Ladder orderings of pairs and RAID performance

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 K_n, except possibly when n ∈ {15, 18, 22}.