Direct computation of nonshared(v, v') using (10) takes time O(dv2dv′2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGKbazdaqhaaWcbaGaemODayhabaGaeGOmaidaaOGaemizaq2aa0baaSqaaiqbdAha2zaafaaabaGaeGOmaidaaaaa@348C@). Each of the subtrees has to be intersected with two disjoint sets in each of the sums. This means that if a subtree is only a leaf, at least one of these intersections will be zero, and the term will be zero. Therefore we can ignore subtrees that consist of a single leaf, just like when computing shared(T, T'), and reduce the time usage to O(idv2idv′2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGPbqAcqWGKbazdaqhaaWcbaGaemODayhabaGaeGOmaidaaOGaemyAaKMaemizaq2aa0baaSqaaiqbdAha2zaafaaabaGaeGOmaidaaaaa@3742@). The time usage of the calculation of nonshared(v, v') can be further improved by rewriting (9):