Fault-tolerant file transmission by information dispersal algorithm in rotator graphs

A directed graph G=(V, E) is called the n-rotator graph if V={a/sub 1/a/sub 2//spl middot//spl middot//spl middot/a/sub n/|a/sub 1/a/sub 2//spl middot//spl middot//spl middot/a/sub n/ is a permutation of 1, 2, /spl middot//spl middot//spl middot/, n} and E={(a/sub 1/a/sub 2//spl middot//spl middot//spl middot/a/sub n/, b/sub 1/b/sub 2//spl middot//spl middot//spl middot/b/sub n/) I for some 2/spl les/i/spl les/n, b/sub 1/b/sub 2//spl middot//spl middot//spl middot/b/sub n/=a/sub 2//spl middot//spl middot//spl middot/a/sub i/a/sub 1/a/sub i+1//spl middot//spl middot//spl middot/a/sub n/}. We show that for any pair of distinct nodes in the n-rotator graph, we can construct n-1 disjoint paths, each with length less than 2n, connecting the two nodes. By using these disjoint paths and information dispersal algorithm (IDA) by M.O. Rabin (1989), we design a file transmission scheme and analyse its reliability.