5 Search Results for "Samadian, Alireza"

Document
DOI: 10.4230/LIPIcs.ESA.2025.46
Max-Distance Sparsification for Diversification and Clustering

Authors: Soh Kumabe

Published in: LIPIcs, Volume 351, 33rd Annual European Symposium on Algorithms (ESA 2025)

Abstract
Let 𝒟 be a set family that is the solution domain of some combinatorial problem. The max-min diversification problem on 𝒟 is the problem to select k sets from 𝒟 such that the Hamming distance between any two selected sets is at least d. FPT algorithms parameterized by k+𝓁, where 𝓁 = max_{D ∈ 𝒟}|D|, and k+d have been actively studied recently for several specific domains. This paper provides unified algorithmic frameworks to solve this problem. Specifically, for each parameterization k+𝓁 and k+d, we provide an FPT oracle algorithm for the max-min diversification problem using oracles related to 𝒟. We then demonstrate that our frameworks provide the first FPT algorithms on several new domains 𝒟, including the domain of t-linear matroid intersection, almost 2-SAT, minimum edge s,t-flows, vertex sets of s,t-mincut, vertex sets of edge bipartization, and Steiner trees. We also demonstrate that our frameworks generalize most of the existing domain-specific tractability results. Our main technical breakthrough is introducing the notion of max-distance sparsifier of 𝒟, a domain on which the max-min diversification problem is equivalent to the same problem on the original domain 𝒟. The core of our framework is to design FPT oracle algorithms that construct a constant-size max-distance sparsifier of 𝒟. Using max-distance sparsifiers, we provide FPT algorithms for the max-min and max-sum diversification problems on 𝒟, as well as k-center and k-sum-of-radii clustering problems on 𝒟, which are also natural problems in the context of diversification and have their own interests.
Cite as

Soh Kumabe. Max-Distance Sparsification for Diversification and Clustering. In 33rd Annual European Symposium on Algorithms (ESA 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 351, pp. 46:1-46:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kumabe:LIPIcs.ESA.2025.46,
  author =	{Kumabe, Soh},
  title =	{{Max-Distance Sparsification for Diversification and Clustering}},
  booktitle =	{33rd Annual European Symposium on Algorithms (ESA 2025)},
  pages =	{46:1--46:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-395-9},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{351},
  editor =	{Benoit, Anne and Kaplan, Haim and Wild, Sebastian 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.2025.46},
  URN =		{urn:nbn:de:0030-drops-245146},
  doi =		{10.4230/LIPIcs.ESA.2025.46},
  annote =	{Keywords: Fixed-Parameter Tractability, Diversification, Clustering}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2025.12
Relational Approximations for Subspace Primitives

Authors: Xiang Liu and Kasturi Varadarajan

Published in: LIPIcs, Volume 353, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)

Abstract
We explore fundamental geometric computations on point sets that are given to the algorithm implicitly. In particular, we are given a database which is a collection of tables with numerical values, and the geometric computation is to be performed on the join of the tables. Explicitly computing this join takes time exponential in the size of the tables. We are therefore interested in geometric problems that can be solved by algorithms whose running time is a polynomial in the size of the tables. Such relational algorithms are typically not able to explicitly compute the join. To avoid the NP-completeness bottleneck, researchers assume that the tables have a tractable combinatorial structure, like being acyclic. Even with this assumption, simple geometric computations turn out to be non-trivial and sometimes intractable. In this article, we study the problem of computing the maximum distance of a point in the join to a given subspace, and develop approximation algorithms for this NP-hard problem.
Cite as

Xiang Liu and Kasturi Varadarajan. Relational Approximations for Subspace Primitives. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 353, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{liu_et_al:LIPIcs.APPROX/RANDOM.2025.12,
  author =	{Liu, Xiang and Varadarajan, Kasturi},
  title =	{{Relational Approximations for Subspace Primitives}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2025)},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-397-3},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{353},
  editor =	{Ene, Alina and Chattopadhyay, Eshan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2025.12},
  URN =		{urn:nbn:de:0030-drops-243781},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2025.12},
  annote =	{Keywords: relational algorithm, Euclidean distance, subspace approximation}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.ICDT.2022.1
On an Information Theoretic Approach to Cardinality Estimation (Invited Talk)

Authors: Hung Q. Ngo

Published in: LIPIcs, Volume 220, 25th International Conference on Database Theory (ICDT 2022)

Abstract
This article is a companion to an invited talk at ICDT'2022 with the same title. Cardinality estimation is among the most important problems in query optimization. It is well-documented that, when query plans go haywire, in most cases one can trace the root cause to the cardinality estimator being far off. In particular, traditional cardinality estimation based on selectivity estimation may sometimes under-estimate cardinalities by orders of magnitudes, because the independence or the uniformity assumptions do not typically hold. This talk outlines an approach to cardinality estimation that is "model-free" from a statistical stand-point. Being model-free means the approach tries to avoid making any distributional assumptions. Our approach is information-theoretic, and generalizes recent results on worst-case output size bounds of queries, allowing the estimator to take into account histogram information from the input relations. The estimator turns out to be the objective of a maximization problem subject to concave constraints, over an exponential number of variables. We then explain how the estimator can be computed in polynomial time for some fragment of these constraints. Overall, the talk introduces a new direction to address the classic problem of cardinality estimation that is designed to circumvent some of the pitfalls of selectivity-based estimation. We will also explain connections to other fundamental problems in information theory and database theory regarding information inequalities. The talk is based on (published and unpublished) joint works with Mahmoud Abo Khamis, Sungjin Im, Hossein Keshavarz, Phokion Kolaitis, Ben Moseley, XuanLong Nguyen, Kirk Pruhs, Dan Suciu, and Alireza Samadian Zakaria
Cite as

Hung Q. Ngo. On an Information Theoretic Approach to Cardinality Estimation (Invited Talk). In 25th International Conference on Database Theory (ICDT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 220, pp. 1:1-1:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{ngo:LIPIcs.ICDT.2022.1,
  author =	{Ngo, Hung Q.},
  title =	{{On an Information Theoretic Approach to Cardinality Estimation}},
  booktitle =	{25th International Conference on Database Theory (ICDT 2022)},
  pages =	{1:1--1:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-223-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{220},
  editor =	{Olteanu, Dan and Vortmeier, Nils},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2022.1},
  URN =		{urn:nbn:de:0030-drops-158750},
  doi =		{10.4230/LIPIcs.ICDT.2022.1},
  annote =	{Keywords: Cardinality Estimation, Information Theory, Polymatroid Bound, Worst-case Optimal Join}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2021.6
An Approximation Algorithm for the Matrix Tree Multiplication Problem

Authors: Mahmoud Abo-Khamis, Ryan Curtin, Sungjin Im, Benjamin Moseley, Hung Ngo, Kirk Pruhs, and Alireza Samadian

Published in: LIPIcs, Volume 202, 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)

Abstract
We consider the Matrix Tree Multiplication problem. This problem is a generalization of the classic Matrix Chain Multiplication problem covered in the dynamic programming chapter of many introductory algorithms textbooks. An instance of the Matrix Tree Multiplication problem consists of a rooted tree with a matrix associated with each edge. The output is, for each leaf in the tree, the product of the matrices on the chain/path from the root to that leaf. Matrix multiplications that are shared between various chains need only be computed once, potentially being shared between different root to leaf chains. Algorithms are evaluated by the number of scalar multiplications performed. Our main result is a linear time algorithm for which the number of scalar multiplications performed is at most 15 times the optimal number of scalar multiplications.
Cite as

Mahmoud Abo-Khamis, Ryan Curtin, Sungjin Im, Benjamin Moseley, Hung Ngo, Kirk Pruhs, and Alireza Samadian. An Approximation Algorithm for the Matrix Tree Multiplication Problem. In 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 202, pp. 6:1-6:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{abokhamis_et_al:LIPIcs.MFCS.2021.6,
  author =	{Abo-Khamis, Mahmoud and Curtin, Ryan and Im, Sungjin and Moseley, Benjamin and Ngo, Hung and Pruhs, Kirk and Samadian, Alireza},
  title =	{{An Approximation Algorithm for the Matrix Tree Multiplication Problem}},
  booktitle =	{46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
  pages =	{6:1--6:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-201-3},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{202},
  editor =	{Bonchi, Filippo and Puglisi, Simon J.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2021.6},
  URN =		{urn:nbn:de:0030-drops-144464},
  doi =		{10.4230/LIPIcs.MFCS.2021.6},
  annote =	{Keywords: Matrix Multiplication, Approximation Algorithm}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.97
Relational Algorithms for k-Means Clustering

Authors: Benjamin Moseley, Kirk Pruhs, Alireza Samadian, and Yuyan Wang

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
This paper gives a k-means approximation algorithm that is efficient in the relational algorithms model. This is an algorithm that operates directly on a relational database without performing a join to convert it to a matrix whose rows represent the data points. The running time is potentially exponentially smaller than N, the number of data points to be clustered that the relational database represents. Few relational algorithms are known and this paper offers techniques for designing relational algorithms as well as characterizing their limitations. We show that given two data points as cluster centers, if we cluster points according to their closest centers, it is NP-Hard to approximate the number of points in the clusters on a general relational input. This is trivial for conventional data inputs and this result exemplifies that standard algorithmic techniques may not be directly applied when designing an efficient relational algorithm. This paper then introduces a new method that leverages rejection sampling and the k-means++ algorithm to construct a O(1)-approximate k-means solution.
Cite as

Benjamin Moseley, Kirk Pruhs, Alireza Samadian, and Yuyan Wang. Relational Algorithms for k-Means Clustering. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 97:1-97:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{moseley_et_al:LIPIcs.ICALP.2021.97,
  author =	{Moseley, Benjamin and Pruhs, Kirk and Samadian, Alireza and Wang, Yuyan},
  title =	{{Relational Algorithms for k-Means Clustering}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{97:1--97:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.97},
  URN =		{urn:nbn:de:0030-drops-141668},
  doi =		{10.4230/LIPIcs.ICALP.2021.97},
  annote =	{Keywords: k-means, clustering, approximation, big-data, databases}
}
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