) ▁link ▁weights . ▁ ▁Yu ▁et ▁al . ▁further ▁improved ▁Sim R ank ▁computation ▁via ▁a ▁fine - gra ined ▁mem o ization ▁method ▁to ▁share ▁small ▁common ▁parts ▁among ▁different ▁partial ▁sums . ▁ ▁Chen ▁and ▁G iles ▁discussed ▁the ▁limitations ▁and ▁proper ▁use ▁cases ▁of ▁Sim R ank . ▁ ▁Part ial ▁S ums ▁Mem o ization ▁▁ ▁L iz ork in ▁et ▁al . ▁proposed ▁three ▁optimization ▁techniques ▁for ▁speed ing ▁up ▁the ▁computation ▁of ▁Sim R ank : ▁▁ ▁Ess ential ▁nodes ▁selection ▁may ▁eliminate ▁the ▁computation ▁of ▁a ▁fraction ▁of ▁node ▁pairs ▁with ▁a - p ri ori ▁zero ▁scores . ▁ ▁Part ial ▁sums ▁mem o ization ▁can ▁effectively ▁reduce ▁repeated ▁calculations ▁of ▁the ▁similarity ▁among ▁different ▁node ▁pairs ▁by ▁caching ▁part ▁of ▁similarity ▁summ ations ▁for ▁later ▁reuse . ▁ ▁A ▁threshold ▁setting ▁on ▁the ▁similarity ▁enables ▁a ▁further ▁reduction ▁in ▁the ▁number ▁of ▁node ▁pairs ▁to ▁be ▁computed . ▁ ▁In ▁particular , ▁the ▁second ▁observation ▁of ▁partial ▁sums ▁mem o ization ▁plays ▁a ▁param ount ▁role ▁in ▁greatly ▁speed ing ▁up ▁the ▁computation ▁of ▁Sim R ank ▁from ▁ ▁to ▁, ▁where ▁ ▁is ▁the ▁number ▁of ▁iterations , ▁ ▁is ▁average ▁degree ▁of ▁a ▁graph , ▁and ▁ ▁is ▁the ▁number ▁of ▁nodes ▁in ▁a ▁graph . ▁The ▁central ▁idea ▁of ▁partial ▁sums ▁mem o ization ▁consists ▁of ▁two ▁steps : ▁ ▁First , ▁the ▁partial ▁sums ▁over ▁ ▁are ▁mem o ized ▁as ▁ ▁and ▁then ▁ ▁is ▁iter atively ▁computed