Jean Campbell, 53, was last seen heading towards Cranhill Park while walking her dog near her home in the east end of Glasgow on Friday December 13 when she was murdered.
Her body was discovered at around 7.40am the next day by her husband, who had gone out to look for her after returning from his night shift and realising she was not home.
The inquiry has seen police take more than 1,500 DNA samples from both men and women in the area.
Detective Chief Inspector Colin Carey, who is leading the hunt for her killer, said: "Jean was a wife, mother and grandmother and her family are devastated at her death, in these circumstances.
"Our inquiries have been intense and thorough, with a dedicated team of experienced detectives working around the clock on the inquiry, however the person responsible for her murder and the reason why it happened have still to be established."
Hundreds of homes have been visited by officers during the probe.