, ▁denoted ▁. ▁ ▁The ▁depth ▁or ▁span ▁is ▁the ▁length ▁of ▁the ▁longest ▁series ▁of ▁operations ▁that ▁have ▁to ▁be ▁performed ▁sequ entially ▁due ▁to ▁data ▁dependencies ▁( the ▁critical ▁path ). ▁The ▁depth ▁may ▁also ▁be ▁called ▁the ▁critical ▁path ▁length ▁of ▁the ▁computation . ▁Min im izing ▁the ▁depth / span ▁is ▁important ▁in ▁design ing ▁parallel ▁algorithms , ▁because ▁the ▁depth / span ▁determ ines ▁the ▁short est ▁possible ▁execution ▁time . ▁Alternatively , ▁the ▁span ▁can ▁be ▁defined ▁as ▁the ▁time ▁ ▁spent ▁computing ▁using ▁an ▁ideal ized ▁machine ▁with ▁an ▁infinite ▁number ▁of ▁process ors . ▁ ▁The ▁cost ▁of ▁the ▁computation ▁is ▁the ▁quantity ▁. ▁This ▁express es ▁the ▁total ▁time ▁spent , ▁by ▁all ▁process ors , ▁in ▁both ▁computing ▁and ▁waiting . ▁ ▁Several ▁useful ▁results ▁follow ▁from ▁the ▁definitions ▁of ▁work , ▁span ▁and ▁cost : ▁▁ ▁Work ▁law . ▁The ▁cost ▁is ▁always ▁at ▁least ▁the ▁work : ▁. ▁This ▁follows ▁from ▁the ▁fact ▁that ▁ ▁process ors ▁can ▁perform ▁at ▁most ▁ ▁operations ▁in ▁parallel . ▁ ▁Span ▁law . ▁A ▁finite ▁number ▁ ▁of ▁process ors ▁cannot ▁out perform ▁an ▁infinite ▁number , ▁so ▁that ▁. ▁ ▁Using ▁these ▁definitions ▁and ▁laws , ▁the ▁following ▁measures ▁of ▁performance ▁can ▁be ▁given : ▁▁ ▁Speed up ▁is ▁the ▁gain ▁in ▁speed ▁made ▁by ▁parallel ▁execution ▁compared ▁to ▁sequ ential ▁execution : ▁. ▁When ▁the ▁speed up ▁is ▁ ▁for ▁input ▁size ▁ ▁( using ▁big ▁O ▁notation ), ▁the ▁speed up