Open AccessProceedings Article
Vertex ordering problems in directed graph streams
Amit Chakrabarti,Prantar Ghosh,Andrew McGregor,Sofya Vorotnikova +3 more
- 05 Jan 2020
pp 1786-1802
18
TL;DR: This work considers directed graph algorithms in a streaming setting, focusing on problems concerning orderings of the vertices, and designs sublinear algorithms for the feedback arc set problem in tournament graphs; for random graphs; and for randomly ordered streams.
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Abstract: We consider directed graph algorithms in a streaming setting, focusing on problems concerning orderings of the vertices. This includes such fundamental problems as topological sorting and acyclicity testing. We also study the related problems of finding a minimum feedback arc set (edges whose removal yields an acyclic graph), and finding a sink vertex. We are interested in both adversarially-ordered and randomly-ordered streams. For arbitrary input graphs with edges ordered adversarially, we show that most of these problems have high space complexity, precluding sublinearspace solutions. Some lower bounds also apply when the stream is randomly ordered: e.g., in our most technical result we show that testing acyclicity in the p-pass random-order model requires roughly n1+1/p space. For other problems, random ordering can make a dramatic difference: e.g., it is possible to find a sink in an acyclic tournament in the one-pass random-order model using polylog(n) space whereas under adversarial ordering roughly n1/p space is necessary and sufficient given Θ(p) passes. We also design sublinear algorithms for the feedback arc set problem in tournament graphs; for random graphs; and for randomly ordered streams. In some cases, we give lower bounds establishing that our algorithms are essentially space-optimal. Together, our results complement the much maturer body of work on algorithms for undirected graph streams.
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Citations
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Multi-Pass Graph Streaming Lower Bounds for Cycle Counting, MAX-CUT, Matching Size, and Other Problems
TL;DR: The first multi-pass lower bound for the gap cycle counting problem is proved, which makes progress on multiple open questions in this line of research dating back to the work of Verbin and Yu.
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Multi-Pass Graph Streaming Lower Bounds for Cycle Counting, MAX-CUT, Matching Size, and Other Problems
Sepehr Assadi,Gillat Kol,Raghuvansh R. Saxena,Huacheng Yu +3 more
- 07 Sep 2020
TL;DR: In this article, a multi-pass lower bound for the gap cycle counting problem was shown, which is the first in the history of the problem, and was shown to be equivalent to the lower bound of Verbin and Yu [SODA 2011].
15
Near-Quadratic Lower Bounds for Two-Pass Graph Streaming Algorithms
Sepehr Assadi,Ran Raz +1 more
- 02 Sep 2020
TL;DR: In this paper, it was shown that any two-pass graph streaming algorithm for the reachability problem in directed graphs requires near-quadratic space of $n 2-o(1) bits.
14
Testable properties in general graphs and random order streaming
Artur Czumaj,Hendrik Fichtenberger,Pan Peng,Christian Sohler +3 more
- 11 Aug 2020
TL;DR: In this paper, a generic transformation of a one-sided error property tester in the random-neighbor model with constant query complexity into a one side error property test with constant space complexity was presented.
8
Streaming Verification for Graph Problems: Optimal Tradeoffs and Nonlinear Sketches.
Amit Chakrabarti,Prantar Ghosh,Justin Thaler +2 more
- 01 Jan 2020
TL;DR: In this paper, Chakrabarti et al. studied graph computations in an enhanced data streaming setting, where a space-bounded client reading the edge stream of a massive graph may delegate some of its work to a cloud service.
4
References
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TL;DR: This work almost settles a long-standing conjecture of Bang-Jensen and Thomassen and shows that unless NP⊆BPP, there is no polynomial time algorithm for the problem of minimum feedback arc set in tournaments.
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Topological sorting of large networks
TL;DR: The approach to the problem presented here centers upon the use of multiple adaptive matched filters that classify normalized signals that compare between machine and human performance.
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Graph stream algorithms: a survey
Andrew McGregor
- 13 May 2014
TL;DR: The techniques developed in this area are now finding applications in other areas including data structures for dynamic graphs, approximation algorithms, and distributed and parallel computation.
Approximating Minimum Feedback Sets and Multicuts in Directed Graphs
TL;DR: A combinatorial algorithm that computes a (1+ɛ) approximation to the fractional optimal feedback vertex set, and a generalization of these problems, in which the feedback set has to intersect only a subset of the directed cycles in the graph.
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Analyzing graph structure via linear measurements
Kook Jin Ahn,Sudipto Guha,Andrew McGregor +2 more
- 17 Jan 2012
TL;DR: The study of graph sketching is initiated, i.e., algorithms that use a limited number of linear measurements of a graph to determine the properties of the graph are studied, including the first dynamic graph semi-streaming algorithms for connectivity, spanning trees, sparsification, and matching problems.