▁edges ▁point ▁to ▁the ▁same ▁node , ▁the ▁node ▁in ▁Z DD s ▁is ▁removed ▁if ▁its ▁positive ▁edge ▁points ▁to ▁the ▁constant ▁node ▁ 0 . ▁The ▁modifications ▁in ▁reduction ▁rule ▁especially ▁improve ▁performance ▁when ▁dealing ▁with ▁sparse ▁sets . ▁ ▁Background ▁In ▁a ▁Binary ▁Dec ision ▁Di agram , ▁a ▁Boolean ▁function ▁can ▁be ▁represented ▁as ▁a ▁root ed , ▁directed , ▁a cyc lic ▁graph , ▁which ▁consists ▁of ▁several ▁decision ▁nodes ▁and ▁terminal ▁nodes . ▁In ▁ 1 9 9 3 , ▁Shin - ichi ▁Min ato ▁from ▁Japan ▁modified ▁Rand al ▁Bry ant ’ s ▁B DD s ▁for ▁solving ▁combin atorial ▁problems . ▁His ▁“ Zero - Supp ress ed ” ▁B DD s ▁aim ▁to ▁represent ▁and ▁manipulate ▁sparse ▁sets ▁of ▁bit ▁vectors . ▁If ▁the ▁data ▁for ▁a ▁problem ▁are ▁represented ▁as ▁bit ▁vectors ▁of ▁length ▁n , ▁then ▁any ▁subset ▁of ▁the ▁vectors ▁can ▁be ▁represented ▁by ▁the ▁Boolean ▁function ▁over ▁n ▁variables ▁yield ing ▁ 1 ▁when ▁the ▁vector ▁corresponding ▁to ▁the ▁variable ▁assignment ▁is ▁in ▁the ▁set . ▁▁ ▁According ▁to ▁Bry ant , ▁it ▁is ▁possible ▁to ▁use ▁forms ▁of ▁logic ▁functions ▁to ▁express ▁problems ▁involving ▁sum - of - products . ▁Such ▁forms ▁are ▁often ▁represented ▁as ▁sets ▁of ▁“ c ub es ”, ▁each ▁denoted ▁by ▁a ▁string ▁containing ▁symbols ▁ 0 , ▁ 1 , ▁and ▁- . ▁For ▁instance , ▁the ▁function ▁ ▁can ▁be ▁illustrated ▁by ▁the ▁set ▁ ▁. ▁By ▁using ▁bits ▁ 1 0