### Abstract

How well can the maximum size of an independent set, or the minimum size of a dominating set of a graph in which all degrees are at most d be approximated by a randomized constant time algorithm ? Motivated by results and questions of Nguyen and Onak, and of Parnas, Ron and Trevisan, we show that the best approximation ratio that can be achieved for the first question (independence number) is between Ω(d/logd) and O(d loglogd/ logd), whereas the answer to the second (domination number) is (1 + o(1)) ln d.

Original language | English (US) |
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Title of host publication | Property Testing - Current Research and Surveys |

Pages | 234-239 |

Number of pages | 6 |

DOIs | |

State | Published - 2010 |

Event | Mini-Workshop on Property Testing - Beijing, China Duration: Jan 8 2010 → Jan 10 2010 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 6390 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | Mini-Workshop on Property Testing |
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Country | China |

City | Beijing |

Period | 1/8/10 → 1/10/10 |

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Keywords

- constant time approximation
- dominating set in a graph
- independence number of a graph

## Fingerprint Dive into the research topics of 'On constant time approximation of parameters of bounded degree graphs'. Together they form a unique fingerprint.

## Cite this

Alon, N. (2010). On constant time approximation of parameters of bounded degree graphs. In

*Property Testing - Current Research and Surveys*(pp. 234-239). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6390 LNCS). https://doi.org/10.1007/978-3-642-16367-8_14