2 Search Results for "Venkat, Prayaag"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2025.128
3.415-Approximation for Coflow Scheduling via Iterated Rounding

Authors: Lars Rohwedder and Leander Schnaars

Published in: LIPIcs, Volume 334, 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)

Abstract
We provide an algorithm giving a 140/41 (< 3.415)-approximation for Coflow Scheduling and a 4.36-approximation for Coflow Scheduling with release dates. This improves upon the best known 4- and respectively 5-approximations and addresses an open question posed by Agarwal, Rajakrishnan, Narayan, Agarwal, Shmoys, and Vahdat [Agarwal et al., 2018], Fukunaga [Fukunaga, 2022], and others. We additionally show that in an asymptotic setting, the algorithm achieves a (2+ε)-approximation, which is essentially optimal under ℙ ≠ NP. The improvements are achieved using a novel edge allocation scheme using iterated LP rounding together with a framework which enables establishing strong bounds for combinations of several edge allocation algorithms.
Cite as

Lars Rohwedder and Leander Schnaars. 3.415-Approximation for Coflow Scheduling via Iterated Rounding. In 52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 334, pp. 128:1-128:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{rohwedder_et_al:LIPIcs.ICALP.2025.128,
  author =	{Rohwedder, Lars and Schnaars, Leander},
  title =	{{3.415-Approximation for Coflow Scheduling via Iterated Rounding}},
  booktitle =	{52nd International Colloquium on Automata, Languages, and Programming (ICALP 2025)},
  pages =	{128:1--128:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-372-0},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{334},
  editor =	{Censor-Hillel, Keren and Grandoni, Fabrizio and Ouaknine, Jo\"{e}l 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.2025.128},
  URN =		{urn:nbn:de:0030-drops-235050},
  doi =		{10.4230/LIPIcs.ICALP.2025.128},
  annote =	{Keywords: Coflow Scheduling, Approximation Algorithms, Iterated Rounding}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.98
Efficient Algorithms for Certifying Lower Bounds on the Discrepancy of Random Matrices

Authors: Prayaag Venkat

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

Abstract
In this paper, we initiate the study of the algorithmic problem of certifying lower bounds on the discrepancy of random matrices: given an input matrix A ∈ ℝ^{m × n}, output a value that is a lower bound on disc(A) = min_{x ∈ {± 1}ⁿ} ‖Ax‖_∞ for every A, but is close to the typical value of disc(A) with high probability over the choice of a random A. This problem is important because of its connections to conjecturally-hard average-case problems such as negatively-spiked PCA [Afonso S. Bandeira et al., 2020], the number-balancing problem [Gamarnik and Kızıldağ, 2021] and refuting random constraint satisfaction problems [Prasad Raghavendra et al., 2017]. We give the first polynomial-time algorithms with non-trivial guarantees for two main settings. First, when the entries of A are i.i.d. standard Gaussians, it is known that disc(A) = Θ (√n2^{-n/m}) with high probability [Karthekeyan Chandrasekaran and Santosh S. Vempala, 2014; Aubin et al., 2019; Paxton Turner et al., 2020] and that super-constant levels of the Sum-of-Squares SDP hierarchy fail to certify anything better than disc(A) ≥ 0 when m < n - o(n) [Mrinalkanti Ghosh et al., 2020]. In contrast, our algorithm certifies that disc(A) ≥ exp(-O(n²/m)) with high probability. As an application, this formally refutes a conjecture of Bandeira, Kunisky, and Wein [Afonso S. Bandeira et al., 2020] on the computational hardness of the detection problem in the negatively-spiked Wishart model. Second, we consider the integer partitioning problem: given n uniformly random b-bit integers a₁, …, a_n, certify the non-existence of a perfect partition, i.e. certify that disc(A) ≥ 1 for A = (a₁, …, a_n). Under the scaling b = α n, it is known that the probability of the existence of a perfect partition undergoes a phase transition from 1 to 0 at α = 1 [Christian Borgs et al., 2001]; our algorithm certifies the non-existence of perfect partitions for some α = O(n). We also give efficient non-deterministic algorithms with significantly improved guarantees, raising the possibility that the landscape of these certification problems closely resembles that of e.g. the problem of refuting random 3SAT formulas in the unsatisfiable regime. Our algorithms involve a reduction to the Shortest Vector Problem and employ the Lenstra-Lenstra-Lovász algorithm.
Cite as

Prayaag Venkat. Efficient Algorithms for Certifying Lower Bounds on the Discrepancy of Random Matrices. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 98:1-98:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{venkat:LIPIcs.ITCS.2023.98,
  author =	{Venkat, Prayaag},
  title =	{{Efficient Algorithms for Certifying Lower Bounds on the Discrepancy of Random Matrices}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{98:1--98:12},
  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.2023.98},
  URN =		{urn:nbn:de:0030-drops-176015},
  doi =		{10.4230/LIPIcs.ITCS.2023.98},
  annote =	{Keywords: Average-case discrepancy theory, lattices, shortest vector problem}
}
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