Story highlights Police say they think a single serial killer is responsible for bodies found in Long Island

Police previously thought only the first set of remains could be the work of a killer or killers

The body of the woman who triggered investigation is still missing

The women who were killed advertised prostitution searches on websites

After a nearly year-long investigation, police say they now believe 10 sets of human remains uncovered along a desolate stretch of Long Island, New York, beach are linked to a single killer.

"The theory is now that we're dealing with one serial killer," Suffolk County Police Commissioner Richard Dormer told CNN affiliate WABC on Tuesday.

He noted the killer did not "necessarily do the same thing all the time."

"What's common here is the dumping ground," he added.

Dormer previously said that only the bodies of four females uncovered in December were thought to be the work of a serial killer or killers.

It is not clear what prompted the change.

Authorities have sifted through more than 1,000 tips related to the case. But it's unclear whether they have shed any light on an investigation that has drawn state and federal agents and garnered national attention.

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In June, police upped the ante in their search for a culprit.

The reward for information leading to an arrest -- once topping out at $5,000 -- was raised five-fold, making it the largest offered in Suffolk County history. It was an apparent bid to fill out a case that some fear has gone cold.

"We're hoping the increased reward money will encourage somebody to come forward by calling the police in respect to the families and to (the) victims," Lt. Robert Donohue said at the time.

At least 10 sets of human remains have been found in Nassau and Suffolk counties since December. But the woman whose disappearance triggered the searches, 23-year-old Shannan Gilbert, remains missing. The New Jersey woman was last seen in May 2010 at a private party at a home in Long Island's Oak Beach community.

The first four bodies have since been identified. They, like Gilbert, had advertised for prostitution services on websites such as Craigslist.

Their remains were found among bushes along a quarter-mile strip of beachfront property, according to police. More human remains were found on March 29 and April 4.

Suffolk County District Attorney Thomas Spota said in May that the newly found remains were not believed to be connected to the first four victims. In September, authorities released composite sketches of what two unidentified victims might have looked like.

Authorities at the time said the evidence suggested two other killers dumped bodies along Ocean Parkway in Gilgo Beach, about 40 miles east of New York City.

"This investigation is not an episode of 'CSI' or 'Criminal Minds' that is going to be solved in a one-hour period," Spota said of the serial killer probe. "Most likely, it ... is going to take a very long period of time to complete."

Spota was not immediately available for comment Wednesday regarding police statements that the killings are now thought to be the work of a single killer.