TUCSON, Ariz. — A Q-tip, a tissue and a pizza crust. To investigators, this seemingly innocuous trash was DNA-laden treasure, helping crack the cases of the University of Idaho murders, the Golden State Killer and the Gilgo Beach slayings, according to authorities, using a forensic tool called investigative genetic genealogy. Investigators in the Nancy Guthrie case hope that science can point to a suspect. But there are challenges. Guthrie, the 84-year-old mother of “TODAY” co-host Savannah Guthrie, was reported missing on Feb. 1. It’s been three agonizing weeks since her disappearance, and authorities haven’t publicly identified a suspect or a person of interest. Officials have cleared the Guthrie family as potential suspects, Pima County Sheriff Chris Nanos said. Nanos, whose agency is leading the investigation along with federal and state partners, said last week that mixed and partial DNA was found at Guthrie’s home. Mixed DNA is a forensic sample that has more than one person’s genetic material.…