4 Search Results for "Srinivasan, Venkatesh"

Document
DOI: 10.4230/LIPIcs.ESA.2024.3
From Donkeys to Kings in Tournaments

Authors: Amir Abboud, Tomer Grossman, Moni Naor, and Tomer Solomon

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
A tournament is an orientation of a complete graph. A vertex that can reach every other vertex within two steps is called a king. We study the complexity of finding k kings in a tournament graph. We show that the randomized query complexity of finding k ≤ 3 kings is O(n), and for the deterministic case it takes the same amount of queries (up to a constant) as finding a single king (the best known deterministic algorithm makes O(n^{3/2}) queries). On the other hand, we show that finding k ≥ 4 kings requires Ω(n²) queries, even in the randomized case. We consider the RAM model for k ≥ 4. We show an algorithm that finds k kings in time O(kn²), which is optimal for constant values of k. Alternatively, one can also find k ≥ 4 kings in time n^{ω} (the time for matrix multiplication). We provide evidence that this is optimal for large k by suggesting a fine-grained reduction from a variant of the triangle detection problem.
Cite as

Amir Abboud, Tomer Grossman, Moni Naor, and Tomer Solomon. From Donkeys to Kings in Tournaments. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 3:1-3:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{abboud_et_al:LIPIcs.ESA.2024.3,
  author =	{Abboud, Amir and Grossman, Tomer and Naor, Moni and Solomon, Tomer},
  title =	{{From Donkeys to Kings in Tournaments}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{3:1--3:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.3},
  URN =		{urn:nbn:de:0030-drops-210740},
  doi =		{10.4230/LIPIcs.ESA.2024.3},
  annote =	{Keywords: Tournament Graphs, Kings, Query Complexity, Fine Grained Complexity}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.60
New Algorithms and Lower Bounds for Streaming Tournaments

Authors: Prantar Ghosh and Sahil Kuchlous

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
We study fundamental directed graph (digraph) problems in the streaming model. An initial investigation by Chakrabarti, Ghosh, McGregor, and Vorotnikova [SODA'20] on streaming digraphs showed that while most of these problems are provably hard in general, some of them become tractable when restricted to the well-studied class of tournament graphs where every pair of nodes shares exactly one directed edge. Thus, we focus on tournaments and improve the state of the art for multiple problems in terms of both upper and lower bounds. Our primary upper bound is a deterministic single-pass semi-streaming algorithm (using Õ(n) space for n-node graphs, where Õ(.) hides polylog(n) factors) for decomposing a tournament into strongly connected components (SCC). It improves upon the previously best-known algorithm by Baweja, Jia, and Woodruff [ITCS'22] in terms of both space and passes: for p ⩾ 1, they used (p+1) passes and Õ(n^{1+1/p}) space. We further extend our algorithm to digraphs that are close to tournaments and establish tight bounds demonstrating that the problem’s complexity grows smoothly with the "distance" from tournaments. Applying our SCC-decomposition framework, we obtain improved - and in some cases, optimal - tournament algorithms for s,t-reachability, strong connectivity, Hamiltonian paths and cycles, and feedback arc set. On the other hand, we prove lower bounds exhibiting that some well-studied problems - such as (exact) feedback arc set and s,t-distance - remain hard (require Ω(n²) space) on tournaments. Moreover, we generalize the former problem’s lower bound to establish space-approximation tradeoffs: any single-pass (1± ε)-approximation algorithm requires Ω(n/√{ε}) space. Finally, we settle the streaming complexities of two basic digraph problems studied by prior work: acyclicity testing of tournaments and sink finding in DAGs. As a whole, our collection of results contributes significantly to the growing literature on streaming digraphs.
Cite as

Prantar Ghosh and Sahil Kuchlous. New Algorithms and Lower Bounds for Streaming Tournaments. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 60:1-60:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{ghosh_et_al:LIPIcs.ESA.2024.60,
  author =	{Ghosh, Prantar and Kuchlous, Sahil},
  title =	{{New Algorithms and Lower Bounds for Streaming Tournaments}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{60:1--60:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John 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.2024.60},
  URN =		{urn:nbn:de:0030-drops-211318},
  doi =		{10.4230/LIPIcs.ESA.2024.60},
  annote =	{Keywords: tournaments, streaming algorithms, graph algorithms, communication complexity, strongly connected components, reachability, feedback arc set}
}
Document
DOI: 10.4230/LIPIcs.CCC.2024.7
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
DOI: 10.4230/LIPIcs.ICDT.2020.24
Reverse Prevention Sampling for Misinformation Mitigation in Social Networks

Authors: Michael Simpson, Venkatesh Srinivasan, and Alex Thomo

Published in: LIPIcs, Volume 155, 23rd International Conference on Database Theory (ICDT 2020)

Abstract
In this work, we consider misinformation propagating through a social network and study the problem of its prevention. In this problem, a "bad" campaign starts propagating from a set of seed nodes in the network and we use the notion of a limiting (or "good") campaign to counteract the effect of misinformation. The goal is to identify a set of k users that need to be convinced to adopt the limiting campaign so as to minimize the number of people that adopt the "bad" campaign at the end of both propagation processes. This work presents RPS (Reverse Prevention Sampling), an algorithm that provides a scalable solution to the misinformation prevention problem. Our theoretical analysis shows that RPS runs in O((k + l)(n + m)(1/(1 - γ)) log n / ε²) expected time and returns a (1 - 1/e - ε)-approximate solution with at least 1 - n^{-l} probability (where γ is a typically small network parameter and l is a confidence parameter). The time complexity of RPS substantially improves upon the previously best-known algorithms that run in time Ω(m n k ⋅ POLY(ε^{-1})). We experimentally evaluate RPS on large datasets and show that it outperforms the state-of-the-art solution by several orders of magnitude in terms of running time. This demonstrates that misinformation prevention can be made practical while still offering strong theoretical guarantees.
Cite as

Michael Simpson, Venkatesh Srinivasan, and Alex Thomo. Reverse Prevention Sampling for Misinformation Mitigation in Social Networks. In 23rd International Conference on Database Theory (ICDT 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 155, pp. 24:1-24:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{simpson_et_al:LIPIcs.ICDT.2020.24,
  author =	{Simpson, Michael and Srinivasan, Venkatesh and Thomo, Alex},
  title =	{{Reverse Prevention Sampling for Misinformation Mitigation in Social Networks}},
  booktitle =	{23rd International Conference on Database Theory (ICDT 2020)},
  pages =	{24:1--24:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-139-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{155},
  editor =	{Lutz, Carsten and Jung, Jean Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2020.24},
  URN =		{urn:nbn:de:0030-drops-119484},
  doi =		{10.4230/LIPIcs.ICDT.2020.24},
  annote =	{Keywords: Graph Algorithms, Social Networks, Misinformation Prevention}
}
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