6 Search Results for "Bhaskara, Aditya"

Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.6
Parameterized Approximation For Robust Clustering in Discrete Geometric Spaces

Authors: Fateme Abbasi, Sandip Banerjee, Jarosław Byrka, Parinya Chalermsook, Ameet Gadekar, Kamyar Khodamoradi, Dániel Marx, Roohani Sharma, and Joachim Spoerhase

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We consider the well-studied Robust (k,z)-Clustering problem, which generalizes the classic k-Median, k-Means, and k-Center problems and arises in the domains of robust optimization [Anthony, Goyal, Gupta, Nagarajan, Math. Oper. Res. 2010] and in algorithmic fairness [Abbasi, Bhaskara, Venkatasubramanian, 2021 & Ghadiri, Samadi, Vempala, 2022]. Given a constant z ≥ 1, the input to Robust (k,z)-Clustering is a set P of n points in a metric space (M,δ), a weight function w: P → ℝ_{≥ 0} and a positive integer k. Further, each point belongs to one (or more) of the m many different groups S_1,S_2,…,S_m ⊆ P. Our goal is to find a set X of k centers such that max_{i ∈ [m]} ∑_{p ∈ S_i} w(p) δ(p,X)^z is minimized. Complementing recent work on this problem, we give a comprehensive understanding of the parameterized approximability of the problem in geometric spaces where the parameter is the number k of centers. We prove the following results: [(i)] 1) For a universal constant η₀ > 0.0006, we devise a 3^z(1-η₀)-factor FPT approximation algorithm for Robust (k,z)-Clustering in discrete high-dimensional Euclidean spaces where the set of potential centers is finite. This shows that the lower bound of 3^z for general metrics [Goyal, Jaiswal, Inf. Proc. Letters, 2023] no longer holds when the metric has geometric structure. 2) We show that Robust (k,z)-Clustering in discrete Euclidean spaces is (√{3/2}- o(1))-hard to approximate for FPT algorithms, even if we consider the special case k-Center in logarithmic dimensions. This rules out a (1+ε)-approximation algorithm running in time f(k,ε)poly(m,n) (also called efficient parameterized approximation scheme or EPAS), giving a striking contrast with the recent EPAS for the continuous setting where centers can be placed anywhere in the space [Abbasi et al., FOCS'23]. 3) However, we obtain an EPAS for Robust (k,z)-Clustering in discrete Euclidean spaces when the dimension is sublogarithmic (for the discrete problem, earlier work [Abbasi et al., FOCS'23] provides an EPAS only in dimension o(log log n)). Our EPAS works also for metrics of sub-logarithmic doubling dimension.
Cite as

Fateme Abbasi, Sandip Banerjee, Jarosław Byrka, Parinya Chalermsook, Ameet Gadekar, Kamyar Khodamoradi, Dániel Marx, Roohani Sharma, and Joachim Spoerhase. Parameterized Approximation For Robust Clustering in Discrete Geometric Spaces. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{abbasi_et_al:LIPIcs.ICALP.2024.6,
  author =	{Abbasi, Fateme and Banerjee, Sandip and Byrka, Jaros{\l}aw and Chalermsook, Parinya and Gadekar, Ameet and Khodamoradi, Kamyar and Marx, D\'{a}niel and Sharma, Roohani and Spoerhase, Joachim},
  title =	{{Parameterized Approximation For Robust Clustering in Discrete Geometric Spaces}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.6},
  URN =		{urn:nbn:de:0030-drops-201494},
  doi =		{10.4230/LIPIcs.ICALP.2024.6},
  annote =	{Keywords: Clustering, approximation algorithms, parameterized complexity}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.50
Fully-Scalable MPC Algorithms for Clustering in High Dimension

Authors: Artur Czumaj, Guichen Gao, Shaofeng H.-C. Jiang, Robert Krauthgamer, and Pavel Veselý

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
We design new parallel algorithms for clustering in high-dimensional Euclidean spaces. These algorithms run in the Massively Parallel Computation (MPC) model, and are fully scalable, meaning that the local memory in each machine may be n^σ for arbitrarily small fixed σ > 0. Importantly, the local memory may be substantially smaller than the number of clusters k, yet all our algorithms are fast, i.e., run in O(1) rounds. We first devise a fast MPC algorithm for O(1)-approximation of uniform Facility Location. This is the first fully-scalable MPC algorithm that achieves O(1)-approximation for any clustering problem in general geometric setting; previous algorithms only provide poly(log n)-approximation or apply to restricted inputs, like low dimension or small number of clusters k; e.g. [Bhaskara and Wijewardena, ICML'18; Cohen-Addad et al., NeurIPS'21; Cohen-Addad et al., ICML'22]. We then build on this Facility Location result and devise a fast MPC algorithm that achieves O(1)-bicriteria approximation for k-Median and for k-Means, namely, it computes (1+ε)k clusters of cost within O(1/ε²)-factor of the optimum for k clusters. A primary technical tool that we introduce, and may be of independent interest, is a new MPC primitive for geometric aggregation, namely, computing for every data point a statistic of its approximate neighborhood, for statistics like range counting and nearest-neighbor search. Our implementation of this primitive works in high dimension, and is based on consistent hashing (aka sparse partition), a technique that was recently used for streaming algorithms [Czumaj et al., FOCS'22].
Cite as

Artur Czumaj, Guichen Gao, Shaofeng H.-C. Jiang, Robert Krauthgamer, and Pavel Veselý. Fully-Scalable MPC Algorithms for Clustering in High Dimension. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 50:1-50:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{czumaj_et_al:LIPIcs.ICALP.2024.50,
  author =	{Czumaj, Artur and Gao, Guichen and Jiang, Shaofeng H.-C. and Krauthgamer, Robert and Vesel\'{y}, Pavel},
  title =	{{Fully-Scalable MPC Algorithms for Clustering in High Dimension}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{50:1--50:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.50},
  URN =		{urn:nbn:de:0030-drops-201938},
  doi =		{10.4230/LIPIcs.ICALP.2024.50},
  annote =	{Keywords: Massively parallel computing, high dimension, facility location, k-median, k-means}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2023.16
Online Learning and Bandits with Queried Hints

Authors: Aditya Bhaskara, Sreenivas Gollapudi, Sungjin Im, Kostas Kollias, and Kamesh Munagala

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

Abstract
We consider the classic online learning and stochastic multi-armed bandit (MAB) problems, when at each step, the online policy can probe and find out which of a small number (k) of choices has better reward (or loss) before making its choice. In this model, we derive algorithms whose regret bounds have exponentially better dependence on the time horizon compared to the classic regret bounds. In particular, we show that probing with k = 2 suffices to achieve time-independent regret bounds for online linear and convex optimization. The same number of probes improve the regret bound of stochastic MAB with independent arms from O(√{nT}) to O(n² log T), where n is the number of arms and T is the horizon length. For stochastic MAB, we also consider a stronger model where a probe reveals the reward values of the probed arms, and show that in this case, k = 3 probes suffice to achieve parameter-independent constant regret, O(n²). Such regret bounds cannot be achieved even with full feedback after the play, showcasing the power of limited "advice" via probing before making the play. We also present extensions to the setting where the hints can be imperfect, and to the case of stochastic MAB where the rewards of the arms can be correlated.
Cite as

Aditya Bhaskara, Sreenivas Gollapudi, Sungjin Im, Kostas Kollias, and Kamesh Munagala. Online Learning and Bandits with Queried Hints. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 16:1-16:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bhaskara_et_al:LIPIcs.ITCS.2023.16,
  author =	{Bhaskara, Aditya and Gollapudi, Sreenivas and Im, Sungjin and Kollias, Kostas and Munagala, Kamesh},
  title =	{{Online Learning and Bandits with Queried Hints}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{16:1--16:24},
  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.2023.16},
  URN =		{urn:nbn:de:0030-drops-175197},
  doi =		{10.4230/LIPIcs.ITCS.2023.16},
  annote =	{Keywords: Online learning, multi-armed bandits, regret}
}
Document
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2018.4
Low Rank Approximation in the Presence of Outliers

Authors: Aditya Bhaskara and Srivatsan Kumar

Published in: LIPIcs, Volume 116, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)

Abstract
We consider the problem of principal component analysis (PCA) in the presence of outliers. Given a matrix A (d x n) and parameters k, m, the goal is to remove a set of at most m columns of A (outliers), so as to minimize the rank-k approximation error of the remaining matrix (inliers). While much of the work on this problem has focused on recovery of the rank-k subspace under assumptions on the inliers and outliers, we focus on the approximation problem. Our main result shows that sampling-based methods developed in the outlier-free case give non-trivial guarantees even in the presence of outliers. Using this insight, we develop a simple algorithm that has bi-criteria guarantees. Further, unlike similar formulations for clustering, we show that bi-criteria guarantees are unavoidable for the problem, under appropriate complexity assumptions.
Cite as

Aditya Bhaskara and Srivatsan Kumar. Low Rank Approximation in the Presence of Outliers. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 116, pp. 4:1-4:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bhaskara_et_al:LIPIcs.APPROX-RANDOM.2018.4,
  author =	{Bhaskara, Aditya and Kumar, Srivatsan},
  title =	{{Low Rank Approximation in the Presence of Outliers}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2018)},
  pages =	{4:1--4:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-085-9},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{116},
  editor =	{Blais, Eric and Jansen, Klaus and D. P. Rolim, Jos\'{e} and Steurer, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2018.4},
  URN =		{urn:nbn:de:0030-drops-94087},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2018.4},
  annote =	{Keywords: Low rank approximation, PCA, Robustness to outliers}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.16
Sublinear Algorithms for MAXCUT and Correlation Clustering

Authors: Aditya Bhaskara, Samira Daruki, and Suresh Venkatasubramanian

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

Abstract
We study sublinear algorithms for two fundamental graph problems, MAXCUT and correlation clustering. Our focus is on constructing core-sets as well as developing streaming algorithms for these problems. Constant space algorithms are known for dense graphs for these problems, while Omega(n) lower bounds exist (in the streaming setting) for sparse graphs. Our goal in this paper is to bridge the gap between these extremes. Our first result is to construct core-sets of size O~(n^{1-delta}) for both the problems, on graphs with average degree n^{delta} (for any delta >0). This turns out to be optimal, under the exponential time hypothesis (ETH). Our core-set analysis is based on studying random-induced sub-problems of optimization problems. To the best of our knowledge, all the known results in our parameter range rely crucially on near-regularity assumptions. We avoid these by using a biased sampling approach, which we analyze using recent results on concentration of quadratic functions. We then show that our construction yields a 2-pass streaming (1+epsilon)-approximation for both problems; the algorithm uses O~(n^{1-delta}) space, for graphs of average degree n^delta.
Cite as

Aditya Bhaskara, Samira Daruki, and Suresh Venkatasubramanian. Sublinear Algorithms for MAXCUT and Correlation Clustering. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 16:1-16:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bhaskara_et_al:LIPIcs.ICALP.2018.16,
  author =	{Bhaskara, Aditya and Daruki, Samira and Venkatasubramanian, Suresh},
  title =	{{Sublinear Algorithms for MAXCUT and Correlation Clustering}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{16:1--16:14},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.16},
  URN =		{urn:nbn:de:0030-drops-90203},
  doi =		{10.4230/LIPIcs.ICALP.2018.16},
  annote =	{Keywords: Sublinear algorithms, Streaming algorithms, Core-sets, Maximum cut, Correlation clustering}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2018.7
Non-Negative Sparse Regression and Column Subset Selection with L1 Error

Authors: Aditya Bhaskara and Silvio Lattanzi

Published in: LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)

Abstract
We consider the problems of sparse regression and column subset selection under L1 error. For both problems, we show that in the non-negative setting it is possible to obtain tight and efficient approximations, without any additional structural assumptions (such as restricted isometry, incoherence, expansion, etc.). For sparse regression, given a matrix A and a vector b with non-negative entries, we give an efficient algorithm to output a vector x of sparsity O(k), for which |Ax - b|_1 is comparable to the smallest error possible using non-negative k-sparse x. We then use this technique to obtain our main result: an efficient algorithm for column subset selection under L1 error for non-negative matrices.
Cite as

Aditya Bhaskara and Silvio Lattanzi. Non-Negative Sparse Regression and Column Subset Selection with L1 Error. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{bhaskara_et_al:LIPIcs.ITCS.2018.7,
  author =	{Bhaskara, Aditya and Lattanzi, Silvio},
  title =	{{Non-Negative Sparse Regression and Column Subset Selection with L1 Error}},
  booktitle =	{9th Innovations in Theoretical Computer Science Conference (ITCS 2018)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-060-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{94},
  editor =	{Karlin, Anna R.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.7},
  URN =		{urn:nbn:de:0030-drops-83548},
  doi =		{10.4230/LIPIcs.ITCS.2018.7},
  annote =	{Keywords: Sparse regression, L1 error optimization, Column subset selection}
}
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