Tobin is currently serving a lengthy sentence for the abduction and murder of 15-year-old Vicky Hamilton, whose remains were buried in a Kent garden, and raping and murdering Polish student Angelika Kluk and hiding her body in a Glasgow church.
Tobin, who has a history of sexual violence, used numerous aliases and lived in several parts of the country.
That prompted the start of Operation Anagram, which has been analysing his movements and sharing information between police forces up and down the country, which have also re-opened files on unsolved disappearances and murders involving young women.
That includes the case of Jessie Earl, whose remains were discovered in undergrowth at Beachy Head nine years after she disappeared in 1980.
Her parents John and Valerie Earl last month told a national newspaper they knew Tobin was in the area when 22-year-old Jessie went missing.
Police asked for samples of Jessie's clothing and took DNA samples from her parents.
Mrs Earl said, "The thing I feel saddest about is that there seems to be so little left of Jessie to make the connection to Tobin or anyone else. But you never know. Things have changed so much since Jessie went missing.
"I felt that some day someone would say something or do something to give us the answers. I wasn't sure we would live to see it or whether our son James would get the news. But with Tobin we feel, ''Maybe this time'."
Jessie was studying at Eastbourne College of Art and Technology and living at a flat in Upperton Gardens at the time of her disappearance. She called her parents from a seafront phone box to tell them she was travelling home to London later that week but never arrived. At the time Tobin was living 25 miles along the coast in Brighton.
The family appeared on Crimewatch and distributed posters but there was no trace until Eastbourne Borough Council worker Gordon Cross made the gruesome discovery as he retrieved his daughter's kite from an overgrown thicket at Beachy Head.
All that remained were her skeletal remains and her bra, tied in a knot where it was used to bind her wrists.
The couple say they hope Operation Anagram will help end the mystery.
Sussex Police, like other forces across the country, is refusing to speculate on specific individuals.
A spokesperson for Sussex Police said, "Like many forces in the UK we are looking at tracking the movements of Peter Tobin over a period of years and in conjunction with this are considering the potential for his involvement in connection with similar matters falling within the Sussex area.
"This work locally is being co-ordinated within our Major Crime Branch. In particular we are focusing on any missing females, particularly those that went missing during the time that Tobin lived in Sussex. At this time there is no evidence or intelligence to link him to any of these specifically.
"There is no plan at this time to search any premises, but these options will be considered should the intelligence and evidence developed within Operation Anagram warrant it."