### Abstract

The main problem we consider in this paper is the Independent Set problem for bounded degree graphs. It is shown that the problem remains MAX SJVP-complete when the maximum degree is bounded by 3. Some related problems are also shown to be MAX SNP-complete at the lowest possible degree bounds. Next we study better poly-time approximation of the problem for degree 3 graphs, and improve the previously best ratio, |, to arbitrarily close to |. This result also provides improved poly-time approximation ratios, (Formula Presented), for odd degree B.

Original language | English (US) |
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Title of host publication | Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings |

Editors | Selim G. Akl, Frank Dehne, Jörg-Rüdiger Sack, Nicola Santoro |

Publisher | Springer Verlag |

Pages | 449-460 |

Number of pages | 12 |

ISBN (Print) | 3540602208, 9783540602200 |

DOIs | |

State | Published - Jan 1 1995 |

Event | 4th Workshop on Algorithms and Data Structures, WADS 1995 - Kingston, Canada Duration: Aug 16 1995 → Aug 18 1995 |

### 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 | 955 |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 4th Workshop on Algorithms and Data Structures, WADS 1995 |
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Country | Canada |

City | Kingston |

Period | 8/16/95 → 8/18/95 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings*(pp. 449-460). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 955). Springer Verlag. https://doi.org/10.1007/3-540-60220-8_84

}

*Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 955, Springer Verlag, pp. 449-460, 4th Workshop on Algorithms and Data Structures, WADS 1995, Kingston, Canada, 8/16/95. https://doi.org/10.1007/3-540-60220-8_84

**On approximation properties of the independent set problem for degree 3 graphs.** / Berman, Piotr; Fujito, Toshihiro.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - On approximation properties of the independent set problem for degree 3 graphs

AU - Berman, Piotr

AU - Fujito, Toshihiro

PY - 1995/1/1

Y1 - 1995/1/1

N2 - The main problem we consider in this paper is the Independent Set problem for bounded degree graphs. It is shown that the problem remains MAX SJVP-complete when the maximum degree is bounded by 3. Some related problems are also shown to be MAX SNP-complete at the lowest possible degree bounds. Next we study better poly-time approximation of the problem for degree 3 graphs, and improve the previously best ratio, |, to arbitrarily close to |. This result also provides improved poly-time approximation ratios, (Formula Presented), for odd degree B.

AB - The main problem we consider in this paper is the Independent Set problem for bounded degree graphs. It is shown that the problem remains MAX SJVP-complete when the maximum degree is bounded by 3. Some related problems are also shown to be MAX SNP-complete at the lowest possible degree bounds. Next we study better poly-time approximation of the problem for degree 3 graphs, and improve the previously best ratio, |, to arbitrarily close to |. This result also provides improved poly-time approximation ratios, (Formula Presented), for odd degree B.

UR - http://www.scopus.com/inward/record.url?scp=84958038732&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958038732&partnerID=8YFLogxK

U2 - 10.1007/3-540-60220-8_84

DO - 10.1007/3-540-60220-8_84

M3 - Conference contribution

AN - SCOPUS:84958038732

SN - 3540602208

SN - 9783540602200

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 449

EP - 460

BT - Algorithms and Data Structures - 4th International Workshop, WADS 1995, Proceedings

A2 - Akl, Selim G.

A2 - Dehne, Frank

A2 - Sack, Jörg-Rüdiger

A2 - Santoro, Nicola

PB - Springer Verlag

ER -