▁is ▁linear , ▁which ▁is ▁optimal ▁in ▁simple ▁models ▁of ▁computation ▁because ▁the ▁work ▁law ▁implies ▁that ▁ ▁( super - linear ▁speed up ▁can ▁occur ▁in ▁practice ▁due ▁to ▁memory ▁hierarchy ▁effects ). ▁The ▁situation ▁ ▁is ▁called ▁perfect ▁linear ▁speed up . ▁An ▁algorithm ▁that ▁exhib its ▁linear ▁speed up ▁is ▁said ▁to ▁be ▁scal able . ▁ ▁E ffic iency ▁is ▁the ▁speed up ▁per ▁processor , ▁. ▁ ▁Par allel ism ▁is ▁the ▁ratio ▁. ▁It ▁represents ▁the ▁maximum ▁possible ▁speed up ▁on ▁any ▁number ▁of ▁process ors . ▁By ▁the ▁span ▁law , ▁the ▁parallel ism ▁bounds ▁the ▁speed up : ▁if ▁, ▁then : ▁▁ ▁. ▁▁ ▁The ▁s lack ness ▁is ▁. ▁A ▁s lack ness ▁less ▁than ▁one ▁implies ▁( by ▁the ▁span ▁law ) ▁that ▁perfect ▁linear ▁speed up ▁is ▁impossible ▁on ▁ ▁process ors . ▁ ▁Exec ution ▁on ▁a ▁limited ▁number ▁of ▁process ors ▁Analysis ▁of ▁parallel ▁algorithms ▁is ▁usually ▁carried ▁out ▁under ▁the ▁assumption ▁that ▁an ▁un bounded ▁number ▁of ▁process ors ▁is ▁available . ▁This ▁is ▁un real istic , ▁but ▁not ▁a ▁problem , ▁since ▁any ▁computation ▁that ▁can ▁run ▁in ▁parallel ▁on ▁ ▁process ors ▁can ▁be ▁executed ▁on ▁ ▁process ors ▁by ▁letting ▁each ▁processor ▁execute ▁multiple ▁units ▁of ▁work . ▁A ▁result ▁called ▁Br ent ' s ▁law ▁states ▁that ▁one ▁can ▁perform ▁such ▁a ▁" sim ulation " ▁in ▁time ▁, ▁bounded ▁by ▁ ▁or , ▁less ▁precisely , ▁ ▁An ▁alternative ▁statement ▁of ▁the