Cluttered orderings for the complete graph

Myra B. Cohen, Charles Colbourn, Dalibor Froncek

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

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 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.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages420-431
Number of pages12
Volume2108
ISBN (Print)9783540424949
StatePublished - 2001
Externally publishedYes
Event7th Annual International Conference on Computing and Combinatorics, COCOON 2001 - Guilin, China
Duration: Aug 20 2001Aug 23 2001

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume2108
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other7th Annual International Conference on Computing and Combinatorics, COCOON 2001
CountryChina
CityGuilin
Period8/20/018/23/01

Fingerprint

Complete Graph
Parity
Disk Array
Graph Model
Simple Graph
Penalty
Consecutive
Update
Optimise
Requirements

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Cohen, M. B., Colbourn, C., & Froncek, D. (2001). Cluttered orderings for the complete graph. In 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.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2108 Springer Verlag, 2001. p. 420-431 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 2108).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Cohen, MB, Colbourn, C & Froncek, D 2001, Cluttered orderings for the complete graph. in 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.
Cohen MB, Colbourn C, Froncek D. Cluttered orderings for the complete graph. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2108. Springer Verlag. 2001. p. 420-431. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
Cohen, Myra B. ; Colbourn, Charles ; Froncek, Dalibor. / Cluttered orderings for the complete graph. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 2108 Springer Verlag, 2001. pp. 420-431 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
@inproceedings{6e76e4d90f6c41bca1f6fe2eaa826af7,
title = "Cluttered orderings for the complete graph",
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 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.",
author = "Cohen, {Myra B.} and Charles Colbourn and Dalibor Froncek",
year = "2001",
language = "English (US)",
isbn = "9783540424949",
volume = "2108",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "420--431",
booktitle = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

}

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 -