@inproceedings{11851, abstract = {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.}, author = {Henzinger, Monika H and Noe, Alexander and Schulz, Christian}, booktitle = {33rd International Parallel and Distributed Processing Symposium}, isbn = {978-1-7281-1247-3}, issn = {1530-2075}, location = {Rio de Janeiro, Brazil}, publisher = {Institute of Electrical and Electronics Engineers}, title = {{Shared-memory exact minimum cuts}}, doi = {10.1109/ipdps.2019.00013}, year = {2019}, } @inproceedings{11865, abstract = {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.}, author = {Daga, Mohit and Henzinger, Monika H and Nanongkai, Danupon and Saranurak, Thatchaphol}, booktitle = {Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing}, isbn = {978-1-4503-6705-9}, issn = {0737-8017}, location = {Phoenix, AZ, United States}, pages = {343–354}, publisher = {Association for Computing Machinery}, title = {{Distributed edge connectivity in sublinear time}}, doi = {10.1145/3313276.3316346}, year = {2019}, } @inproceedings{11871, 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 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.}, author = {Bernstein, Aaron and Forster, Sebastian and Henzinger, Monika H}, booktitle = {30th Annual ACM-SIAM Symposium on Discrete Algorithms}, location = {San Diego, CA, United States}, pages = {1899--1918}, publisher = {Society for Industrial and Applied Mathematics}, title = {{A deamortization approach for dynamic spanner and dynamic maximal matching}}, doi = {10.1137/1.9781611975482.115}, year = {2019}, } @article{11898, abstract = {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.}, author = {Bhattacharya, Sayan and Henzinger, Monika H and Neumann, Stefan}, issn = {0304-3975}, journal = {Theoretical Computer Science}, pages = {72--87}, publisher = {Elsevier}, title = {{New amortized cell-probe lower bounds for dynamic problems}}, doi = {10.1016/j.tcs.2019.01.043}, volume = {779}, year = {2019}, } @article{11957, abstract = {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.}, author = {Pieber, Bartholomäus and Malik, Jamal A. and Cavedon, Cristian and Gisbertz, Sebastian and Savateev, Aleksandr and Cruz, Daniel and Heil, Tobias and Zhang, Guigang and Seeberger, Peter H.}, issn = {1521-3773}, journal = {Angewandte Chemie International Edition}, number = {28}, pages = {9575--9580}, publisher = {Wiley}, title = {{Semi‐heterogeneous dual nickel/photocatalysis using carbon nitrides: Esterification of carboxylic acids with aryl halides}}, doi = {10.1002/anie.201902785}, volume = {58}, year = {2019}, }