19 Search Results for "Peng, Richard"


Document
Distance Queries over Dynamic Interval Graphs

Authors: Jingbang Chen, Meng He, J. Ian Munro, Richard Peng, Kaiyu Wu, and Daniel J. Zhang

Published in: LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)


Abstract
We design the first dynamic distance oracles for interval graphs, which are intersection graphs of a set of intervals on the real line, and for proper interval graphs, which are intersection graphs of a set of intervals in which no interval is properly contained in another. For proper interval graphs, we design a linear space data structure which supports distance queries (computing the distance between two query vertices) and vertex insertion or deletion in O(lg n) worst-case time, where n is the number of vertices currently in G. Under incremental (insertion only) or decremental (deletion only) settings, we design linear space data structures that support distance queries in O(lg n) worst-case time and vertex insertion or deletion in O(lg n) amortized time, where n is the maximum number of vertices in the graph. Under fully dynamic settings, we design a data structure that represents an interval graph G in O(n) words of space to support distance queries in O(n lg n/S(n)) worst-case time and vertex insertion or deletion in O(S(n)+lg n) worst-case time, where n is the number of vertices currently in G and S(n) is an arbitrary function that satisfies S(n) = Ω(1) and S(n) = O(n). This implies an O(n)-word solution with O(√{nlg n})-time support for both distance queries and updates. All four data structures can answer shortest path queries by reporting the vertices in the shortest path between two query vertices in O(lg n) worst-case time per vertex. We also study the hardness of supporting distance queries under updates over an intersection graph of 3D axis-aligned line segments, which generalizes our problem to 3D. Finally, we solve the problem of computing the diameter of a dynamic connected interval graph.

Cite as

Jingbang Chen, Meng He, J. Ian Munro, Richard Peng, Kaiyu Wu, and Daniel J. Zhang. Distance Queries over Dynamic Interval Graphs. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 18:1-18:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{chen_et_al:LIPIcs.ISAAC.2023.18,
  author =	{Chen, Jingbang and He, Meng and Munro, J. Ian and Peng, Richard and Wu, Kaiyu and Zhang, Daniel J.},
  title =	{{Distance Queries over Dynamic Interval Graphs}},
  booktitle =	{34th International Symposium on Algorithms and Computation (ISAAC 2023)},
  pages =	{18:1--18:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-289-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{283},
  editor =	{Iwata, Satoru and Kakimura, Naonori},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.18},
  URN =		{urn:nbn:de:0030-drops-193207},
  doi =		{10.4230/LIPIcs.ISAAC.2023.18},
  annote =	{Keywords: interval graph, proper interval graph, intersection graph, geometric intersection graph, distance oracle, distance query, shortest path query, dynamic graph}
}
Document
A Simple Boosting Framework for Transshipment

Authors: Goran Zuzic

Published in: LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023)


Abstract
Transshipment is an important generalization of both the shortest path problem and the optimal transport problem. The task asks to route a demand using a flow of minimum cost over (uncapacitated) edges. Transshipment has recently received extensive attention in theoretical computer science as it is the centerpiece of all modern theoretical breakthroughs in parallel and distributed (approximate) shortest-path computation, a classic and well-studied problem. The key advantage of transshipment over shortest paths is the so-called boosting property: one can often boost a crude approximate solution to a (near-optimal) (1+ε)-approximate solution. However, our understanding of this phenomenon is limited: it is not clear which approximators can be boosted. Moreover, all current boosting frameworks are built with a specific type of approximator in mind and are relatively complicated. The main takeaway of our paper is conceptual: any black-box oracle that computes an approximate dual solution can be boosted to an (1+ε)-approximator. This decouples and simplifies all known near-optimal (1+ε)-approximate transshipment and shortest paths results: they all (implicitly) construct approximate dual solutions and boost them. We provide a very simple analysis based on the multiplicative weights framework. Furthermore, to keep the paper completely self-contained, we provide a new (and arguably much simpler) analysis of multiplicative weights that leverages well-known optimization tools to bypass the ad-hoc calculations used in the standard analyses.

Cite as

Goran Zuzic. A Simple Boosting Framework for Transshipment. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 104:1-104:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{zuzic:LIPIcs.ESA.2023.104,
  author =	{Zuzic, Goran},
  title =	{{A Simple Boosting Framework for Transshipment}},
  booktitle =	{31st Annual European Symposium on Algorithms (ESA 2023)},
  pages =	{104:1--104:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-295-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{274},
  editor =	{G{\o}rtz, Inge Li and Farach-Colton, Martin and Puglisi, Simon J. and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.104},
  URN =		{urn:nbn:de:0030-drops-187570},
  doi =		{10.4230/LIPIcs.ESA.2023.104},
  annote =	{Keywords: mixed continuous-discrete optimization, boosting, multiplicative weights, theoretical computer science, shortest path, parallel algorithms}
}
Document
Invited Talk
An Almost-Linear Time Algorithm for Maximum Flow and More (Invited Talk)

Authors: Rasmus Kyng

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)


Abstract
In this talk, I will explain a new algorithm for computing exact maximum and minimum-cost flows in almost-linear time, settling the time complexity of these basic graph problems up to subpolynomial factors. Our algorithm uses a novel interior point method that builds the optimal flow as a sequence of approximate minimum-ratio cycles, each of which is computed and processed very efficiently using a new dynamic data structure. By well-known reductions, our result implies almost-linear time algorithms for several problems including bipartite matching, optimal transport, and undirected vertex connectivity. Our framework also extends to minimizing general edge-separable convex functions to high accuracy, yielding the first almost-linear time algorithms for many other problems including entropy-regularized optimal transport, matrix scaling, p-norm flows, and isotonic regression. This talk is based on joint work with Li Chen, Yang P. Liu, Richard Peng, Maximilian Probst Gutenberg, and Sushant Sachdeva [Chen et al., 2022]. Our result appeared in FOCS'22 and won the FOCS best paper award.

Cite as

Rasmus Kyng. An Almost-Linear Time Algorithm for Maximum Flow and More (Invited Talk). In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, p. 2:1, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{kyng:LIPIcs.ICALP.2023.2,
  author =	{Kyng, Rasmus},
  title =	{{An Almost-Linear Time Algorithm for Maximum Flow and More}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.2},
  URN =		{urn:nbn:de:0030-drops-180543},
  doi =		{10.4230/LIPIcs.ICALP.2023.2},
  annote =	{Keywords: Maximum flow, Minimum cost flow, Data structures, Interior point methods, Convex optimization}
}
Document
Track A: Algorithms, Complexity and Games
Efficient Data Structures for Incremental Exact and Approximate Maximum Flow

Authors: Gramoz Goranci and Monika Henzinger

Published in: LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)


Abstract
We show an (1+ε)-approximation algorithm for maintaining maximum s-t flow under m edge insertions in m^{1/2+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. Furthermore we give an algorithm that maintains an exact maximum s-t flow under m edge insertions in an n-node graph in Õ(n^{5/2}) total update time. For sufficiently dense graphs, this gives to the first exact incremental algorithm with sub-linear amortized update time for maintaining maximum flows.

Cite as

Gramoz Goranci and Monika Henzinger. Efficient Data Structures for Incremental Exact and Approximate Maximum Flow. In 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 261, pp. 69:1-69:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{goranci_et_al:LIPIcs.ICALP.2023.69,
  author =	{Goranci, Gramoz and Henzinger, Monika},
  title =	{{Efficient Data Structures for Incremental Exact and Approximate Maximum Flow}},
  booktitle =	{50th International Colloquium on Automata, Languages, and Programming (ICALP 2023)},
  pages =	{69:1--69:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-278-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{261},
  editor =	{Etessami, Kousha and Feige, Uriel and Puppis, Gabriele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.69},
  URN =		{urn:nbn:de:0030-drops-181212},
  doi =		{10.4230/LIPIcs.ICALP.2023.69},
  annote =	{Keywords: dynamic graph algorithms, maximum flow, data structures}
}
Document
A Combinatorial Cut-Toggling Algorithm for Solving Laplacian Linear Systems

Authors: Monika Henzinger, Billy Jin, Richard Peng, and David P. Williamson

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)


Abstract
Over the last two decades, a significant line of work in theoretical algorithms has made progress in solving linear systems of the form 𝐋𝐱 = 𝐛, where 𝐋 is the Laplacian matrix of a weighted graph with weights w(i,j) > 0 on the edges. The solution 𝐱 of the linear system can be interpreted as the potentials of an electrical flow in which the resistance on edge (i,j) is 1/w(i,j). Kelner, Orrechia, Sidford, and Zhu [Kelner et al., 2013] give a combinatorial, near-linear time algorithm that maintains the Kirchoff Current Law, and gradually enforces the Kirchoff Potential Law by updating flows around cycles (cycle toggling). In this paper, we consider a dual version of the algorithm that maintains the Kirchoff Potential Law, and gradually enforces the Kirchoff Current Law by cut toggling: each iteration updates all potentials on one side of a fundamental cut of a spanning tree by the same amount. We prove that this dual algorithm also runs in a near-linear number of iterations. We show, however, that if we abstract cut toggling as a natural data structure problem, this problem can be reduced to the online vector-matrix-vector problem (OMv), which has been conjectured to be difficult for dynamic algorithms [Henzinger et al., 2015]. The conjecture implies that the data structure does not have an O(n^{1-ε}) time algorithm for any ε > 0, and thus a straightforward implementation of the cut-toggling algorithm requires essentially linear time per iteration. To circumvent the lower bound, we batch update steps, and perform them simultaneously instead of sequentially. An appropriate choice of batching leads to an Õ(m^{1.5}) time cut-toggling algorithm for solving Laplacian systems. Furthermore, we show that if we sparsify the graph and call our algorithm recursively on the Laplacian system implied by batching and sparsifying, we can reduce the running time to O(m^{1 + ε}) for any ε > 0. Thus, the dual cut-toggling algorithm can achieve (almost) the same running time as its primal cycle-toggling counterpart.

Cite as

Monika Henzinger, Billy Jin, Richard Peng, and David P. Williamson. A Combinatorial Cut-Toggling Algorithm for Solving Laplacian Linear Systems. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 69:1-69:22, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{henzinger_et_al:LIPIcs.ITCS.2023.69,
  author =	{Henzinger, Monika and Jin, Billy and Peng, Richard and Williamson, David P.},
  title =	{{A Combinatorial Cut-Toggling Algorithm for Solving Laplacian Linear Systems}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{69:1--69:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.69},
  URN =		{urn:nbn:de:0030-drops-175720},
  doi =		{10.4230/LIPIcs.ITCS.2023.69},
  annote =	{Keywords: Laplacian solver, electrical flow, data structure}
}
Document
Vertex Sparsification for Edge Connectivity in Polynomial Time

Authors: Yang P. Liu

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)


Abstract
An important open question in the area of vertex sparsification is whether (1+ε)-approximate cut-preserving vertex sparsifiers with size close to the number of terminals exist. The work [Parinya Chalermsook et al., 2021] (SODA 2021) introduced a relaxation called connectivity-c mimicking networks, which asks to construct a vertex sparsifier which preserves connectivity among k terminals exactly up to the value of c, and showed applications to dynamic connectivity data structures and survivable network design. We show that connectivity-c mimicking networks with Õ(kc³) edges exist and can be constructed in polynomial time in n and c, improving over the results of [Parinya Chalermsook et al., 2021] for any c ≥ log n, whose runtimes depended exponentially on c.

Cite as

Yang P. Liu. Vertex Sparsification for Edge Connectivity in Polynomial Time. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 83:1-83:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2023)


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@InProceedings{liu:LIPIcs.ITCS.2023.83,
  author =	{Liu, Yang P.},
  title =	{{Vertex Sparsification for Edge Connectivity in Polynomial Time}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{83:1--83:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.83},
  URN =		{urn:nbn:de:0030-drops-175863},
  doi =		{10.4230/LIPIcs.ITCS.2023.83},
  annote =	{Keywords: Vertex-sparsification, edge-connectivity, Gammoids}
}
Document
Vertex Sparsifiers for Hyperedge Connectivity

Authors: Han Jiang, Shang-En Huang, Thatchaphol Saranurak, and Tian Zhang

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)


Abstract
Recently, Chalermsook et al. {[}SODA'21{]} introduces a notion of vertex sparsifiers for c-edge connectivity, which has found applications in parameterized algorithms for network design and also led to exciting dynamic algorithms for c-edge st-connectivity {[}Jin and Sun FOCS'22{]}. We study a natural extension called vertex sparsifiers for c-hyperedge connectivity and construct a sparsifier whose size matches the state-of-the-art for normal graphs. More specifically, we show that, given a hypergraph G = (V,E) with n vertices and m hyperedges with k terminal vertices and a parameter c, there exists a hypergraph H containing only O(kc³) hyperedges that preserves all minimum cuts (up to value c) between all subset of terminals. This matches the best bound of O(kc³) edges for normal graphs by [Liu'20]. Moreover, H can be constructed in almost-linear O(p^{1+o(1)} + n(rclog n)^{O(rc)}log m) time where r = max_{e ∈ E}|e| is the rank of G and p = ∑_{e ∈ E}|e| is the total size of G, or in poly(m, n) time if we slightly relax the size to O(kc³log^{1.5}(kc)) hyperedges.

Cite as

Han Jiang, Shang-En Huang, Thatchaphol Saranurak, and Tian Zhang. Vertex Sparsifiers for Hyperedge Connectivity. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 70:1-70:13, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{jiang_et_al:LIPIcs.ESA.2022.70,
  author =	{Jiang, Han and Huang, Shang-En and Saranurak, Thatchaphol and Zhang, Tian},
  title =	{{Vertex Sparsifiers for Hyperedge Connectivity}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{70:1--70:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.70},
  URN =		{urn:nbn:de:0030-drops-170081},
  doi =		{10.4230/LIPIcs.ESA.2022.70},
  annote =	{Keywords: Vertex sparsifier, hypergraph, connectivity}
}
Document
Track A: Algorithms, Complexity and Games
Decremental Matching in General Graphs

Authors: Sepehr Assadi, Aaron Bernstein, and Aditi Dudeja

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)


Abstract
We consider the problem of maintaining an approximate maximum integral matching in a dynamic graph G, while the adversary makes changes to the edges of the graph. The goal is to maintain a (1+ε)-approximate maximum matching for constant ε > 0, while minimizing the update time. In the fully dynamic setting, where both edge insertion and deletions are allowed, Gupta and Peng (see [Manoj Gupta and Richard Peng, 2013]) gave an algorithm for this problem with an update time of O(√m/ε²). Motivated by the fact that the O_ε(√m) barrier is hard to overcome (see Henzinger, Krinninger, Nanongkai, and Saranurak [Henzinger et al., 2015]; Kopelowitz, Pettie, and Porat [Kopelowitz et al., 2016]), we study this problem in the decremental model, where the adversary is only allowed to delete edges. Recently, Bernstein, Probst-Gutenberg, and Saranurak (see [Bernstein et al., 2020]) gave an O(poly({log n}/ε)) update time decremental algorithm for this problem in bipartite graphs. However, beating O(√m) update time remained an open problem for general graphs. In this paper, we bridge the gap between bipartite and general graphs, by giving an O_ε(poly(log n)) update time algorithm that maintains a (1+ε)-approximate maximum integral matching under adversarial deletions. Our algorithm is randomized, but works against an adaptive adversary. Together with the work of Grandoni, Leonardi, Sankowski, Schwiegelshohn, and Solomon [Fabrizio Grandoni et al., 2019] who give an O_ε(1) update time algorithm for general graphs in the incremental (insertion-only) model, our result essentially completes the picture for partially dynamic matching.

Cite as

Sepehr Assadi, Aaron Bernstein, and Aditi Dudeja. Decremental Matching in General Graphs. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 11:1-11:19, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{assadi_et_al:LIPIcs.ICALP.2022.11,
  author =	{Assadi, Sepehr and Bernstein, Aaron and Dudeja, Aditi},
  title =	{{Decremental Matching in General Graphs}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{11:1--11:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.11},
  URN =		{urn:nbn:de:0030-drops-163528},
  doi =		{10.4230/LIPIcs.ICALP.2022.11},
  annote =	{Keywords: Dynamic algorithms, matching, primal-dual algorithms}
}
Document
Faster Sparse Matrix Inversion and Rank Computation in Finite Fields

Authors: Sílvia Casacuberta and Rasmus Kyng

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)


Abstract
We improve the current best running time value to invert sparse matrices over finite fields, lowering it to an expected O(n^{2.2131}) time for the current values of fast rectangular matrix multiplication. We achieve the same running time for the computation of the rank and nullspace of a sparse matrix over a finite field. This improvement relies on two key techniques. First, we adopt the decomposition of an arbitrary matrix into block Krylov and Hankel matrices from Eberly et al. (ISSAC 2007). Second, we show how to recover the explicit inverse of a block Hankel matrix using low displacement rank techniques for structured matrices and fast rectangular matrix multiplication algorithms. We generalize our inversion method to block structured matrices with other displacement operators and strengthen the best known upper bounds for explicit inversion of block Toeplitz-like and block Hankel-like matrices, as well as for explicit inversion of block Vandermonde-like matrices with structured blocks. As a further application, we improve the complexity of several algorithms in topological data analysis and in finite group theory.

Cite as

Sílvia Casacuberta and Rasmus Kyng. Faster Sparse Matrix Inversion and Rank Computation in Finite Fields. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 33:1-33:24, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)


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@InProceedings{casacuberta_et_al:LIPIcs.ITCS.2022.33,
  author =	{Casacuberta, S{\'\i}lvia and Kyng, Rasmus},
  title =	{{Faster Sparse Matrix Inversion and Rank Computation in Finite Fields}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{33:1--33:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.33},
  URN =		{urn:nbn:de:0030-drops-156290},
  doi =		{10.4230/LIPIcs.ITCS.2022.33},
  annote =	{Keywords: Matrix inversion, rank computation, displacement operators, numerical linear algebra}
}
Document
Sampling Arborescences in Parallel

Authors: Nima Anari, Nathan Hu, Amin Saberi, and Aaron Schild

Published in: LIPIcs, Volume 185, 12th Innovations in Theoretical Computer Science Conference (ITCS 2021)


Abstract
We study the problem of sampling a uniformly random directed rooted spanning tree, also known as an arborescence, from a possibly weighted directed graph. Classically, this problem has long been known to be polynomial-time solvable; the exact number of arborescences can be computed by a determinant [Tutte, 1948], and sampling can be reduced to counting [Jerrum et al., 1986; Jerrum and Sinclair, 1996]. However, the classic reduction from sampling to counting seems to be inherently sequential. This raises the question of designing efficient parallel algorithms for sampling. We show that sampling arborescences can be done in RNC. For several well-studied combinatorial structures, counting can be reduced to the computation of a determinant, which is known to be in NC [Csanky, 1975]. These include arborescences, planar graph perfect matchings, Eulerian tours in digraphs, and determinantal point processes. However, not much is known about efficient parallel sampling of these structures. Our work is a step towards resolving this mystery.

Cite as

Nima Anari, Nathan Hu, Amin Saberi, and Aaron Schild. Sampling Arborescences in Parallel. In 12th Innovations in Theoretical Computer Science Conference (ITCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 185, pp. 83:1-83:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{anari_et_al:LIPIcs.ITCS.2021.83,
  author =	{Anari, Nima and Hu, Nathan and Saberi, Amin and Schild, Aaron},
  title =	{{Sampling Arborescences in Parallel}},
  booktitle =	{12th Innovations in Theoretical Computer Science Conference (ITCS 2021)},
  pages =	{83:1--83:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-177-1},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{185},
  editor =	{Lee, James R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2021.83},
  URN =		{urn:nbn:de:0030-drops-136225},
  doi =		{10.4230/LIPIcs.ITCS.2021.83},
  annote =	{Keywords: parallel algorithms, arborescences, spanning trees, random sampling}
}
Document
Invited Talk
Convex Optimization and Dynamic Data Structure (Invited Talk)

Authors: Yin Tat Lee

Published in: LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)


Abstract
In the last three years, there are many breakthroughs in optimization such as nearly quadratic time algorithms for bipartite matching, linear programming algorithms that are as fast as Ax = b. All of these algorithms are based on a careful combination of optimization techniques and dynamic data structures. In this talk, we will explain the framework underlying all the recent breakthroughs. Joint work with Jan van den Brand, Michael B. Cohen, Sally Dong, Haotian Jiang, Tarun Kathuria, Danupon Nanongkai, Swati Padmanabhan, Richard Peng, Thatchaphol Saranurak, Aaron Sidford, Zhao Song, Di Wang, Sam Chiu-wai Wong, Guanghao Ye, Qiuyi Zhang.

Cite as

Yin Tat Lee. Convex Optimization and Dynamic Data Structure (Invited Talk). In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, p. 3:1, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)


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@InProceedings{lee:LIPIcs.FSTTCS.2020.3,
  author =	{Lee, Yin Tat},
  title =	{{Convex Optimization and Dynamic Data Structure}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{3:1--3:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Saxena, Nitin and Simon, Sunil},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.3},
  URN =		{urn:nbn:de:0030-drops-132440},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.3},
  annote =	{Keywords: Convex Optimization, Dynamic Data Structure}
}
Document
Fault Tolerant and Fully Dynamic DFS in Undirected Graphs: Simple Yet Efficient

Authors: Surender Baswana, Shiv Gupta, and Ayush Tulsyan

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


Abstract
We present an algorithm for a fault tolerant Depth First Search (DFS) Tree in an undirected graph. This algorithm is drastically simpler than the current state-of-the-art algorithms for this problem, uses optimal space and optimal preprocessing time, and still achieves better time complexity. This algorithm also leads to a better time complexity for maintaining a DFS tree in a fully dynamic environment.

Cite as

Surender Baswana, Shiv Gupta, and Ayush Tulsyan. Fault Tolerant and Fully Dynamic DFS in Undirected Graphs: Simple Yet Efficient. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 65:1-65:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{baswana_et_al:LIPIcs.MFCS.2019.65,
  author =	{Baswana, Surender and Gupta, Shiv and Tulsyan, Ayush},
  title =	{{Fault Tolerant and Fully Dynamic DFS in Undirected Graphs: Simple Yet Efficient}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{65:1--65:16},
  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.2019.65},
  URN =		{urn:nbn:de:0030-drops-110096},
  doi =		{10.4230/LIPIcs.MFCS.2019.65},
  annote =	{Keywords: Depth first search, DFS, Dynamic graph algorithms, Fault tolerant}
}
Document
The Dynamic Practice and Static Theory of Gradual Typing

Authors: Michael Greenberg

Published in: LIPIcs, Volume 136, 3rd Summit on Advances in Programming Languages (SNAPL 2019)


Abstract
We can tease apart the research on gradual types into two `lineages': a pragmatic, implementation-oriented dynamic-first lineage and a formal, type-theoretic, static-first lineage. The dynamic-first lineage’s focus is on taming particular idioms - `pre-existing conditions' in untyped programming languages. The static-first lineage’s focus is on interoperation and individual type system features, rather than the collection of features found in any particular language. Both appear in programming languages research under the name "gradual typing", and they are in active conversation with each other. What are these two lineages? What challenges and opportunities await the static-first lineage? What progress has been made so far?

Cite as

Michael Greenberg. The Dynamic Practice and Static Theory of Gradual Typing. In 3rd Summit on Advances in Programming Languages (SNAPL 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 136, pp. 6:1-6:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{greenberg:LIPIcs.SNAPL.2019.6,
  author =	{Greenberg, Michael},
  title =	{{The Dynamic Practice and Static Theory of Gradual Typing}},
  booktitle =	{3rd Summit on Advances in Programming Languages (SNAPL 2019)},
  pages =	{6:1--6:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-113-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{136},
  editor =	{Lerner, Benjamin S. and Bod{\'\i}k, Rastislav and Krishnamurthi, Shriram},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SNAPL.2019.6},
  URN =		{urn:nbn:de:0030-drops-105495},
  doi =		{10.4230/LIPIcs.SNAPL.2019.6},
  annote =	{Keywords: dynamic typing, gradual typing, static typing, implementation, theory, challenge problems}
}
Document
High-Performance Graph Algorithms (Dagstuhl Seminar 18241)

Authors: Henning Meyerhenke, Richard Peng, and Ilya Safro

Published in: Dagstuhl Reports, Volume 8, Issue 6 (2019)


Abstract
This report documents the program and outcomes of Dagstuhl Seminar 18241 ``High-performance Graph Algorithms''. The seminar reflected the ongoing qualitative change how graph algorithms are used in practice due to (i) the complex structure of graphs in new and emerging applications, (ii) the size of typical inputs, and (iii) the computer systems with which graph problems are solved. This change is having a tremendous impact on the field of graph algorithms in terms of algorithm theory and implementation as well as hardware requirements and application areas. The seminar covered recent advances in all these aspects, trying to balance and mediate between theory and practice. The abstracts included in this report contain and survey recent state-of-the-art results, but also point to promising new directions for high-performance graph algorithms and their applications, both from a theoretical and a practical point of view.

Cite as

Henning Meyerhenke, Richard Peng, and Ilya Safro. High-Performance Graph Algorithms (Dagstuhl Seminar 18241). In Dagstuhl Reports, Volume 8, Issue 6, pp. 19-39, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2018)


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@Article{meyerhenke_et_al:DagRep.8.6.19,
  author =	{Meyerhenke, Henning and Peng, Richard and Safro, Ilya},
  title =	{{High-Performance Graph Algorithms (Dagstuhl Seminar 18241)}},
  pages =	{19--39},
  journal =	{Dagstuhl Reports},
  ISSN =	{2192-5283},
  year =	{2018},
  volume =	{8},
  number =	{6},
  editor =	{Meyerhenke, Henning and Peng, Richard and Safro, Ilya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagRep.8.6.19},
  URN =		{urn:nbn:de:0030-drops-100475},
  doi =		{10.4230/DagRep.8.6.19},
  annote =	{Keywords: algorithm engineering, combinatorial scientific computing, graph algorithms, high-performance computing, theoretical computer science}
}
Document
Density Independent Algorithms for Sparsifying k-Step Random Walks

Authors: Gorav Jindal, Pavel Kolev, Richard Peng, and Saurabh Sawlani

Published in: LIPIcs, Volume 81, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)


Abstract
We give faster algorithms for producing sparse approximations of the transition matrices of k-step random walks on undirected and weighted graphs. These transition matrices also form graphs, and arise as intermediate objects in a variety of graph algorithms. Our improvements are based on a better understanding of processes that sample such walks, as well as tighter bounds on key weights underlying these sampling processes. On a graph with n vertices and m edges, our algorithm produces a graph with about nlog(n) edges that approximates the k-step random walk graph in about m + k^2 nlog^4(n) time. In order to obtain this runtime bound, we also revisit "density independent" algorithms for sparsifying graphs whose runtime overhead is expressed only in terms of the number of vertices.

Cite as

Gorav Jindal, Pavel Kolev, Richard Peng, and Saurabh Sawlani. Density Independent Algorithms for Sparsifying k-Step Random Walks. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 81, pp. 14:1-14:17, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)


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@InProceedings{jindal_et_al:LIPIcs.APPROX-RANDOM.2017.14,
  author =	{Jindal, Gorav and Kolev, Pavel and Peng, Richard and Sawlani, Saurabh},
  title =	{{Density Independent Algorithms for Sparsifying k-Step Random Walks}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2017)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-044-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{81},
  editor =	{Jansen, Klaus and Rolim, Jos\'{e} D. P. and Williamson, David P. and Vempala, Santosh S.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2017.14},
  URN =		{urn:nbn:de:0030-drops-75638},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2017.14},
  annote =	{Keywords: random walks, graph sparsification, spectral graph theory, effective resistances}
}
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