# Sublinear-Time Computation in the Presence of Online Erasures

@article{Kalemaj2021SublinearTimeCI, title={Sublinear-Time Computation in the Presence of Online Erasures}, author={Iden Kalemaj and Sofya Raskhodnikova and Nithin M. Varma}, journal={ArXiv}, year={2021}, volume={abs/2109.08745} }

We initiate the study of sublinear-time algorithms that access their input via an online adversarial erasure oracle. After answering each query to the input object, such an oracle can erase t input values. Our goal is to understand the complexity of basic computational tasks in extremely adversarial situations, where the algorithm’s access to data is blocked during the execution of the algorithm in response to its actions. Specifically, we focus on property testing in the model with online… Expand

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SHOWING 1-10 OF 80 REFERENCES

Erasure-Resilient Property Testing

- Computer Science, Mathematics
- ICALP
- 2016

A study of property testers that are resilient to the presence of adversarially erased function values and gives efficient erasure-resilient testers for several important classes of such properties of functions including monotonicity, the Lipschitz property, and convexity. Expand

Erasures vs. Errors in Local Decoding and Property Testing

- Computer Science
- ITCS
- 2019

It is shown that the Hadamard code is locally list decodable in the presence of a constant fraction of erasures, arbitrary close to 1, with list sizes and query complexity better than in the Goldreich-Levin theorem. Expand

Erasure-Resilient Sublinear-Time Graph Algorithms

- Computer Science
- Electron. Colloquium Comput. Complex.
- 2020

The erasure-resilient algorithm (for the special case with no erasures) is an improvement over the previously known algorithm for connectedness in the standard property testing model and has optimal dependence on the proximity parameter $\varepsilon$. Expand

Parameterized Property Testing of Functions

- Mathematics, Computer Science
- Electron. Colloquium Comput. Complex.
- 2017

This work parameterizes the query complexity of property testers in terms of the size r of the image of the input function, and obtains testers for monotonicity and convexity of functions of the form f:[n]→ R with query complexity O (log r), with no dependence on n. Expand

Gowers uniformity, influence of variables, and PCPs

- Computer Science, Mathematics
- STOC '06
- 2006

A connection between the Gowers uniformity of a Boolean function and the influence of its variables is found and the proof that "Gowers uniform" functions pass the "hypergraph linearity test" approximately with the same probability of a random function is proved. Expand

Randomness-efficient low degree tests and short PCPs via epsilon-biased sets

- Mathematics, Computer Science
- STOC '03
- 2003

We present the first explicit construction of Probabilistically Checkable Proofs (PCPs) and Locally Testable Codes (LTCs) of fixed constant query complexity which have almost-linear (= n * 2Õ(√log… Expand

Derandomizing homomorphism testing in general groups

- Mathematics, Computer Science
- STOC '04
- 2004

The main result of this paper is a near-optimal derandomization of the affine homomorphism test of Blum, Luby and Rubinfeld, and shows that for any groups G and Γ, and any expanding generating set S of G, the natural derandomized version of the BLR test performs nearly as well as the original test. Expand

Testing the Lipschitz Property over Product Distributions with Applications to Data Privacy

- Mathematics, Computer Science
- TCC
- 2013

A computationally efficient algorithm is designed that verifies whether $\cal T}_{priv}$ satisfies differential privacy on typical datasets (DPTD) guarantee in time sublinear in the size of the domain of the datasets. Expand

Estimating the Distance to a Monotone Function

- Mathematics, Computer Science
- APPROX-RANDOM
- 2004

The running time of the algorithm is optimal within a factor of log log e -1 f and represents a substantial improvement over previous work, and it is given a second algorithm with an expectedRunning time of O(e - 1 f log n log log log n). Expand

Probabilistically checkable proofs with low amortized query complexity

- Computer Science, Mathematics
- Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280)
- 1998

The precise rate at which the error goes down in an optimal protocol is determined, and substantial progress is made toward a tight resolution of this question. Expand