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Documents authored by Dhulipala, Laxman

Document
DOI: 10.4230/LIPIcs.DISC.2024.19
Parallel Set Cover and Hypergraph Matching via Uniform Random Sampling

Authors: Laxman Dhulipala, Michael Dinitz, Jakub Łącki, and Slobodan Mitrović

Published in: LIPIcs, Volume 319, 38th International Symposium on Distributed Computing (DISC 2024)

Abstract
The SetCover problem has been extensively studied in many different models of computation, including parallel and distributed settings. From an approximation point of view, there are two standard guarantees: an O(log Δ)-approximation (where Δ is the maximum set size) and an O(f)-approximation (where f is the maximum number of sets containing any given element). In this paper, we introduce a new, surprisingly simple, model-independent approach to solving SetCover in unweighted graphs. We obtain multiple improved algorithms in the MPC and CRCW PRAM models. First, in the MPC model with sublinear space per machine, our algorithms can compute an O(f) approximation to SetCover in Ô(√{log Δ} + log f) rounds and a O(log Δ) approximation in O(log^{3/2} n) rounds. Moreover, in the PRAM model, we give a O(f) approximate algorithm using linear work and O(log n) depth. All these bounds improve the existing round complexity/depth bounds by a log^{Ω(1)} n factor. Moreover, our approach leads to many other new algorithms, including improved algorithms for the HypergraphMatching problem in the MPC model, as well as simpler SetCover algorithms that match the existing bounds.
Cite as

Laxman Dhulipala, Michael Dinitz, Jakub Łącki, and Slobodan Mitrović. Parallel Set Cover and Hypergraph Matching via Uniform Random Sampling. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 19:1-19:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dhulipala_et_al:LIPIcs.DISC.2024.19,
  author =	{Dhulipala, Laxman and Dinitz, Michael and {\L}\k{a}cki, Jakub and Mitrovi\'{c}, Slobodan},
  title =	{{Parallel Set Cover and Hypergraph Matching via Uniform Random Sampling}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{19:1--19:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-352-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{319},
  editor =	{Alistarh, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2024.19},
  URN =		{urn:nbn:de:0030-drops-212453},
  doi =		{10.4230/LIPIcs.DISC.2024.19},
  annote =	{Keywords: approximate maximum matching, set cover, hypergraph matching, PRAM, massively parallel computation}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.18
It’s Hard to HAC Average Linkage!

Authors: MohammadHossein Bateni, Laxman Dhulipala, Kishen N. Gowda, D. Ellis Hershkowitz, Rajesh Jayaram, and Jakub Łącki

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

Abstract
Average linkage Hierarchical Agglomerative Clustering (HAC) is an extensively studied and applied method for hierarchical clustering. Recent applications to massive datasets have driven significant interest in near-linear-time and efficient parallel algorithms for average linkage HAC. We provide hardness results that rule out such algorithms. On the sequential side, we establish a runtime lower bound of n^{3/2-ε} on n node graphs for sequential combinatorial algorithms under standard fine-grained complexity assumptions. This essentially matches the best-known running time for average linkage HAC. On the parallel side, we prove that average linkage HAC likely cannot be parallelized even on simple graphs by showing that it is CC-hard on trees of diameter 4. On the possibility side, we demonstrate that average linkage HAC can be efficiently parallelized (i.e., it is in NC) on paths and can be solved in near-linear time when the height of the output cluster hierarchy is small.
Cite as

MohammadHossein Bateni, Laxman Dhulipala, Kishen N. Gowda, D. Ellis Hershkowitz, Rajesh Jayaram, and Jakub Łącki. It’s Hard to HAC Average Linkage!. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 18:1-18:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bateni_et_al:LIPIcs.ICALP.2024.18,
  author =	{Bateni, MohammadHossein and Dhulipala, Laxman and Gowda, Kishen N. and Hershkowitz, D. Ellis and Jayaram, Rajesh and {\L}\k{a}cki, Jakub},
  title =	{{It’s Hard to HAC Average Linkage!}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{18:1--18:18},
  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.2024.18},
  URN =		{urn:nbn:de:0030-drops-201613},
  doi =		{10.4230/LIPIcs.ICALP.2024.18},
  annote =	{Keywords: Clustering, Hierarchical Graph Clustering, HAC, Fine-Grained Complexity, Parallel Algorithms, CC}
}
Document
DOI: 10.4230/LIPIcs.WABI.2023.16
Fast, Parallel, and Cache-Friendly Suffix Array Construction

Authors: Jamshed Khan, Tobias Rubel, Laxman Dhulipala, Erin Molloy, and Rob Patro

Published in: LIPIcs, Volume 273, 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023)

Abstract
String indexes such as the suffix array (SA) and the closely related longest common prefix (LCP) array are fundamental objects in bioinformatics and have a wide variety of applications. Despite their importance in practice, few scalable parallel algorithms for constructing these are known, and the existing algorithms can be highly non-trivial to implement and parallelize. In this paper we present CaPS-SA, a simple and scalable parallel algorithm for constructing these string indexes inspired by samplesort. Due to its design, CaPS-SA has excellent memory-locality and thus incurs fewer cache misses and achieves strong performance on modern multicore systems with deep cache hierarchies. We show that despite its simple design, CaPS-SA outperforms existing state-of-the-art parallel SA and LCP-array construction algorithms on modern hardware. Finally, motivated by applications in modern aligners where the query strings have bounded lengths, we introduce the notion of a bounded-context SA and show that CaPS-SA can easily be extended to exploit this structure to obtain further speedups.
Cite as

Jamshed Khan, Tobias Rubel, Laxman Dhulipala, Erin Molloy, and Rob Patro. Fast, Parallel, and Cache-Friendly Suffix Array Construction. In 23rd International Workshop on Algorithms in Bioinformatics (WABI 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 273, pp. 16:1-16:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{khan_et_al:LIPIcs.WABI.2023.16,
  author =	{Khan, Jamshed and Rubel, Tobias and Dhulipala, Laxman and Molloy, Erin and Patro, Rob},
  title =	{{Fast, Parallel, and Cache-Friendly Suffix Array Construction}},
  booktitle =	{23rd International Workshop on Algorithms in Bioinformatics (WABI 2023)},
  pages =	{16:1--16:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-294-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{273},
  editor =	{Belazzougui, Djamal and Ouangraoua, A\"{i}da},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.WABI.2023.16},
  URN =		{urn:nbn:de:0030-drops-186424},
  doi =		{10.4230/LIPIcs.WABI.2023.16},
  annote =	{Keywords: Suffix Array, Longest Common Prefix, Data Structures, Indexing, Parallel Algorithms}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.88
ParGeo: A Library for Parallel Computational Geometry

Authors: Yiqiu Wang, Rahul Yesantharao, Shangdi Yu, Laxman Dhulipala, Yan Gu, and Julian Shun

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

Abstract
This paper presents ParGeo, a multicore library for computational geometry. ParGeo contains modules for fundamental tasks including kd-tree based spatial search, spatial graph generation, and algorithms in computational geometry. We focus on three new algorithmic contributions provided in the library. First, we present a new parallel convex hull algorithm based on a reservation technique to enable parallel modifications to the hull. We also provide the first parallel implementations of the randomized incremental convex hull algorithm as well as a divide-and-conquer convex hull algorithm in ℝ³. Second, for the smallest enclosing ball problem, we propose a new sampling-based algorithm to quickly reduce the size of the data set. We also provide the first parallel implementation of Welzl’s classic algorithm for smallest enclosing ball. Third, we present the BDL-tree, a parallel batch-dynamic kd-tree that allows for efficient parallel updates and k-NN queries over dynamically changing point sets. BDL-trees consist of a log-structured set of kd-trees which can be used to efficiently insert, delete, and query batches of points in parallel. On 36 cores with two-way hyper-threading, our fastest convex hull algorithm achieves up to 44.7x self-relative parallel speedup and up to 559x speedup against the best existing sequential implementation. Our smallest enclosing ball algorithm using our sampling-based algorithm achieves up to 27.1x self-relative parallel speedup and up to 178x speedup against the best existing sequential implementation. Our implementation of the BDL-tree achieves self-relative parallel speedup of up to 46.1x. Across all of the algorithms in ParGeo, we achieve self-relative parallel speedup of 8.1-46.61x.
Cite as

Yiqiu Wang, Rahul Yesantharao, Shangdi Yu, Laxman Dhulipala, Yan Gu, and Julian Shun. ParGeo: A Library for Parallel Computational Geometry. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 88:1-88:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{wang_et_al:LIPIcs.ESA.2022.88,
  author =	{Wang, Yiqiu and Yesantharao, Rahul and Yu, Shangdi and Dhulipala, Laxman and Gu, Yan and Shun, Julian},
  title =	{{ParGeo: A Library for Parallel Computational Geometry}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{88:1--88:19},
  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.2022.88},
  URN =		{urn:nbn:de:0030-drops-170265},
  doi =		{10.4230/LIPIcs.ESA.2022.88},
  annote =	{Keywords: Computational Geometry, Parallel Algorithms, Libraries}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.2
Parallel Batch-Dynamic Trees via Change Propagation

Authors: Umut A. Acar, Daniel Anderson, Guy E. Blelloch, Laxman Dhulipala, and Sam Westrick

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
The dynamic trees problem is to maintain a forest subject to edge insertions and deletions while facilitating queries such as connectivity, path weights, and subtree weights. Dynamic trees are a fundamental building block of a large number of graph algorithms. Although traditionally studied in the single-update setting, dynamic algorithms capable of supporting batches of updates are increasingly relevant today due to the emergence of rapidly evolving dynamic datasets. Since processing updates on a single processor is often unrealistic for large batches of updates, designing parallel batch-dynamic algorithms that achieve provably low span is important for many applications. In this work, we design the first work-efficient parallel batch-dynamic algorithm for dynamic trees that is capable of supporting both path queries and subtree queries, as well as a variety of nonlocal queries. Previous work-efficient dynamic trees of Tseng et al. were only capable of handling subtree queries [ALENEX'19, (2019), pp. 92 - 106]. To achieve this, we propose a framework for algorithmically dynamizing static round-synchronous algorithms to obtain parallel batch-dynamic algorithms. In our framework, the algorithm designer can apply the technique to any suitably defined static algorithm. We then obtain theoretical guarantees for algorithms in our framework by defining the notion of a computation distance between two executions of the underlying algorithm. Our dynamic trees algorithm is obtained by applying our dynamization framework to the parallel tree contraction algorithm of Miller and Reif [FOCS'85, (1985), pp. 478 - 489], and then performing a novel analysis of the computation distance of this algorithm under batch updates. We show that k updates can be performed in O(klog(1+n/k)) work in expectation, which matches the algorithm of Tseng et al. while providing support for a substantially larger number of queries and applications.
Cite as

Umut A. Acar, Daniel Anderson, Guy E. Blelloch, Laxman Dhulipala, and Sam Westrick. Parallel Batch-Dynamic Trees via Change Propagation. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 2:1-2:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{acar_et_al:LIPIcs.ESA.2020.2,
  author =	{Acar, Umut A. and Anderson, Daniel and Blelloch, Guy E. and Dhulipala, Laxman and Westrick, Sam},
  title =	{{Parallel Batch-Dynamic Trees via Change Propagation}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{2:1--2:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.2},
  URN =		{urn:nbn:de:0030-drops-128686},
  doi =		{10.4230/LIPIcs.ESA.2020.2},
  annote =	{Keywords: Dynamic trees, Graph algorithms, Parallel algorithms, Dynamic algorithms}
}
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