Just to add: Before this breakthrough, Police had gathered the DNA from about 6000 people via voluntary interrogations without any match. They even collected DNA form mothers of men who had killed themselves (and matched the description/profile etc) in the years after the murder.
In fact, they had actually sent a letter to the murder asking for a sample in the months before starting the new approach, but he didn't show up and they hadn't gotten to taking it further.
So in the end, they might have had a chance of solving it the traditional way. But at the same time, it takes a lot of evidence in Sweden to forcibly collect a DNA sample, which probably is not so easy for a 16 year old case.
Right, this is also important info. They did, early this year, ask the murderer for a voluntary DNA sample, and they had received a tip that placed the murderer on the police radar. It's possible they would have solved it eventually, but it's unlikely the police would have been allowed to forcibly collect DNA based on a vague tip that amounted to "he owned a similar hat and had discussed violence in his teens".
To forcibly collect someone's DNA, the authorities need to establish the person as a reasonable suspect (skäligen misstänkt), which requires a preponderance of evidence and isn't that easy to establish. In this case, the police would have definitely needed more than the person fitting the same vague profile as thousands of others, and it was definitely hard to obtain any extra evidence given that the murderer indeed lacked any connection to the victims or to the crime scene.
In fact, they had actually sent a letter to the murder asking for a sample in the months before starting the new approach, but he didn't show up and they hadn't gotten to taking it further.
So in the end, they might have had a chance of solving it the traditional way. But at the same time, it takes a lot of evidence in Sweden to forcibly collect a DNA sample, which probably is not so easy for a 16 year old case.