TY - JOUR

T1 - Ladder orderings of pairs and RAID performance

AU - Cohen, Myra B.

AU - Colbourn, Charles

N1 - Funding Information:
Research of the authors is supported by the Army Research Office (USA) under grants numbered DAAG55-98-1-0272 and DAAD19-01-1-0406 (Colbourn).

PY - 2004/3/29

Y1 - 2004/3/29

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. Based on simulations of RAID performance, an ordering of the edges in which every sequence of three consecutive edges in the order induces as few vertices as possible is found to optimize access performance of the disk array. The ladder orderings to optimize performance are shown to exist for the complete graph Kn, except possibly when n ∈ {15, 18, 22}.

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. Based on simulations of RAID performance, an ordering of the edges in which every sequence of three consecutive edges in the order induces as few vertices as possible is found to optimize access performance of the disk array. The ladder orderings to optimize performance are shown to exist for the complete graph Kn, except possibly when n ∈ {15, 18, 22}.

KW - Edge access cost

KW - Edge ordering in graphs

KW - RAID disk array

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U2 - 10.1016/S0166-218X(03)00268-3

DO - 10.1016/S0166-218X(03)00268-3

M3 - Article

AN - SCOPUS:1242264787

SN - 0166-218X

VL - 138

SP - 35

EP - 46

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

IS - 1-2

ER -