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Cell-Probe Lower Bounds from Online Communication Complexity [article]

Josh Alman, Joshua R. Wang, Huacheng Yu
2017 arXiv   pre-print
Using online communication complexity, we prove a tight cell-probe lower bound for each: spending o( n) (even amortized) time per operation results in at best an (-δ^2 n) probability of correctly answering  ...  The online communication model prevents a batching trick that classic communication complexity allows, and yields a stronger lower bound.  ...  Acknowledgment We would like to thank Pritish Kamath for pointing out an improvement to our original online set intersection protocol.  ... 
arXiv:1704.06185v2 fatcat:fexrkwzaqjaxhiotuhxdkszw3y

Tight Cell-Probe Bounds for Online Hamming Distance Computation [article]

Raphael Clifford, Markus Jalsenius, Benjamin Sach
2012 arXiv   pre-print
We show tight bounds for online Hamming distance computation in the cell-probe model with word size w.  ...  The lower bound holds under randomisation and amortisation.  ...  We thank Kasper Green Larssen in particular for pointing out that the cell-probe lower bounds we give are in fact tight.  ... 
arXiv:1207.1885v3 fatcat:ybari7qv7zcznc7yvsywz2cs24

Tight Cell-Probe Bounds for Online Hamming Distance Computation [chapter]

Raphaël Clifford, Markus Jalsenius, Benjamin Sach
2013 Proceedings of the Twenty-Fourth Annual ACM-SIAM Symposium on Discrete Algorithms  
We show tight bounds for online Hamming distance computation in the cell-probe model with word size w.  ...  The lower bound holds under randomisation and amortisation. * Supported by EPSRC.  ...  We thank Kasper Green Larsen in particular for pointing out that the cell-probe lower bounds we give are in fact tight. We also thank the anonymous reviewers for their helpful comments.  ... 
doi:10.1137/1.9781611973105.48 dblp:conf/soda/CliffordJS13 fatcat:bk7iqzfwlzhp5i5sny37q24sg4

Tight Cell-Probe Bounds for Online Integer Multiplication and Convolution [article]

Raphael Clifford, Markus Jalsenius
2012 arXiv   pre-print
We show tight bounds for both online integer multiplication and convolution in the cell-probe model with word size w.  ...  The online algorithm outputs a single new digit from the product of the numbers before step i+1.  ...  Acknowledgements We are grateful to Mihai Pǎtraşcu for suggesting the connection between online lower bounds and the recent cell-probe results for dynamic data structures and for very helpful discussions  ... 
arXiv:1101.0768v4 fatcat:elmq77nklfdi5ccvrnisf52eme

Lower Bounds for Online Integer Multiplication and Convolution in the Cell-Probe Model [chapter]

Raphaël Clifford, Markus Jalsenius
2011 Lecture Notes in Computer Science  
Acknowledgements We are grateful to Mihai Pǎtraşcu for suggesting the connection between online lower bounds and the recent cell-probe results for dynamic data structures and for very helpful discussions  ...  We would also like to thank Kasper Green Larsen for the observation that our lower bounds are in fact tight within the cell-probe model. MJ was supported by the EPSRC.  ...  As we discussed above, our lower bounds are also tight within the cell-probe model for the online problems.  ... 
doi:10.1007/978-3-642-22006-7_50 fatcat:airnkeai6rfzpn3irhepyi5wxe

Yes, There is an Oblivious RAM Lower Bound! [chapter]

Kasper Green Larsen, Jesper Buus Nielsen
2018 Lecture Notes in Computer Science  
the lower bound of Goldreich and Ostrovsky in the online setting.  ...  Boyle and Naor showed that removing the "balls in bins" assumption would result in super linear lower bounds for sorting circuits, a long standing open problem in circuit complexity.  ...  Lower Bound In this section, we prove our lower bound for oblivious cell probe data structures solving the array maintenance problem and thus indirectly also prove a lower bound for online ORAMs.  ... 
doi:10.1007/978-3-319-96881-0_18 fatcat:zmm5kkfvsbapncpihh7oih6jua

Time Bounds for Streaming Problems

Raphaël Clifford, Markus Jalsenius, Benjamin Sach
2019 Theory of Computing  
We argue that these bounds are in fact tight within the cell probe model.  ...  We give tight cell-probe bounds for the time to compute convolution, multiplication and Hamming distance in a stream.  ...  We study these problems in an online or streaming context and provide matching upper and lower bounds in the cell-probe model.  ... 
doi:10.4086/toc.2019.v015a002 dblp:journals/toc/CliffordJS19 fatcat:fnvfj6gqfzazlgw6uecuhsqeda

Time Bounds for Streaming Problems [article]

Raphael Clifford, Markus Jalsenius, Benjamin Sach
2014 arXiv   pre-print
We argue that these bound are in fact tight within the cell probe model.  ...  We give tight cell-probe bounds for the time to compute convolution, multiplication and Hamming distance in a stream.  ...  We thank Kasper Green Larsen in particular for pointing out that the cell-probe lower bounds we give are in fact tight.  ... 
arXiv:1412.6935v1 fatcat:yxxsxlx6bfe3tmtv22lxzb5eja

Stronger Lower Bounds for Online ORAM [article]

Pavel Hubáček, Michal Koucký, Karel Král, Veronika Slívová
2019 arXiv   pre-print
Larsen and Nielsen [CRYPTO'18] were the first to give a general Ω(log n) lower bound for any online ORAM, i.e., an ORAM that must process its inputs in an online manner.  ...  We give an Ω(log n) lower bound for the bandwidth overhead of any online ORAM even when the adversary has no access to this information.  ...  secure ORAMs from [LN18] .  ... 
arXiv:1903.03385v3 fatcat:gih4y5jikfh7zlpvuepb2holtm

New Unconditional Hardness Results for Dynamic and Online Problems [article]

Raphael Clifford, Allan Grønlund, Kasper Green Larsen
2015 arXiv   pre-print
In this paper we make progress in this direction by studying the cell probe complexity of two conjectured to be hard problems of particular importance: matrix-vector multiplication and a version of dynamic  ...  These conditional lower bounds have become important and popular due to the painfully slow progress on proving strong unconditional lower bounds.  ...  In this paper we add to the understanding of the true complexity of dynamic and online problems by giving new unconditional lower bounds for Pǎtraşcu's Multiphase Problem as well as online and dynamic  ... 
arXiv:1504.01836v1 fatcat:juktwct3tzbxtawzrfv2e3t7ey

New Unconditional Hardness Results for Dynamic and Online Problems

Raphael Clifford. Allan Gronlund, Kasper Green Larsen
2015 2015 IEEE 56th Annual Symposium on Foundations of Computer Science  
In this paper we add to the understanding of the true complexity of dynamic and online problems by giving new unconditional lower bounds for Pǎtraşcu's Multiphase Problem as well as online and dynamic  ...  Proving such polynomial lower bounds in the cell probe model is far out of reach.  ...  We bound the probability that k≤r:i k ∈G h {j k } < n/4 for all h = 1, . . . , r/(2n).  ... 
doi:10.1109/focs.2015.71 dblp:conf/focs/CliffordGL15 fatcat:pya76oztdjg2zaojk34fdgnpzq

Cell-probe Lower Bounds for Dynamic Problems via a New Communication Model [article]

Huacheng Yu
2015 arXiv   pre-print
In this paper, we develop a new communication model to prove a data structure lower bound for the dynamic interval union problem.  ...  Interestingly, we use the sparse set disjointness protocol of Håstad and Wigderson [ToC'07] to speed up a reduction from a new kind of nondeterministic communication games, for which we prove lower bounds  ...  Previous Cell-probe Lower Bounds In 1989, Fredman and Saks introduced the chronogram method to prove an Ω(log n/ log log n) lower bound for partial sum in their seminal paper [9] .  ... 
arXiv:1512.01293v1 fatcat:yl32fnk2pzda3oi7dxdj2zml6a

Lower Bounds for Oblivious Near-Neighbor Search [article]

Kasper Green Larsen and Tal Malkin and Omri Weinstein and Kevin Yeo
2019 arXiv   pre-print
We prove an Ω(d n/ ( n)^2) lower bound on the dynamic cell-probe complexity of statistically oblivious approximate-near-neighbor search (ANN) over the d-dimensional Hamming cube.  ...  For the natural setting of d = Θ( n), our result implies an Ω̃(^2 n) lower bound, which is a quadratic improvement over the highest (non-oblivious) cell-probe lower bound for ANN.  ...  Oblivious cell-probe lower bounds.  ... 
arXiv:1904.04828v1 fatcat:r3hafauyw5cuhfdvsejv3narsm

Tight Cell Probe Bounds for Succinct Boolean Matrix-Vector Multiplication [article]

Diptarka Chakraborty, Lior Kamma, Kasper Green Larsen
2017 arXiv   pre-print
Since lower bounds in the cell probe model also apply to classic word-RAM data structures, the lower bounds naturally carry over.  ...  In this paper, we essentially settle the cell probe complexity of succinct Boolean matrix-vector multiplication.  ...  Amortized dynamic cell-probe lower bounds from four-party communication. In 57th Annual IEEE Symposium on Foundations of Computer Science, pages 305–314, 2016. [Yao81] A. C. Yao.  ... 
arXiv:1711.04467v1 fatcat:cn36ivwoundwln2d6ydy4gg6ee

An Adaptive Step Toward the Multiphase Conjecture [article]

Young Kun Ko, Omri Weinstein
2019 arXiv   pre-print
Our main technical result is a communication lower bound on a 4-party variant of Pǎtraşcu's Number-On-Forehead Multiphase game, using information complexity techniques.  ...  We show an Ω̃(√(n)) cell-probe lower bound on the Multiphase problem for data structures with general (adaptive) updates, and queries with unbounded but "layered" adaptivity.  ...  In the same paper, Pǎtraşcu [Pat10] proposed an approach to prove an unconditional cell-probe lower bound on the Multiphase problem, by reduction to the following 3-party Number-On-Forehead (NOF) communication  ... 
arXiv:1910.13543v1 fatcat:im5ibxtpbzgzpnkzzkh5zcvvfi
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