PMC:1592098 / 67115-68123 JSONTXT

{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/1592098","sourcedb":"PMC","sourceid":"1592098","source_url":"https://www.ncbi.nlm.nih.gov/pmc/1592098","text":"There are O(idv2 MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGPbqAcqWGKbazdaqhaaWcbaGaemODayhabaGaeGOmaidaaaaa@31EC@) of these sums and each takes time O(idv') to calculate, so the time complexity for calculating all sums is O(idv2idv′ MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaacqWGPbqAcqWGKbazdaqhaaWcbaGaemODayhabaGaeGOmaidaaOGaemyAaKMaemizaq2aaSbaaSqaaiqbdAha2zaafaaabeaaaaa@364F@). In the case that idv' ≤ idv, we can switch v and v' and thus get time usage O(idvidv' min{idv, idv'}). Assuming that the sums have been calculated, (9) can now be calculated in time O(idvidv'min{idv, idv'}) by the expression:","tracks":[]}