Sequence Alignment Algorithms for Run-Length-Encoded Strings

Hardness of comparing two run-length encoded strings

“…The costs of these operations on different symbols are specified by a given scoring matrix. Given two strings of lengths M and N, compressed into m and n runs, Mäkinen et al [18] and Crochemore et al [10] independently proposed an upper bound of O(mN + Mn) for the weighted edit distance model; a recent work improved the bound to O(min{mN, Mn}) [14]. In this paper, we establish the 3sum-hardness for the Hamming distance setting, in which a substitution of each symbol costs 1 and an insertion or deletion costs ∞.…”

“…For a similar reason, this coding is also largely applied in optical character recognition, in which the inputs are usually images of large scales of identically valued pixels [20]. Other applications appear in bioinformatics, where rle compression is employed to speed up the comparison of two biological sequences [10,14,18].…”

“…Since then this has been an active research field, and several papers have delved into compressed pattern matching problems under various compression schemes (e.g., rle compression, LZ-family compression, or straight-line programs). For the rle scheme, some papers took one step further by considering problems of comparing two rle strings using different cost functions, such as the LCS metric [5,17,19], the Levenshtein distance [16,18], and arbitrary alignment scores [10,14]. In this paper, we investigate the hardness of comparing (or approximately matching) two strings both compressed into the rle format.…”