### Abstract

In a systematic erasure code for the correction of two simultaneous erasures, each information symbol must have two associated parity symbols. When implemented in a redundant array of independent disks (RAID), performance requirements on the update penalty necessitate that each information symbol be associated with no more parity symbols than the two required. This leads to a simple graph model of the erasure codes, with parity symbols as vertices and information symbols as edges. Ordering the edges so that no more than f check disks (vertices) appear amongan y set of d consecutive edges is found to optimize access performance of the disk array when d is maximized. These cluttered orderings are examined for the complete graph K_{n}. The maximum number d of edges is determined precisely when f ≤ 5 and when f = n - 1, and bounds are derived in the remaining cases.

Original language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Publisher | Springer Verlag |

Pages | 420-431 |

Number of pages | 12 |

Volume | 2108 |

ISBN (Print) | 9783540424949 |

State | Published - 2001 |

Externally published | Yes |

Event | 7th Annual International Conference on Computing and Combinatorics, COCOON 2001 - Guilin, China Duration: Aug 20 2001 → Aug 23 2001 |

### 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 | 2108 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 7th Annual International Conference on Computing and Combinatorics, COCOON 2001 |
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Country | China |

City | Guilin |

Period | 8/20/01 → 8/23/01 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 2108, pp. 420-431). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2108). Springer Verlag.

**Cluttered orderings for the complete graph.** / Cohen, Myra B.; Colbourn, Charles; Froncek, Dalibor.

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

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 2108, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 2108, Springer Verlag, pp. 420-431, 7th Annual International Conference on Computing and Combinatorics, COCOON 2001, Guilin, China, 8/20/01.

}

TY - GEN

T1 - Cluttered orderings for the complete graph

AU - Cohen, Myra B.

AU - Colbourn, Charles

AU - Froncek, Dalibor

PY - 2001

Y1 - 2001

N2 - In a systematic erasure code for the correction of two simultaneous erasures, each information symbol must have two associated parity symbols. When implemented in a redundant array of independent disks (RAID), performance requirements on the update penalty necessitate that each information symbol be associated with no more parity symbols than the two required. This leads to a simple graph model of the erasure codes, with parity symbols as vertices and information symbols as edges. Ordering the edges so that no more than f check disks (vertices) appear amongan y set of d consecutive edges is found to optimize access performance of the disk array when d is maximized. These cluttered orderings are examined for the complete graph Kn. The maximum number d of edges is determined precisely when f ≤ 5 and when f = n - 1, and bounds are derived in the remaining cases.

AB - In a systematic erasure code for the correction of two simultaneous erasures, each information symbol must have two associated parity symbols. When implemented in a redundant array of independent disks (RAID), performance requirements on the update penalty necessitate that each information symbol be associated with no more parity symbols than the two required. This leads to a simple graph model of the erasure codes, with parity symbols as vertices and information symbols as edges. Ordering the edges so that no more than f check disks (vertices) appear amongan y set of d consecutive edges is found to optimize access performance of the disk array when d is maximized. These cluttered orderings are examined for the complete graph Kn. The maximum number d of edges is determined precisely when f ≤ 5 and when f = n - 1, and bounds are derived in the remaining cases.

UR - http://www.scopus.com/inward/record.url?scp=23044530394&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23044530394&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9783540424949

VL - 2108

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

SP - 420

EP - 431

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

PB - Springer Verlag

ER -