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Two days after Christmas 1977, police found Shelley H. dead in her apartment in Long Beach, California. The 17-year-old had been sexually assaulted and strangled: She was lying on the end of her bed, her feet touching the ground, with an electrical wire tied around her neck.

Vaginal swabs were taken during her autopsy, but at the time, there was no DNA testing. So the samples went into storage, and the case went cold for the next three decades.

Then in 2011, a private DNA lab matched the samples to a man who had lived in Long Beach at the time, Martell Chubbs. The DNA, according to his attorney, is the only evidence linking him to the victim.

And these DNA samples were particularly tough to read, tangled with the genetic traces of one or two people in addition to Shelley. What were the chances that the match was correct? Dr. Mark Perlin, the CEO of a Pittsburgh company called Cybergenetics, said his computer program could figure it out.

In pop culture, DNA is often portrayed...