3 Search Results for "Yu, Shangdi"


Document
Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy

Authors: Sepehr Assadi, Prantar Ghosh, Bruno Loff, Parth Mittal, and Sagnik Mukhopadhyay

Published in: LIPIcs, Volume 300, 39th Computational Complexity Conference (CCC 2024)


Abstract
The following question arises naturally in the study of graph streaming algorithms: Is there any graph problem which is "not too hard", in that it can be solved efficiently with total communication (nearly) linear in the number n of vertices, and for which, nonetheless, any streaming algorithm with Õ(n) space (i.e., a semi-streaming algorithm) needs a polynomial n^Ω(1) number of passes? Assadi, Chen, and Khanna [STOC 2019] were the first to prove that this is indeed the case. However, the lower bounds that they obtained are for rather non-standard graph problems. Our first main contribution is to present the first polynomial-pass lower bounds for natural "not too hard" graph problems studied previously in the streaming model: k-cores and degeneracy. We devise a novel communication protocol for both problems with near-linear communication, thus showing that k-cores and degeneracy are natural examples of "not too hard" problems. Indeed, previous work have developed single-pass semi-streaming algorithms for approximating these problems. In contrast, we prove that any semi-streaming algorithm for exactly solving these problems requires (almost) Ω(n^{1/3}) passes. The lower bound follows by a reduction from a generalization of the hidden pointer chasing (HPC) problem of Assadi, Chen, and Khanna, which is also the basis of their earlier semi-streaming lower bounds. Our second main contribution is improved round-communication lower bounds for the underlying communication problems at the basis of these reductions: - We improve the previous lower bound of Assadi, Chen, and Khanna for HPC to achieve optimal bounds for this problem. - We further observe that all current reductions from HPC can also work with a generalized version of this problem that we call MultiHPC, and prove an even stronger and optimal lower bound for this generalization. These two results collectively allow us to improve the resulting pass lower bounds for semi-streaming algorithms by a polynomial factor, namely, from n^{1/5} to n^{1/3} passes.

Cite as

Sepehr Assadi, Prantar Ghosh, Bruno Loff, Parth Mittal, and Sagnik Mukhopadhyay. Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy. In 39th Computational Complexity Conference (CCC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 300, pp. 7:1-7:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{assadi_et_al:LIPIcs.CCC.2024.7,
  author =	{Assadi, Sepehr and Ghosh, Prantar and Loff, Bruno and Mittal, Parth and Mukhopadhyay, Sagnik},
  title =	{{Polynomial Pass Semi-Streaming Lower Bounds for K-Cores and Degeneracy}},
  booktitle =	{39th Computational Complexity Conference (CCC 2024)},
  pages =	{7:1--7:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-331-7},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{300},
  editor =	{Santhanam, Rahul},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2024.7},
  URN =		{urn:nbn:de:0030-drops-204035},
  doi =		{10.4230/LIPIcs.CCC.2024.7},
  annote =	{Keywords: Graph streaming, Lower bounds, Communication complexity, k-Cores and degeneracy}
}
Document
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
A Parallel Batch-Dynamic Data Structure for the Closest Pair Problem

Authors: Yiqiu Wang, Shangdi Yu, Yan Gu, and Julian Shun

Published in: LIPIcs, Volume 189, 37th International Symposium on Computational Geometry (SoCG 2021)


Abstract
We propose a theoretically-efficient and practical parallel batch-dynamic data structure for the closest pair problem. Our solution is based on a serial dynamic closest pair data structure by Golin et al., and supports batches of insertions and deletions in parallel. For a data set of size n, our data structure supports a batch of insertions or deletions of size m in O(m(1+log ((n+m)/m))) expected work and O(log (n+m)log^*(n+m)) depth with high probability, and takes linear space. The key techniques for achieving these bounds are a new work-efficient parallel batch-dynamic binary heap, and careful management of the computation across sets of points to minimize work and depth. We provide an optimized multicore implementation of our data structure using dynamic hash tables, parallel heaps, and dynamic k-d trees. Our experiments on a variety of synthetic and real-world data sets show that it achieves a parallel speedup of up to 38.57x (15.10x on average) on 48 cores with hyper-threading. In addition, we also implement and compare four parallel algorithms for static closest pair problem, for which we are not aware of any existing practical implementations. On 48 cores with hyper-threading, the static algorithms achieve up to 51.45x (29.42x on average) speedup, and Rabin’s algorithm performs the best on average. Comparing our dynamic algorithm to the fastest static algorithm, we find that it is advantageous to use the dynamic algorithm for batch sizes of up to 20% of the data set. As far as we know, our work is the first to experimentally evaluate parallel closest pair algorithms, in both the static and the dynamic settings.

Cite as

Yiqiu Wang, Shangdi Yu, Yan Gu, and Julian Shun. A Parallel Batch-Dynamic Data Structure for the Closest Pair Problem. In 37th International Symposium on Computational Geometry (SoCG 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 189, pp. 60:1-60:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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@InProceedings{wang_et_al:LIPIcs.SoCG.2021.60,
  author =	{Wang, Yiqiu and Yu, Shangdi and Gu, Yan and Shun, Julian},
  title =	{{A Parallel Batch-Dynamic Data Structure for the Closest Pair Problem}},
  booktitle =	{37th International Symposium on Computational Geometry (SoCG 2021)},
  pages =	{60:1--60:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-184-9},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{189},
  editor =	{Buchin, Kevin and Colin de Verdi\`{e}re, \'{E}ric},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2021.60},
  URN =		{urn:nbn:de:0030-drops-138594},
  doi =		{10.4230/LIPIcs.SoCG.2021.60},
  annote =	{Keywords: Closest Pair, Parallel Algorithms, Dynamic Algorithms, Experimental Algorithms}
}
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