# Local Algorithms for Sparse Spanning Graphs

@inproceedings{Levi2014LocalAF,
title={Local Algorithms for Sparse Spanning Graphs},
author={Reut Levi and Dana Ron and Ronitt Rubinfeld},
booktitle={APPROX-RANDOM},
year={2014}
}
• Published in APPROX-RANDOM 2014
• Mathematics, Computer Science
• We initiate the study of the problem of designing sublinear-time (local) algorithms that, given an edge $(u,v)$ in a connected graph $G=(V,E)$, decide whether $(u,v)$ belongs to a sparse spanning graph $G' = (V,E')$ of $G$. Namely, $G'$ should be connected and $|E'|$ should be upper bounded by $(1+\epsilon)|V|$ for a given parameter $\epsilon > 0$. To this end the algorithms may query the incidence relation of the graph $G$, and we seek algorithms whose query complexity and running time (per… CONTINUE READING

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• Algorithmica
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CITES BACKGROUND

#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 50 REFERENCES

## On the shortest spanning subtree of a graph and the traveling salesman problem

VIEW 7 EXCERPTS
HIGHLY INFLUENTIAL

## A Quasi-Polynomial Time Partition Oracle for Graphs with an Excluded Minor

• Mathematics, Computer Science
• TALG
• 2015

## Flow-Based Algorithms for Local Graph Clustering

• Computer Science, Mathematics
• SODA
• 2014

## A Local Algorithm for Finding Well-Connected Clusters

• Computer Science
• ICML
• 2013

## A Local Computation Approximation Scheme to Maximum Matching

• Computer Science, Mathematics
• APPROX-RANDOM
• 2013

## A Simple Online Competitive Adaptation of Lempel-Ziv Compression with Efficient Random Access Support

• Computer Science, Mathematics
• 2013 Data Compression Conference
• 2013
VIEW 1 EXCERPT

## Testing and Reconstruction of Lipschitz Functions with Applications to Data Privacy

• Mathematics, Computer Science
• SIAM J. Comput.
• 2013

## Converting Online Algorithms to Local Computation Algorithms

• Mathematics, Computer Science
• ICALP
• 2012

## Local Reconstructors and Tolerant Testers for Connectivity and Diameter

• Mathematics, Computer Science
• APPROX-RANDOM
• 2012
VIEW 1 EXCERPT

## Space-efficient local computation algorithms

• Computer Science, Mathematics
• SODA
• 2012