}, author = {Henzinger, Monika H and Peng, Pan}, issn = {0890-5401}, journal = {Information and Computation}, number = {12}, publisher = {Elsevier}, title = {{Constant-time dynamic weight approximation for minimum spanning forest}}, doi = {10.1016/j.ic.2021.104805}, volume = {281}, year = {2021}, } @inproceedings{11771, abstract = {Classic dynamic data structure problems maintain a data structure subject to a sequence S of updates and they answer queries using the latest version of the data structure, i.e., the data structure after processing the whole sequence. To handle operations that change the sequence S of updates, Demaine et al. [7] introduced retroactive data structures (RDS). A retroactive operation modifies the update sequence S in a given position t, called time, and either creates or cancels an update in S at time t. A fully retroactive data structure supports queries at any time t: a query at time t is answered using only the updates of S up to time t. While efficient RDS have been proposed for classic data structures, e.g., stack, priority queue and binary search tree, the retroactive version of graph problems are rarely studied. In this paper we study retroactive graph problems including connectivity, minimum spanning forest (MSF), maximum degree, etc. We show that under the OMv conjecture (proposed by Henzinger et al. [15]), there does not exist fully RDS maintaining connectivity or MSF, or incremental fully RDS maintaining the maximum degree with 𝑂(𝑛1−𝜖) time per operation, for any constant 𝜖>0. Furthermore, We provide RDS with almost tight time per operation. We give fully RDS for maintaining the maximum degree, connectivity and MSF in 𝑂̃ (𝑛) time per operation. We also give an algorithm for the incremental (insertion-only) fully retroactive connectivity with 𝑂̃ (1) time per operation, showing that the lower bound cannot be extended to this setting. We also study a restricted version of RDS, where the only change to S is the swap of neighboring updates and show that for this problem we can beat the above hardness result. This also implies the first non-trivial dynamic Reeb graph computation algorithm.}, author = {Henzinger, Monika H and Wu, Xiaowei}, booktitle = {17th International Symposium on Algorithms and Data Structures}, isbn = {9783030835071}, issn = {1611-3349}, location = {Virtual}, pages = {471–484}, publisher = {Springer Nature}, title = {{Upper and lower bounds for fully retroactive graph problems}}, doi = {10.1007/978-3-030-83508-8_34}, volume = {12808}, year = {2021}, } @inproceedings{11814, abstract = {Differentially private algorithms protect individuals in data analysis scenarios by ensuring that there is only a weak correlation between the existence of the user in the data and the result of the analysis. Dynamic graph algorithms maintain the solution to a problem (e.g., a matching) on an evolving input, i.e., a graph where nodes or edges are inserted or deleted over time. They output the value of the solution after each update operation, i.e., continuously. We study (event-level and user-level) differentially private algorithms for graph problems under continual observation, i.e., differentially private dynamic graph algorithms. We present event-level private algorithms for partially dynamic counting-based problems such as triangle count that improve the additive error by a polynomial factor (in the length T of the update sequence) on the state of the art, resulting in the first algorithms with additive error polylogarithmic in T. We also give ε-differentially private and partially dynamic algorithms for minimum spanning tree, minimum cut, densest subgraph, and maximum matching. The additive error of our improved MST algorithm is O(W log^{3/2}T / ε), where W is the maximum weight of any edge, which, as we show, is tight up to a (√{log T} / ε)-factor. For the other problems, we present a partially-dynamic algorithm with multiplicative error (1+β) for any constant β > 0 and additive error O(W log(nW) log(T) / (ε β)). Finally, we show that the additive error for a broad class of dynamic graph algorithms with user-level privacy must be linear in the value of the output solution’s range.}, author = {Fichtenberger, Hendrik and Henzinger, Monika H and Ost, Wolfgang}, booktitle = {29th Annual European Symposium on Algorithms}, isbn = {9783959772044}, issn = {1868-8969}, location = {Lisbon, Portual}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, title = {{Differentially private algorithms for graphs under continual observation}}, doi = {10.4230/LIPIcs.ESA.2021.42}, volume = {204}, year = {2021}, } @article{11886, abstract = {We present a deterministic (1+𝑜(1))-approximation (𝑛1/2+𝑜(1)+𝐷1+𝑜(1))-time algorithm for solving the single-source shortest paths problem on distributed weighted networks (the \sf CONGEST model); here 𝑛 is the number of nodes in the network, 𝐷 is its (hop) diameter, and edge weights are positive integers from 1 to poly(𝑛). This is the first nontrivial deterministic algorithm for this problem. It also improves (i) the running time of the randomized (1+𝑜(1))-approximation 𝑂̃ (𝑛√𝐷1/4+𝐷)-time algorithm of Nanongkai [in Proceedings of STOC, 2014, pp. 565--573] by a factor of as large as 𝑛1/8, and (ii) the 𝑂(𝜖−1log𝜖−1)-approximation factor of Lenzen and Patt-Shamir's 𝑂̃ (𝑛1/2+𝜖+𝐷)-time algorithm [in Proceedings of STOC, 2013, pp. 381--390] within the same running time. (Throughout, we use 𝑂̃ (⋅) to hide polylogarithmic factors in 𝑛.) Our running time matches the known time lower bound of Ω(𝑛/log𝑛‾‾‾‾‾‾‾√+𝐷) [M. Elkin, SIAM J. Comput., 36 (2006), pp. 433--456], thus essentially settling the status of this problem which was raised at least a decade ago [M. Elkin, SIGACT News, 35 (2004), pp. 40--57]. It also implies a (2+𝑜(1))-approximation (𝑛1/2+𝑜(1)+𝐷1+𝑜(1))-time algorithm for approximating a network's weighted diameter which almost matches the lower bound by Holzer and Pinsker [in Proceedings of OPODIS, 2015, Schloss Dagstuhl. Leibniz-Zent. Inform., Wadern, Germany, 2016, 6]. In achieving this result, we develop two techniques which might be of independent interest and useful in other settings: (i) a deterministic process that replaces the “hitting set argument” commonly used for shortest paths computation in various settings, and (ii) a simple, deterministic construction of an (𝑛𝑜(1),𝑜(1))-hop set of size 𝑛1+𝑜(1). We combine these techniques with many distributed algorithmic techniques, some of which are from problems that are not directly related to shortest paths, e.g., ruling sets [A. V. Goldberg, S. A. Plotkin, and G. E. Shannon, SIAM J. Discrete Math., 1 (1988), pp. 434--446], source detection [C. Lenzen and D. Peleg, in Proceedings of PODC, 2013, pp. 375--382], and partial distance estimation [C. Lenzen and B. Patt-Shamir, in Proceedings of PODC, 2015, pp. 153--162]. Our hop set construction also leads to single-source shortest paths algorithms in two other settings: (i) a (1+𝑜(1))-approximation 𝑛𝑜(1)-time algorithm on congested cliques, and (ii) a (1+𝑜(1))-approximation 𝑛𝑜(1)-pass 𝑛1+𝑜(1)-space streaming algorithm. The first result answers an open problem in [D. Nanongkai, in Proceedings of STOC, 2014, pp. 565--573]. The second result partially answers an open problem raised by McGregor in 2006 [List of Open Problems in Sublinear Algorithms: Problem 14].}, author = {Henzinger, Monika H and Krinninger, Sebastian and Nanongkai, Danupon}, issn = {1095-7111}, journal = {SIAM Journal on Computing}, number = {3}, pages = {STOC16--98--STOC16--137}, publisher = {Society for Industrial & Applied Mathematics}, title = {{A deterministic almost-tight distributed algorithm for approximating single-source shortest paths}}, doi = {10.1137/16m1097808}, volume = {50}, year = {2021}, } @inproceedings{11919, abstract = {Maintaining and updating shortest paths information in a graph is a fundamental problem with many applications. As computations on dense graphs can be prohibitively expensive, and it is preferable to perform the computations on a sparse skeleton of the given graph that roughly preserves the shortest paths information. Spanners and emulators serve this purpose. Unfortunately, very little is known about dynamically maintaining sparse spanners and emulators as the graph is modified by a sequence of edge insertions and deletions. This paper develops fast dynamic algorithms for spanner and emulator maintenance and provides evidence from fine-grained complexity that these algorithms are tight. For unweighted undirected m-edge n-node graphs we obtain the following results. Under the popular OMv conjecture, there can be no decremental or incremental algorithm that maintains an n1+o(1) edge (purely additive) +nδ-emulator for any δ < 1/2 with arbitrary polynomial preprocessing time and total update time m1+o(1). Also, under the Combinatorial k-Clique hypothesis, any fully dynamic combinatorial algorithm that maintains an n1+o(1) edge (1 + ∊, no(1))-spanner or emulator for small ∊ must either have preprocessing time mn1–o(1) or amortized update time m1–o(1). Both of our conditional lower bounds are tight. As the above fully dynamic lower bound only applies to combinatorial algorithms, we also develop an algebraic spanner algorithm that improves over the m1–o(1) update time for dense graphs. For any constant ∊ ∊ (0, 1], there is a fully dynamic algorithm with worst-case update time O(n1.529) that whp maintains an n1+o(1) edge (1 + ∊, no(1))-spanner. Our new algebraic techniques allow us to also obtain a new fully dynamic algorithm for All-Pairs Shortest Paths (APSP) that can perform both edge updates and can report shortest paths in worst-case time O(n1.9), which are correct whp. This is the first path-reporting fully dynamic APSP algorithm with a truly subquadratic query time that beats O(n2.5) update time. It works against an oblivious adversary. Finally, we give two applications of our new dynamic spanner algorithms: (1) a fully dynamic (1 + ∊)-approximate APSP algorithm with update time O(n1.529) that can report approximate shortest paths in n1+o(1) time per query; previous subquadratic update/query algorithms could only report the distance, but not obtain the paths; (2) a fully dynamic algorithm for near-2-approximate Steiner tree maintenance with both terminal and edge updates.}, author = {Bergamaschi, Thiago and Henzinger, Monika H and Gutenberg, Maximilian Probst and Williams, Virginia Vassilevska and Wein, Nicole}, booktitle = {32nd Annual ACM-SIAM Symposium on Discrete Algorithms}, location = {Alexandria, VA, United States}, pages = {1836--1855}, publisher = {Society for Industrial and Applied Mathematics}, title = {{New techniques and fine-grained hardness for dynamic near-additive spanners}}, doi = {10.1137/1.9781611976465.110}, year = {2021}, } @inproceedings{11920, abstract = {In the dynamic minimum set cover problem, a challenge is to minimize the update time while guaranteeing close to the optimal min(O(log n), f) approximation factor. (Throughout, m, n, f, and C are parameters denoting the maximum number of sets, number of elements, frequency, and the cost range.) In the high-frequency range, when f = Ω(log n), this was achieved by a deterministic O(log n)-approximation algorithm with O(f log n) amortized update time [Gupta et al. STOC'17]. In the low-frequency range, the line of work by Gupta et al. [STOC'17], Abboud et al. [STOC'19], and Bhattacharya et al. [ICALP'15, IPCO'17, FOCS'19] led to a deterministic (1 + ∊) f-approximation algorithm with O(f log(Cn)/∊2) amortized update time. In this paper we improve the latter update time and provide the first bounds that subsume (and sometimes improve) the state-of-the-art dynamic vertex cover algorithms. We obtain: (1) (1 + ∊) f-approximation ratio in O(f log2(Cn)/∊3) worst-case update time: No non-trivial worst-case update time was previously known for dynamic set cover. Our bound subsumes and improves by a logarithmic factor the O(log3 n/poly(∊)) worst-case update time for unweighted dynamic vertex cover (i.e., when f = 2 and C = 1) by Bhattacharya et al. [SODA'17]. (2) (1 + ∊) f-approximation ratio in O ((f2/∊3) + (f/∊2) log C) amortized update time: This result improves the previous O(f log (Cn)/∊2) update time bound for most values of f in the low-frequency range, i.e. whenever f = o(log n). It is the first that is independent of m and n. It subsumes the constant amortized update time of Bhattacharya and Kulkarni [SODA'19] for unweighted dynamic vertex cover (i.e., when f = 2 and C = 1). These results are achieved by leveraging the approximate complementary slackness and background schedulers techniques. These techniques were used in the local update scheme for dynamic vertex cover. Our main technical contribution is to adapt these techniques within the global update scheme of Bhattacharya et al. [FOCS'19] for the dynamic set cover problem.}, author = {Bhattacharya, Sayan and Henzinger, Monika H and Nanongkai, Danupon and Wu, Xiaowei}, booktitle = {32nd Annual ACM-SIAM Symposium on Discrete Algorithms}, location = {Alexandria, VA, United States}, pages = {2537--2549}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Dynamic set cover: Improved amortized and worst-case update time}}, doi = {10.1137/1.9781611976465.150}, year = {2021}, } @inproceedings{11923, abstract = {We consider the following online optimization problem. We are given a graph G and each vertex of the graph is assigned to one of ℓ servers, where servers have capacity k and we assume that the graph has ℓ · k vertices. Initially, G does not contain any edges and then the edges of G are revealed one-by-one. The goal is to design an online algorithm ONL, which always places the connected components induced by the revealed edges on the same server and never exceeds the server capacities by more than ∊k for constant ∊ > 0. Whenever ONL learns about a new edge, the algorithm is allowed to move vertices from one server to another. Its objective is to minimize the number of vertex moves. More specifically, ONL should minimize the competitive ratio: the total cost ONL incurs compared to an optimal offline algorithm OPT. The problem was recently introduced by Henzinger et al. (SIGMETRICS'2019) and is related to classic online problems such as online paging and scheduling. It finds applications in the context of resource allocation in the cloud and for optimizing distributed data structures such as union–find data structures. Our main contribution is a polynomial-time randomized algorithm, that is asymptotically optimal: we derive an upper bound of O(log ℓ + log k) on its competitive ratio and show that no randomized online algorithm can achieve a competitive ratio of less than Ω(log ℓ + log k). We also settle the open problem of the achievable competitive ratio by deterministic online algorithms, by deriving a competitive ratio of Θ(ℓ log k); to this end, we present an improved lower bound as well as a deterministic polynomial-time online algorithm. Our algorithms rely on a novel technique which combines efficient integer programming with a combinatorial approach for maintaining ILP solutions. More precisely, we use an ILP to assign the connected components induced by the revealed edges to the servers; this is similar to existing approximation schemes for scheduling algorithms. However, we cannot obtain our competitive ratios if we run the ILP after each edge insertion. Instead, we identify certain types of edge insertions, after which we can manually obtain an optimal ILP solution at zero cost without resolving the ILP. We believe this technique is of independent interest and will find further applications in the future.}, author = {Henzinger, Monika H and Neumann, Stefan and Räcke, Harald and Schmid, Stefan}, booktitle = {32nd Annual ACM-SIAM Symposium on Discrete Algorithms}, location = {Alexandria, VA, United States}, pages = {2799--2818}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Tight bounds for online graph partitioning}}, doi = {10.1137/1.9781611976465.166}, year = {2021}, } @inproceedings{11931, abstract = {Clustering is one of the most fundamental problems in unsupervised learning with a large number of applications. However, classical clustering algorithms assume that the data is static, thus failing to capture many real-world applications where data is constantly changing and evolving. Driven by this, we study the metric k-center clustering problem in the fully dynamic setting, where the goal is to efficiently maintain a clustering while supporting an intermixed sequence of insertions and deletions of points. This model also supports queries of the form (1) report whether a given point is a center or (2) determine the cluster a point is assigned to. We present a deterministic dynamic algorithm for the k-center clustering problem that provably achieves a (2 + ∊)-approximation in nearly logarithmic update and query time, if the underlying metric has bounded doubling dimension, its aspect ratio is bounded by a polynomial and ∊ is a constant. An important feature of our algorithm is that the update and query times are independent of k. We confirm the practical relevance of this feature via an extensive experimental study which shows that for large values of k, our algorithmic construction outperforms the state-of-the-art algorithm in terms of solution quality and running time.}, author = {Goranci, Gramoz and Henzinger, Monika H and Leniowski, Dariusz and Schulz, Christian and Svozil, Alexander}, booktitle = {2021 Proceedings of the Workshop on Algorithm Engineering and Experiments}, issn = {2164-0300}, location = {Alexandria, VA, United States}, pages = {143 --153}, publisher = {Society for Industrial and Applied Mathematics}, title = {{Fully dynamic k-center clustering in low dimensional metrics}}, doi = {10.1137/1.9781611976472.11}, year = {2021}, } @article{11956, abstract = {Controlling the selectivity of a chemical reaction with external stimuli is common in thermal processes, but rare in visible-light photocatalysis. Here we show that the redox potential of a carbon nitride photocatalyst (CN-OA-m) can be tuned by changing the irradiation wavelength to generate electron holes with different oxidation potentials. This tuning was the key to realizing photo-chemo-enzymatic cascades that give either the (S)- or the (R)-enantiomer of phenylethanol. In combination with an unspecific peroxygenase from Agrocybe aegerita, green light irradiation of CN-OA-m led to the enantioselective hydroxylation of ethylbenzene to (R)-1-phenylethanol (99 % ee). In contrast, blue light irradiation triggered the photocatalytic oxidation of ethylbenzene to acetophenone, which in turn was enantioselectively reduced with an alcohol dehydrogenase from Rhodococcus ruber to form (S)-1-phenylethanol (93 % ee).}, author = {Schmermund, Luca and Reischauer, Susanne and Bierbaumer, Sarah and Winkler, Christoph K. and Diaz‐Rodriguez, Alba and Edwards, Lee J. and Kara, Selin and Mielke, Tamara and Cartwright, Jared and Grogan, Gideon and Pieber, Bartholomäus and Kroutil, Wolfgang}, issn = {1521-3773}, journal = {Angewandte Chemie International Edition}, number = {13}, pages = {6965--6969}, publisher = {Wiley}, title = {{Chromoselective photocatalysis enables stereocomplementary biocatalytic pathways}}, doi = {10.1002/anie.202100164}, volume = {60}, year = {2021}, } @article{11965, abstract = {Metallaphotocatalytic cross-coupling reactions are typically carried out by combining homogeneous or heterogeneous photocatalysts with a soluble nickel complex. Previous attempts to realize recyclable catalytic systems use immobilized iridium complexes to harvest light. We present bifunctional materials based on semiconductors for metallaphotocatalytic C−S cross-coupling reactions that can be reused without losing their catalytic activity. Key to the success is the permanent immobilization of a nickel complex on the surface of a heterogeneous semiconductor through phosphonic acid anchors. The optimized catalyst harvests a broad range of the visible light spectrum and requires a nickel loading of only ∼0.1 mol %.}, author = {Reischauer, Susanne and Pieber, Bartholomäus}, issn = {2367-0932}, journal = {ChemPhotoChem}, number = {8}, pages = {716--720}, publisher = {Wiley}, title = {{Recyclable, bifunctional metallaphotocatalysts for C−S cross‐coupling reactions}}, doi = {10.1002/cptc.202100062}, volume = {5}, year = {2021}, } @article{11972, abstract = {Carbon dots have been previosly immobilized on titanium dioxide to generate photocatalysts for pollutant degradation and water splitting. Here we demonstrate that these nanocomposites are valuable photocatalysts for metallaphotocatalytic carbon–heteroatom cross-couplings. These sustainable materials show a large applicability, high photostability, excellent reusability, and broadly absorb across the visible-light spectrum.}, author = {Zhao, Zhouxiang and Reischauer, Susanne and Pieber, Bartholomäus and Delbianco, Martina}, issn = {1463-9270}, journal = {Green Chemistry}, number = {12}, pages = {4524--4530}, publisher = {Royal Society of Chemistry}, title = {{Carbon dot/TiO₂ nanocomposites as photocatalysts for metallaphotocatalytic carbon-heteroatom cross-couplings}}, doi = {10.1039/d1gc01284c}, volume = {23}, year = {2021}, } @article{11974, abstract = {Visible light photocatalysis has become a powerful tool in organic synthesis that uses photons as traceless, sustainable reagents. Most of the activities in the field focus on the development of new reactions via common photoredox cycles, but recently a number of exciting new concepts and strategies entered less charted territories. We survey approaches that enable the use of longer wavelengths and show that the wavelength and intensity of photons are import parameters that enable tuning of the reactivity of a photocatalyst to control or change the selectivity of chemical reactions. In addition, we discuss recent efforts to substitute strong reductants, such as elemental lithium and sodium, by light and technological advances in the field.}, author = {Reischauer, Susanne and Pieber, Bartholomäus}, issn = {2589-0042}, journal = {iScience}, number = {3}, publisher = {Elsevier}, title = {{Emerging concepts in photocatalytic organic synthesis}}, doi = {10.1016/j.isci.2021.102209}, volume = {24}, year = {2021}, } @article{11981, abstract = {The cleavage of benzyl ethers by catalytic hydrogenolysis or Birch reduction suffers from poor functional group compatibility and limits their use as a protecting group. The visible-light-mediated debenzylation disclosed here renders benzyl ethers temporary protective groups, enabling new orthogonal protection strategies. Using 2,3-dichloro-5,6-dicyano-1,4-benzoquinone (DDQ) as a stoichiometric or catalytic photooxidant, benzyl ethers can be cleaved in the presence of azides, alkenes, and alkynes. The reaction time can be reduced from hours to minutes in continuous flow.}, author = {Cavedon, Cristian and Sletten, Eric T. and Madani, Amiera and Niemeyer, Olaf and Seeberger, Peter H. and Pieber, Bartholomäus}, issn = {1523-7052}, journal = {Organic Letters}, number = {2}, pages = {514--518}, publisher = {American Chemical Society}, title = {{Visible-light-mediated oxidative debenzylation enables the use of benzyl ethers as temporary protecting groups}}, doi = {10.1021/acs.orglett.0c04026}, volume = {23}, year = {2021}, } @unpublished{12068, abstract = {Metallaphotocatalysis typically requires a photocatalyst to harness the energy of visible-light and transfer it to a transition metal catalyst to trigger chemical reactions. The most prominent example is the merger of photo- and nickel catalysis that unlocked various cross-couplings. However, the high reactivity of excited photocatalyst can lead to unwanted side reactions thus limiting this approach. Here we show that a bipyridine ligand that is subtly decorated with two carbazole groups forms a nickel complex that absorbs visible-light and promotes several carbon–heteroatom cross-couplings in the absence of an exogenous photocatalysts. The ligand can be polymerized in a simple one-step procedure to afford a porous organic polymer that can be used for heterogeneous nickel catalysis in the same reactions. The material can be easily recovered and reused multiple times maintaining high catalytic activity and selectivity.}, author = {Cavedon, Cristian and Gisbertz, Sebastian and Vogl, Sarah and Richter, Noah and Schrottke, Stefanie and Teutloff, Christian and Seeberger, Peter H. and Thomas, Arne and Pieber, Bartholomäus}, publisher = {ChemRxiv}, title = {{Photocatalyst-free, visible-light-mediated nickel catalyzed carbon–heteroatom cross-couplings}}, doi = {10.26434/chemrxiv-2021-kt2wr}, year = {2021}, }