# The cell probe complexity of dynamic range counting

@inproceedings{Larsen2012TheCP, title={The cell probe complexity of dynamic range counting}, author={Kasper Green Larsen}, booktitle={STOC '12}, year={2012} }

In this paper we develop a new technique for proving lower bounds on the update time and query time of dynamic data structures in the cell probe model. With this technique, we prove the highest lower bound to date for any explicit problem, namely a lower bound of tq=Ω((lg n/lg(wtu))2). Here n is the number of update operations, w the cell size, tq the query time and tu the update time. In the most natural setting of cell size w=Θ(lg n), this gives a lower bound of tq=Ω((lg n/lg lg n)2) for any…

## 74 Citations

Crossing the logarithmic barrier for dynamic Boolean data structure lower bounds

- Computer ScienceSTOC
- 2018

A new approach is introduced and used to prove a Ω(log1.5 n) lower bound on the operational time of a wide range of boolean data structure problems, most notably, on the query time of dynamic range counting over F2.

New Amortized Cell-Probe Lower Bounds for Dynamic Problems

- Computer Science, MathematicsTheor. Comput. Sci.
- 2019

Higher Cell Probe Lower Bounds for Evaluating Polynomials

- Computer Science2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
- 2012

The cell probe complexity of evaluating an n-degree polynomial P over a finite field F of size at least n1+Ω(1) is studied to show that any static data structure for evaluating P(x), where x ∈ F, must use Ω(lg|F|/ lg(Sw/n lg |F|) cell probes to answer a query, which is the highest static cell probe lower bound to date.

Tight Static Lower Bounds for Non-Adaptive Data Structures

- Computer ScienceElectron. Colloquium Comput. Complex.
- 2020

It is proved an $\Omega(\log m / \log (sw/n\log m)$ static cell probe complexity lower bound for non-adaptive data structures that solve the fundamental dictionary problem where $s$ denotes the space of the data structure in the number of cells and $w$ is the cell size in bits.

Crossing the Logarithmic Barrier for Dynamic Boolean Data Structure Lower Bounds

- Computer ScienceElectron. Colloquium Comput. Complex.
- 2017

A new way of “weakly” simulating dynamic data structures using efficient one-way communication protocols with small advantage over random guessing is introduced, which implies the first super-logarithmic lower bounds on the cell probe complexity of dynamic boolean data structure problems.

Cell-probe lower bounds for dynamic problems via a new communication model

- Computer Science, MathematicsSTOC
- 2016

A new communication model is developed to prove a data structure lower bound for the dynamic interval union problem, and the sparse set disjointness protocol of Håstad and Wigderson is used to speed up a reduction from a new kind of nondeterministic communication games, for which lower bounds are proved.

Space efficient data structures for dynamic orthogonal range counting

- Computer ScienceComput. Geom.
- 2014

New Unconditional Hardness Results for Dynamic and Online Problems

- Computer Science, Mathematics2015 IEEE 56th Annual Symposium on Foundations of Computer Science
- 2015

Improved unconditional lower bounds for matrix-vector multiplication and a version of dynamic set disjointness known as Patrascu's Multiphase Problem are given by studying the cell probe complexity of two conjectured to be hard problems of particular importance.

Amortized Dynamic Cell-Probe Lower Bounds from Four-Party Communication

- Computer Science2016 IEEE 57th Annual Symposium on Foundations of Computer Science (FOCS)
- 2016

This paper develops a new technique for proving amortized, randomized cell-probe lower bounds on dynamic data structure problems. We introduce a new randomized nondeterministic four-party…

3SUM Hardness in (Dynamic) Data Structures

- Computer Science, MathematicsArXiv
- 2014

We prove lower bounds for several (dynamic) data structure problems conditioned on the well known conjecture that 3SUM cannot be solved in $O(n^{2-\Omega(1)})$ time. This continues a line of work…

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