5 Search Results for "Liu, Yang P."


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-dev.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
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-dev.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-dev.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
A Gaussian Fixed Point Random Walk

Authors: Yang P. Liu, Ashwin Sah, and Mehtaab Sawhney

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


Abstract
In this note, we design a discrete random walk on the real line which takes steps 0,±1 (and one with steps in {±1,2}) where at least 96% of the signs are ±1 in expectation, and which has 𝒩(0,1) as a stationary distribution. As an immediate corollary, we obtain an online version of Banaszczyk’s discrepancy result for partial colorings and ±1,2 signings. Additionally, we recover linear time algorithms for logarithmic bounds for the Komlós conjecture in an oblivious online setting.

Cite as

Yang P. Liu, Ashwin Sah, and Mehtaab Sawhney. A Gaussian Fixed Point Random Walk. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 101:1-101:10, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


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@InProceedings{liu_et_al:LIPIcs.ITCS.2022.101,
  author =	{Liu, Yang P. and Sah, Ashwin and Sawhney, Mehtaab},
  title =	{{A Gaussian Fixed Point Random Walk}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{101:1--101:10},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.101},
  URN =		{urn:nbn:de:0030-drops-156975},
  doi =		{10.4230/LIPIcs.ITCS.2022.101},
  annote =	{Keywords: Discrepancy, Partial Coloring}
}
Document
An Exponential Separation Between MA and AM Proofs of Proximity

Authors: Tom Gur, Yang P. Liu, and Ron D. Rothblum

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)


Abstract
Interactive proofs of proximity allow a sublinear-time verifier to check that a given input is close to the language, using a small amount of communication with a powerful (but untrusted) prover. In this work we consider two natural minimally interactive variants of such proofs systems, in which the prover only sends a single message, referred to as the proof. The first variant, known as MA-proofs of Proximity (MAP), is fully non-interactive, meaning that the proof is a function of the input only. The second variant, known as AM-proofs of Proximity (AMP), allows the proof to additionally depend on the verifier's (entire) random string. The complexity of both MAPs and AMPs is the total number of bits that the verifier observes - namely, the sum of the proof length and query complexity. Our main result is an exponential separation between the power of MAPs and AMPs. Specifically, we exhibit an explicit and natural property Pi that admits an AMP with complexity O(log n), whereas any MAP for Pi has complexity Omega~(n^{1/4}), where n denotes the length of the input in bits. Our MAP lower bound also yields an alternate proof, which is more general and arguably much simpler, for a recent result of Fischer et al. (ITCS, 2014). Lastly, we also consider the notion of oblivious proofs of proximity, in which the verifier's queries are oblivious to the proof. In this setting we show that AMPs can only be quadratically stronger than MAPs. As an application of this result, we show an exponential separation between the power of public and private coin for oblivious interactive proofs of proximity.

Cite as

Tom Gur, Yang P. Liu, and Ron D. Rothblum. An Exponential Separation Between MA and AM Proofs of Proximity. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 73:1-73:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{gur_et_al:LIPIcs.ICALP.2018.73,
  author =	{Gur, Tom and Liu, Yang P. and Rothblum, Ron D.},
  title =	{{An Exponential Separation Between MA and AM Proofs of Proximity}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{73:1--73:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.73},
  URN =		{urn:nbn:de:0030-drops-90772},
  doi =		{10.4230/LIPIcs.ICALP.2018.73},
  annote =	{Keywords: Property testing, Probabilistic proof systems, Proofs of proximity}
}
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