Chattopadhyay, A., Koucký, M., Loff, B. et al. (1 more author) (2018) Simulation beats richness: new data-structure lower bounds. In: Diakonikolas, I. and Kempe, D., (eds.) STOC 2018: Proceedings of the 50th Annual ACM SIGACT Symposium on Theory of Computing. STOC '18: Symposium on Theory of Computing, 25-29 Jun 2018, CA, Los Angeles, USA. Association for Computing Machinery (ACM) , pp. 1013-1020. ISBN 9781450355599
Abstract
We develop a new technique for proving lower bounds in the setting of asymmetric communication, a model that was introduced in the famous works of Miltersen (STOC’94) and Miltersen, Nisan, Safra and Wigderson (STOC’95). At the core of our technique is the first simulation theorem in the asymmetric setting, where Alice gets a p × n matrix x over F2 and Bob gets a vector y ∈ F2n. Alice and Bob need to evaluate f(x· y) for a Boolean function f: {0,1}p → {0,1}. Our simulation theorems show that a deterministic/randomized communication protocol exists for this problem, with cost C· n for Alice and C for Bob, if and only if there exists a deterministic/randomized *parity decision tree* of cost Θ(C) for evaluating f.
As applications of this technique, we obtain the following results:
1. The first strong lower-bounds against randomized data-structure schemes for the Vector-Matrix-Vector product problem over F2. Moreover, our method yields strong lower bounds even when the data-structure scheme has tiny advantage over random guessing.
2. The first lower bounds against randomized data-structures schemes for two natural Boolean variants of Orthogonal Vector Counting.
3. We construct an asymmetric communication problem and obtain a deterministic lower-bound for it which is provably better than any lower-bound that may be obtained by the classical Richness Method of Miltersen et al. (STOC ’95). This seems to be the first known limitation of the Richness Method in the context of proving deterministic lower bounds.
Metadata
Item Type: | Proceedings Paper |
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Authors/Creators: |
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Editors: |
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Copyright, Publisher and Additional Information: | © 2018 ACM. |
Keywords: | 14 Life Below Water |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 28 Jun 2023 15:45 |
Last Modified: | 29 Jun 2023 14:17 |
Status: | Published |
Publisher: | Association for Computing Machinery (ACM) |
Refereed: | Yes |
Identification Number: | 10.1145/3188745.3188874 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:200978 |