# Tight Cell-Probe Bounds for Online Hamming Distance Computation

@inproceedings{Clifford2013TightCB, title={Tight Cell-Probe Bounds for Online Hamming Distance Computation}, author={Rapha{\"e}l Clifford and Markus Jalsenius and Benjamin Sach}, booktitle={SODA}, year={2013} }

We show tight bounds for online Hamming distance computation in the cell-probe model with word size w. The task is to output the Hamming distance between a fixed string of length n and the last n symbols of a stream. We give a lower bound of Ω(δ/w log n) time on average per output, where δ is the number of bits needed to represent an input symbol. We argue that this bound is tight within the model. The lower bound holds under randomisation and amortisation.

## 7 Citations

### Cell-probe bounds for online edit distance and other pattern matching problems

- Computer ScienceSODA
- 2015

Cell-probe bounds for the computation of edit distance, Hamming distance, convolution and longest common subsequence in a stream are given and an exponential gap between the known cell- Probe and RAM model complexities is established.

### Cell-Probe Lower Bounds for Bit Stream Computation

- Computer Science, MathematicsESA
- 2016

A lop-sided information transfer proof technique which enables us to prove meaningful lower bounds even for constant size input alphabets and gives the first non-trivial cell probe lower bound for any online problem on bit streams that still holds when the cell size is large.

### Time Bounds for Streaming Problems

- Computer Science, MathematicsTheory Comput.
- 2019

Tight cell-probe bounds for the time to compute convolution, multiplication and Hamming distance in a stream are given within the cell probe model, a particularly strong computational model that subsumes the popular word RAM model.

### The complexity of computation in bit streams

- Computer Science, MathematicsArXiv
- 2015

This work uses a new lop-sided information transfer proof technique which enables them to prove meaningful lower bounds even for constant size input alphabets and proves an amortised cell probe lower bound of $\Omega(\lg^2 n/(w\cdot \lg \ lg n))$ time per arriving bit for an online version of a well studied problem known as pattern matching with address errors.

### Time Lower Bounds for Nonadaptive Turnstile Streaming Algorithms

- Computer ScienceSTOC
- 2015

This work proves the first non-trivial update time lower bounds for both randomized and deterministic turnstile streaming algorithms, which hold when the algorithms are non-adaptive.

### 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.

### 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.

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