Adaptive Data Structures for Permutations and Binary Relations

Compressed Spaced Suffix Arrays

“…Barbay et al's result holds even when we are given a partition of a permutation into ρ increasing or decreasing subsequences, and some authors [1,10] have found that using both increasing and decreasing subsequences often improves compression in practice. Computing a partition into the minimum number of such subsequences is NP-hard, however, and we see no reason why SA −1 •SSA should contain long decreasing subsequences.…”

“…For our example, we can partition both SSA and SA into [4,6,9,2], for T ′ i = a; [7, 0], for [8,1], for T ′ i = r; and [10], for T ′ i = ǫ. In this particular case, however, we could just as well partition both SSA and SA into only two common subsequences: e.g., [10,7,0] and [3,5,8,1,4,6,9,2].…”

“…For example, if π[0..12] = [12,11,6,3,8,0,5,7,4,9,1,10,2] π[0..11] = [11,10,7,0,3,5,8,1,4,6,9,2] then the elements in their subsequences [12,11,8,0,9,1,10,2] and [11,10,7,0,8,1,9,2]…”

“…, for T ′ i = r; and [10], for T ′ i = ǫ. In this particular case, however, we could just as well partition both SSA and SA into only two common subsequences: e.g., [10,7,0] and [3, 5, 8, 1, 4, 6, 9, 2].…”

“…Supowit [28] gave a simple algorithm that partitions SA −1 • SSA into ρ increasing subsequences in O(n lg ρ) ⊆ O(n min(w, ℓ − w) lg σ) time. When applied to SA −1 • SSA in our example, Supowit's algorithm partitions it into [0, 3,4] and [1,2,5,6,7,8,9,10].…”