research-article

Robust lower bounds for communication and stream computation

Authors:

Amit Chakrabarti,

Graham Cormode,

Andrew McGregorAuthors Info & Claims

STOC '08: Proceedings of the fortieth annual ACM symposium on Theory of computing

Pages 641 - 650

https://doi.org/10.1145/1374376.1374470

Published: 17 May 2008 Publication History

Abstract

We study the communication complexity of evaluating functions when the input data is randomly allocated (according to some known distribution) amongst two or more players, possibly with information overlap. This naturally extends previously studied variable partition models such as the best-case and worst-case partition models [32,29]. We aim to understand whether the hardness of a communication problem holds for almost every allocation of the input, as opposed to holding for perhaps just a few atypical partitions.

A key application is to the heavily studied data stream model. There is a strong connection between our communication lower bounds and lower bounds in the data stream model that are "robust" to the ordering of the data. That is, we prove lower bounds for when the order of the items in the stream is chosen not adversarially but rather uniformly (or near-uniformly) from the set of all permuations. This random-order data stream model has attracted recent interest, since lower bounds here give stronger evidence for the inherent hardness of streaming problems. Our results include the first random-partition communication lower bounds for problems including multi-party set disjointness and gap-Hamming-distance. Both are tight. We also extend and improve previous results [19,7] for a form of pointer jumping that is relevant to the problem of selection (in particular, median finding). Collectively, these results yield lower bounds for a variety of problems in the random-order data stream model, including estimating the number of distinct elements, approximating frequency moments, and quantile estimation.

References

[1]

F. Ablayev. Lower bounds for one-way probabilistic communication complexity and their application to space complexity. Theoretical Computer Science, 175(2):139--159, 1996.

Digital Library

[2]

A. V. Aho, J. D. Ullman, and M. Yannakakis. On notions of information transfer in VLSI circuits. In STOC, pages 133--139, 1983.

Digital Library

[3]

N. Alon, Y. Matias, and M. Szegedy. The space complexity of approximating the frequency moments. Journal of Computer and System Sciences, 58(1):137--147, 1999.

Digital Library

[4]

Z. Bar-Yossef, T. Jayram, R. Kumar, D. Sivakumar, and L. Trevisan. Counting distinct elements in a data stream. In Proc. 6th International Workshop on Randomization and Approximation Techniques in Computer Science, pages 1--10, 2002.

Digital Library

[5]

Z. Bar-Yossef, T. S. Jayram, R. Kumar, and D. Sivakumar. An information statistics approach to data stream and communication complexity. J. Comput. Syst. Sci., 68(4):702--732, 2004.

Digital Library

[6]

A. Chakrabarti, G. Cormode, and A. McGregor. A near-optimal algorithm for computing the entropy of a stream. In ACM-SIAM Symposium on Discrete Algorithms, pages 328--335, 2007.

Digital Library

[7]

A. Chakrabarti, T. Jayram, and M. Patrascu. Tight lower bounds for selection in randomly ordered streams. In ACM-SIAM Symposium on Discrete Algorithms, 2008.

Digital Library

[8]

A. Chakrabarti, S. Khot, and X. Sun. Near-optimal lower bounds on the multi-party communication complexity of set disjointness. In IEEE Conference on Computational Complexity, pages 107--117, 2003.

[9]

A. Chakrabarti, Y. Shi, A. Wirth, and A. C. Yao. Informational complexity and the direct sum problem for simultaneous message complexity. In IEEE Symposium on Foundations of Computer Science, pages 270--278, 2001.

Digital Library

[10]

E. D. Demaine, A. López-Ortiz, and J. I. Munro. Frequency estimation of internet packet streams with limited space. In European Symposium on Algorithms, pages 348--360, 2002.

Digital Library

[11]

J. Edmonds and R. Impagliazzo. Manuscript. Unpublished, 1994.

[12]

J. Feigenbaum, S. Kannan, A. McGregor, S. Suri, and J. Zhang. Graph distances in the data-stream model. Manuscript: http://talk.ucsd.edu/andrewm/papers/07-graphdistances.pdf (Conference Version SODA 2005, pp. 745-754), 2007.

Digital Library

[13]

J. Feigenbaum, S. Kannan, M. Strauss, and M. Viswanathan. An approximate L¹ difference algorithm for massive data streams. SIAM Journal on Computing, 32(1):131--151, 2002.

Digital Library

[14]

P. Flajolet and G. N. Martin. Probabilistic counting algorithms for data base applications. J. Comput. Syst. Sci., 31(2):182--209, 1985.

Digital Library

[15]

M. Greenwald and S. Khanna. Efficient online computation of quantile summaries. In ACM International Conference on Management of Data, pages 58--66, 2001.

Digital Library

[16]

S. Guha, P. Indyk, and A. McGregor. Sketching information divergences. In Conference on Learning Theory, pages 424--438, 2007.

Digital Library

[17]

S. Guha and A. McGregor. Approximate quantiles and the order of the stream. In ACM Symposium on Principles of Database Systems, pages 273--279, 2006.

Digital Library

[18]

S. Guha and A. McGregor. A general approach to multi-pass stream lower-bounds. Manuscript, 2007.

[19]

S. Guha and A. McGregor. Lower bounds for quantile estimation in random-order and multi-pass streaming. In International Colloquium on Automata, Languages and Programming, pages 704--715, 2007.

Digital Library

[20]

S. Guha and A. McGregor. Space-efficient sampling. In AISTATS, pages 169--176, 2007.

[21]

S. Guha, A. McGregor, and S. Venkatasubramanian. Streaming and sublinear approximation of entropy and information distances. In ACM-SIAM Symposium on Discrete Algorithms, pages 733--742, 2006.

Digital Library

[22]

M. R. Henzinger, P. Raghavan, and S. Rajagopalan. Computing on data streams. External memory algorithms, pages 107--118, 1999.

Digital Library

[23]

P. Indyk and D. P. Woodruff. Tight lower bounds for the distinct elements problem. IEEE Symposium on Foundations of Computer Science, pages 283--288, 2003.

Digital Library

[24]

P. Indyk and D. P. Woodruff. Optimal approximations of the frequency moments of data streams. In ACM Symposium on Theory of Computing, pages 202--208, 2005.

Digital Library

[25]

T. S. Jayram, R. Kumar, and D. Sivakumar. Two applications of information complexity. In ACM Symposium on Theory of Computing, pages 673--682, 2003.

Digital Library

[26]

T. S. Jayram, R. Kumar, and D. Sivakumar. The one-way communication complexity of gap hamming distance. In Manuscript http://www.madalgo.au.dk/img/SumSchoo2007_Lecture%20slides/Bibliograph%y/p14_Jayram_07_Manusc_ghd.pdf, 2007.

[27]

H. Klauck, A. Nayak, A. Ta-Shma, and D. Zuckerman. Interaction in quantum communication and the complexity of set disjointness. In ACM Symposium on Theory of Computing, pages 124--133, 2001.

Digital Library

[28]

E. Kushilevitz and N. Nisan. Communication Complexity. Cambridge University Press, 1997.

Digital Library

[29]

T. W. Lam and W. L. Ruzzo. Results on communication complexity classes. J. Comput. Syst. Sci., 44(2):324--342, 1992.

Digital Library

[30]

P. B. Miltersen, N. Nisan, S. Safra, and A. Wigderson. On data structures and asymmetric communication complexity. J. Comput. Syst. Sci., 57(1):37--49, 1998.

Digital Library

[31]

J. I. Munro and M. Paterson. Selection and sorting with limited storage. Theor. Comput. Sci., 12:315--323, 1980.

[32]

C. H. Papadimitriou and M. Sipser. Communication complexity. J. Comput. Syst. Sci., 28(2):260--269, 1984.

[33]

P. Pudlák and J. Sgall. An upper bound for a communication game related to time-space tradeoffs. Electronic Colloquium on Computational Complexity (ECCC), 2(10), 1995.

[34]

P. Sen. Lower bounds for predecessor searching in the cell probe model. In IEEE Conference on Computational Complexity, pages 73--83, 2003.

[35]

D. P. Woodruff. Optimal space lower bounds for all frequency moments. In ACM-SIAM Symposium on Discrete Algorithms, pages 167--175, 2004.

Digital Library

[36]

D. P. Woodruff. Distinct elements is hard even for random streams. Manuscript, 2008.

[37]

A. C. Yao. Some complexity questions related to distributive computing (preliminary report). ACM Symposium on Theory of Computing, pages 209--213, 1979.

Digital Library

Cited By

Braverman MGarg SLi QWang SWoodruff DZhang JMohar BShinkar IO'Donnell R(2024)A New Information Complexity Measure for Multi-pass Streaming with ApplicationsProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649672(1781-1792)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649672
Assadi SSundaresan JSaha BServedio R(2023)(Noisy) Gap Cycle Counting Strikes Back: Random Order Streaming Lower Bounds for Connected Components and BeyondProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585192(183-195)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585192
Lovett SZhang J(2023)Streaming Lower Bounds and Asymmetric Set-Disjointness2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00056(871-882)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00056
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Index Terms

Robust lower bounds for communication and stream computation
1. Theory of computation
  1. Design and analysis of algorithms

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cover image ACM Conferences

STOC '08: Proceedings of the fortieth annual ACM symposium on Theory of computing

May 2008

712 pages

ISBN:9781605580470

DOI:10.1145/1374376

General Chair:
Richard Ladner
University of Washington
,
Program Chair:
Cynthia Dwork
Microsoft Research, Silicon Valley

Copyright © 2008 ACM.

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Published: 17 May 2008

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May 17 - 20, 2008

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STOC '08 Paper Acceptance Rate 80 of 325 submissions, 25%;

Overall Acceptance Rate 1,469 of 4,586 submissions, 32%

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Cited By

Braverman MGarg SLi QWang SWoodruff DZhang JMohar BShinkar IO'Donnell R(2024)A New Information Complexity Measure for Multi-pass Streaming with ApplicationsProceedings of the 56th Annual ACM Symposium on Theory of Computing10.1145/3618260.3649672(1781-1792)Online publication date: 10-Jun-2024
https://dl.acm.org/doi/10.1145/3618260.3649672
Assadi SSundaresan JSaha BServedio R(2023)(Noisy) Gap Cycle Counting Strikes Back: Random Order Streaming Lower Bounds for Connected Components and BeyondProceedings of the 55th Annual ACM Symposium on Theory of Computing10.1145/3564246.3585192(183-195)Online publication date: 2-Jun-2023
https://dl.acm.org/doi/10.1145/3564246.3585192
Lovett SZhang J(2023)Streaming Lower Bounds and Asymmetric Set-Disjointness2023 IEEE 64th Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS57990.2023.00056(871-882)Online publication date: 6-Nov-2023
https://doi.org/10.1109/FOCS57990.2023.00056
Chiplunkar AKallaugher JKapralov MPrice E(2022)Factorial Lower Bounds for (Almost) Random Order Streams2022 IEEE 63rd Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS54457.2022.00053(486-497)Online publication date: Oct-2022
https://doi.org/10.1109/FOCS54457.2022.00053
Assadi SN VKhuller SVassilevska Williams V(2021)Graph streaming lower bounds for parameter estimation and property testing via a streaming XOR lemmaProceedings of the 53rd Annual ACM SIGACT Symposium on Theory of Computing10.1145/3406325.3451110(612-625)Online publication date: 15-Jun-2021
https://dl.acm.org/doi/10.1145/3406325.3451110
Assadi SKol GSaxena RYu H(2020)Multi-Pass Graph Streaming Lower Bounds for Cycle Counting, MAX-CUT, Matching Size, and Other Problems2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS46700.2020.00041(354-364)Online publication date: Nov-2020
https://doi.org/10.1109/FOCS46700.2020.00041
Assadi SRaz R(2020)Near-Quadratic Lower Bounds for Two-Pass Graph Streaming Algorithms2020 IEEE 61st Annual Symposium on Foundations of Computer Science (FOCS)10.1109/FOCS46700.2020.00040(342-353)Online publication date: Nov-2020
https://doi.org/10.1109/FOCS46700.2020.00040
Assadi SChen YKhanna SCharikar MCohen E(2019)Polynomial pass lower bounds for graph streaming algorithmsProceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing10.1145/3313276.3316361(265-276)Online publication date: 23-Jun-2019
https://dl.acm.org/doi/10.1145/3313276.3316361
Assadi SKarpov NZhang QSuciu DSkritek SKoch C(2019)Distributed and Streaming Linear Programming in Low DimensionsProceedings of the 38th ACM SIGMOD-SIGACT-SIGAI Symposium on Principles of Database Systems10.1145/3294052.3319697(236-253)Online publication date: 25-Jun-2019
https://dl.acm.org/doi/10.1145/3294052.3319697
Peng PSohler CCzumaj A(2018)Estimating graph parameters from random order streamsProceedings of the Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3174304.3175462(2449-2466)Online publication date: 7-Jan-2018
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