# Algorithms column: sublinear time algorithms

@article{Kumar2003AlgorithmsCS, title={Algorithms column: sublinear time algorithms}, author={Ravi Kumar and Ronitt Rubinfeld}, journal={SIGACT News}, year={2003}, volume={34}, pages={57-67} }

With the recent tremendous increase in computational power and cheap storage, we are blessed with a multitude of available, and possibly useful, information. It is always nice to have something for (almost) nothing. However, this blessing is also something of a curse, for we may also be asked to do something meaningful with all of this data. The scale of these data sets, coupled with the typical situation in which there is very little time to perform our computations, raises the question of…

## 26 Citations

### Something for (Almost) Nothing: New Advances in Sublinear-Time Algorithms

- MathematicsHandbook of Big Data
- 2016

This chapter focuses on a formalization of approximate solutions that has been widely studied in an area of theoretical computer science known as property testing, and a close connection between property testing and the general parameter estimation.

### Separating sublinear time computations by approximate diameter

- Mathematics, Computer ScienceJ. Comb. Optim.
- 2009

It is shown that, for any parameter r∈(0,1), the bounded error randomized sublinear time computation in time O(nr) cannot be simulated by any zero error randomizedSublinear time algorithm in o(n) time or queries; and the same is true forzero error randomized computation versus deterministic computation.

### Algebraic Property Testing

- Computer Science
- 2011

It is shown that sparsity and invariance under the affine group of permutations are sufficient conditions for a notion of very structured testing, and a new characterization of the extensively studied BCH codes is revealed.

### Sampling subproblems of heterogeneous Max-Cut problems and approximation algorithms

- Computer Science
- 2008

An algorithm is developed and analyzed which uses a novel sampling method to obtain improved bounds for approximating the Max-Cut of a graph and it is shown that by judicious choice of sampling probabilities one can obtain error bounds that are superior to the ones obtained by uniform sampling.

### Separating Sublinear Time Computations by Approximate Diameter

- MathematicsCOCOA
- 2008

A class of separations about the sublinear time computations are obtained using various versions of the approximate diameter problem based on the restriction about the format of input data.

### Sampling subproblems of heterogeneous Max‐Cut problems and approximation algorithms

- Computer ScienceRandom Struct. Algorithms
- 2008

An algorithm is developed and analyzed which uses a novel sampling method to obtain improved bounds for approximating the Max‐Cut of a graph and it is shown that by judicious choice of sampling probabilities one can obtain error bounds that are superior to the ones obtained by uniform sampling.

### Removing the Haystack to Find the Needle(s): Minesweeper, an adaptive join algorithm

- Computer Science, Mathematics
- 2013

A new algorithm is described, Minesweeper, that is able to satisfy stronger runtime guarantees than previous join algorithms (colloquially, ‘beyond worst-case guarantees’) for data in indexed search trees and a dichotomy theorem is developed for the certificate-based notion of complexity.

### Sublinear-time approximation algorithms for clustering via random sampling

- Computer Science
- 2007

Using a novel analysis of a random sampling approach for four clustering problems in metric spaces, this work obtains the first time approximation algorithms that have running time independent of the input size, and depending on k and the diameter of the metric space only.

### Beyond worst-case analysis for joins with minesweeper

- Computer Science, MathematicsPODS
- 2014

A new algorithm is described, Minesweeper, that is able to satisfy stronger runtime guarantees than previous join algorithms (colloquially ``beyond worst-case'' guarantees) for data in indexed search trees and a dichotomy theorem is developed for the certificate-based notion of complexity.

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The matrix approximation is generalized to multi-dimensional arrays and from that derive approximation algorithms for all dense Max-SNP problems and the Regularity Lemma is derived.

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This work develops the study of testing graph properties as initiated by Goldreich, Goldwasser and Ron and presents randomized algorithms for testing whether an unknown bounded-degree graph is connected, k -connected (for k>1 ), cycle-free and Eulerian.