@inproceedings{14769,
  abstract     = {For a set of points in Rd, the Euclidean k-means problems consists of finding k centers such that the sum of distances squared from each data point to its closest center is minimized. Coresets are one the main tools developed recently to solve this problem in a big data context. They allow to compress the initial dataset while preserving its structure: running any algorithm on the coreset provides a guarantee almost equivalent to running it on the full data. In this work, we study coresets in a fully-dynamic setting: points are added and deleted with the goal to efficiently maintain a coreset with which a k-means solution can be computed. Based on an algorithm from Henzinger and Kale [ESA'20], we present an efficient and practical implementation of a fully dynamic coreset algorithm, that improves the running time by up to a factor of 20 compared to our non-optimized implementation of the algorithm by Henzinger and Kale, without sacrificing more than 7% on the quality of the k-means solution.},
  author       = {Henzinger, Monika H and Saulpic, David and Sidl, Leonhard},
  booktitle    = {2024 Proceedings of the Symposium on Algorithm Engineering and Experiments},
  location     = {Alexandria, VA, United States},
  pages        = {220--233},
  publisher    = {Society for Industrial & Applied Mathematics},
  title        = {{Experimental evaluation of fully dynamic k-means via coresets}},
  doi          = {10.1137/1.9781611977929.17},
  year         = {2024},
}

@inproceedings{15008,
  abstract     = {Oblivious routing is a well-studied paradigm that uses static precomputed routing tables for selecting routing paths within a network. Existing oblivious routing schemes with polylogarithmic competitive ratio for general networks are tree-based, in the sense that routing is performed according to a convex combination of trees. However, this restriction to trees leads to a construction that has time quadratic in the size of the network and does not parallelize well. 
In this paper we study oblivious routing schemes based on electrical routing. In particular, we show that general networks with n vertices and m edges admit a routing scheme that has competitive ratio O(log² n) and consists of a convex combination of only O(√m) electrical routings. This immediately leads to an improved construction algorithm with time Õ(m^{3/2}) that can also be implemented in parallel with Õ(√m) depth.},
  author       = {Goranci, Gramoz and Henzinger, Monika H and Räcke, Harald and Sachdeva, Sushant and Sricharan, A. R.},
  booktitle    = {15th Innovations in Theoretical Computer Science Conference},
  isbn         = {9783959773096},
  issn         = {1868-8969},
  location     = {Berkeley, CA, United States},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{Electrical flows for polylogarithmic competitive oblivious routing}},
  doi          = {10.4230/LIPIcs.ITCS.2024.55},
  volume       = {287},
  year         = {2024},
}

@article{14558,
  abstract     = {n the dynamic minimum set cover problem, the challenge is to minimize the update time while guaranteeing a close-to-optimal min{O(log n), f} approximation factor. (Throughout, n, m, f , and C are parameters denoting the maximum number of elements, the number of sets, the 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 by Gupta et al. [Online and dynamic algorithms for set cover, in Proceedings STOC 2017, ACM, pp. 537–550]. In this paper we consider the low-frequency range, when f = O(log n) , and obtain deterministic algorithms with a (1 + ∈)f -approximation ratio and the following guarantees on the update time. (1)  O ((f/∈)-log(Cn)) amortized update time: Prior to our work, the best approximation ratio guaranteed by deterministic algorithms was O(f2) of Bhattacharya, Henzinger, and Italiano [Design of dynamic algorithms via primal-dual method, in Proceedings ICALP 2015, Springer, pp. 206–218]. In contrast, the only result with O(f) -approximation was that of Abboud et al. [Dynamic set cover: Improved algorithms and lower bounds, in Proceedings STOC 2019, ACM, pp. 114–125], who designed a randomized (1+∈)f -approximation algorithm with  amortized update time. (2) O(f2/∈3 + (f/∈2).logC) amortized update time: This result improves the above update time bound for most values of f
 in the low-frequency range, i.e., f=o(log n) . It is also the first result that is independent of m
 and n. It subsumes the constant amortized update time of Bhattacharya and Kulkarni [Deterministically maintaining a (2 + ∈) -approximate minimum vertex cover in O(1/∈2) amortized update time, in Proceedings SODA 2019, SIAM, pp. 1872–1885] for unweighted dynamic vertex cover (i.e., when f = 2 and C = 1). (3) O((f/∈3).log2(Cn)) worst-case update time: No nontrivial worst-case update time was previously known for the dynamic set cover problem. Our bound subsumes and improves by a logarithmic factor the O(log3n/poly (∈)) 
 worst-case update time for the unweighted dynamic vertex cover problem (i.e., when f = 2
 and C =1) of Bhattacharya, Henzinger, and Nanongkai [Fully dynamic approximate maximum matching and minimum vertex cover in O(log3)n worst case update time, in Proceedings SODA 2017, SIAM, pp. 470–489]. We achieve our results via the primal-dual approach, by maintaining a fractional packing solution as a dual certificate. Prior work in dynamic algorithms that employs the primal-dual approach uses a local update scheme that maintains relaxed complementary slackness conditions for every set. For our first result we use instead a global update scheme that does not always maintain complementary slackness conditions. For our second result we combine the global and the local update schema. To achieve our third result we use a hierarchy of background schedulers. It is an interesting open question whether this background scheduler technique can also be used to transform algorithms with amortized running time bounds into algorithms with worst-case running time bounds.},
  author       = {Bhattacharya, Sayan and Henzinger, Monika H and Nanongkai, Danupon and Wu, Xiaowei},
  issn         = {1095-7111},
  journal      = {SIAM Journal on Computing},
  number       = {5},
  pages        = {1132--1192},
  publisher    = {Society for Industrial and Applied Mathematics},
  title        = {{Deterministic near-optimal approximation algorithms for dynamic set cover}},
  doi          = {10.1137/21M1428649},
  volume       = {52},
  year         = {2023},
}

@inproceedings{14085,
  abstract     = {We show an (1+ϵ)-approximation algorithm for maintaining maximum s-t flow under m edge insertions in m1/2+o(1)ϵ−1/2 amortized update time for directed, unweighted graphs. This constitutes the first sublinear dynamic maximum flow algorithm in general sparse graphs with arbitrarily good approximation guarantee.},
  author       = {Goranci, Gramoz and Henzinger, Monika H},
  booktitle    = {50th International Colloquium on Automata, Languages, and Programming},
  isbn         = {9783959772785},
  issn         = {1868-8969},
  location     = {Paderborn, Germany},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{Efficient data structures for incremental exact and approximate maximum flow}},
  doi          = {10.4230/LIPIcs.ICALP.2023.69},
  volume       = {261},
  year         = {2023},
}

@inproceedings{14086,
  abstract     = {The maximization of submodular functions have found widespread application in areas such as machine learning, combinatorial optimization, and economics, where practitioners often wish to enforce various constraints; the matroid constraint has been investigated extensively due to its algorithmic properties and expressive power. Though tight approximation algorithms for general matroid constraints exist in theory, the running times of such algorithms typically scale quadratically, and are not practical for truly large scale settings. Recent progress has focused on fast algorithms for important classes of matroids given in explicit form. Currently, nearly-linear time algorithms only exist for graphic and partition matroids [Alina Ene and Huy L. Nguyen, 2019]. In this work, we develop algorithms for monotone submodular maximization constrained by graphic, transversal matroids, or laminar matroids in time near-linear in the size of their representation. Our algorithms achieve an optimal approximation of 1-1/e-ε and both generalize and accelerate the results of Ene and Nguyen [Alina Ene and Huy L. Nguyen, 2019]. In fact, the running time of our algorithm cannot be improved within the fast continuous greedy framework of Badanidiyuru and Vondrák [Ashwinkumar Badanidiyuru and Jan Vondrák, 2014].
To achieve near-linear running time, we make use of dynamic data structures that maintain bases with approximate maximum cardinality and weight under certain element updates. These data structures need to support a weight decrease operation and a novel Freeze operation that allows the algorithm to freeze elements (i.e. force to be contained) in its basis regardless of future data structure operations. For the laminar matroid, we present a new dynamic data structure using the top tree interface of Alstrup, Holm, de Lichtenberg, and Thorup [Stephen Alstrup et al., 2005] that maintains the maximum weight basis under insertions and deletions of elements in O(log n) time. This data structure needs to support certain subtree query and path update operations that are performed every insertion and deletion that are non-trivial to handle in conjunction. For the transversal matroid the Freeze operation corresponds to requiring the data structure to keep a certain set S of vertices matched, a property that we call S-stability. While there is a large body of work on dynamic matching algorithms, none are S-stable and maintain an approximate maximum weight matching under vertex updates. We give the first such algorithm for bipartite graphs with total running time linear (up to log factors) in the number of edges.},
  author       = {Henzinger, Monika H and Liu, Paul and Vondrák, Jan and Zheng, Da Wei},
  booktitle    = {50th International Colloquium on Automata, Languages, and Programming},
  isbn         = {9783959772785},
  issn         = {18688969},
  location     = {Paderborn, Germany},
  publisher    = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik},
  title        = {{Faster submodular maximization for several classes of matroids}},
  doi          = {10.4230/LIPIcs.ICALP.2023.74},
  volume       = {261},
  year         = {2023},
}