s ▁" standard ▁strategy "; ▁in ▁ 1 9 8 9 , ▁Richard ▁Bird ▁derived ▁it ▁by ▁purely ▁algebraic ▁manip ulation ▁of ▁the ▁br ute - force ▁algorithm ▁using ▁the ▁Bird – Me ert ens ▁formal ism . ▁ ▁Gren ander ' s ▁two - dimensional ▁general ization ▁can ▁be ▁solved ▁in ▁O ( n 3 ) ▁time ▁either ▁by ▁using ▁K ad ane ' s ▁algorithm ▁as ▁a ▁sub rout ine , ▁or ▁through ▁a ▁divide - and - con quer ▁approach . ▁ ▁S light ly ▁faster ▁algorithms ▁based ▁on ▁distance ▁matrix ▁multiplication ▁have ▁been ▁proposed ▁by ▁ ▁and ▁by ▁. ▁There ▁is ▁some ▁evidence ▁that ▁no ▁significantly ▁faster ▁algorithm ▁exists ; ▁an ▁algorithm ▁that ▁solves ▁the ▁two - dimensional ▁maximum ▁sub array ▁problem ▁in ▁O ( n 3 − ε ) ▁time , ▁for ▁any ▁ ε > 0 , ▁would ▁imply ▁a ▁similarly ▁fast ▁algorithm ▁for ▁the ▁all - p airs ▁short est ▁paths ▁problem . ▁ ▁App lications ▁▁ ▁Max imum ▁sub array ▁problems ▁arise ▁in ▁many ▁fields , ▁such ▁as ▁genom ic ▁sequence ▁analysis ▁and ▁computer ▁vision . ▁ ▁Gen omic ▁sequence ▁analysis ▁emp lo ys ▁maximum ▁sub array ▁algorithms ▁to ▁identify ▁important ▁bi ological ▁segments ▁of ▁protein ▁sequences . ▁These ▁problems ▁include ▁conser ved ▁segments , ▁GC - rich ▁regions , ▁tan dem ▁repe ats , ▁low - complex ity ▁filter , ▁DNA ▁binding ▁domains , ▁and ▁regions ▁of ▁high ▁charge . ▁ ▁In ▁computer ▁vision , ▁maximum - sub array ▁algorithms ▁are ▁used ▁on ▁bitmap