▁ Σ , ▁a ▁com pressed ▁suffix ▁array ▁supports ▁searching ▁for ▁arbitrary ▁patterns ▁in ▁T . ▁ ▁For ▁an ▁input ▁pattern ▁P ▁of ▁m ▁characters , ▁the ▁search ▁time ▁is ▁typically ▁O ( m ) ▁or ▁O ( m ▁+ ▁log ( n )). ▁The ▁space ▁used ▁is ▁typically ▁, ▁where ▁ ▁is ▁the ▁k - th ▁order ▁empir ical ▁entropy ▁of ▁the ▁text ▁T . ▁The ▁time ▁and ▁space ▁to ▁construct ▁a ▁com pressed ▁suffix ▁array ▁are ▁normally ▁. ▁ ▁The ▁original ▁instanti ation ▁of ▁the ▁com pressed ▁suffix ▁array ▁solved ▁a ▁long - standing ▁open ▁problem ▁by ▁showing ▁that ▁fast ▁pattern ▁matching ▁was ▁possible ▁using ▁only ▁a ▁linear - space ▁data ▁structure , ▁namely , ▁one ▁proportional ▁to ▁the ▁size ▁of ▁the ▁text ▁T , ▁which ▁takes ▁ ▁bits . ▁ ▁The ▁conventional ▁suffix ▁array ▁and ▁suffix ▁tree ▁use ▁ ▁bits , ▁which ▁is ▁substantial ly ▁larger . ▁ ▁The ▁basis ▁for ▁the ▁data ▁structure ▁is ▁a ▁recursive ▁decomposition ▁using ▁the ▁" ne igh bor ▁function ," ▁which ▁allows ▁a ▁suffix ▁array ▁to ▁be ▁represented ▁by ▁one ▁of ▁half ▁its ▁length . ▁ ▁The ▁construction ▁is ▁repeated ▁multiple ▁times ▁until ▁the ▁resulting ▁suffix ▁array ▁uses ▁a ▁linear ▁number ▁of ▁bits . ▁ ▁Following ▁work ▁showed ▁that ▁the ▁actual ▁storage ▁space ▁was ▁related ▁to ▁the ▁z er oth - order ▁entropy ▁and ▁that ▁the ▁index ▁supports ▁self - index ing . ▁ ▁The ▁space ▁bound ▁was ▁further ▁improved ▁ach ieving ▁the ▁ult imate ▁goal ▁of ▁higher - order ▁entropy ; ▁the ▁compression