Jean Campbell, 53, was last seen heading towards Cranhill Park while walking her dog within sight of her home in the east end of Glasgow on Friday, December 13.
Her body was discovered the next morning by her husband who, on returning from his night shift, saw she was not home and went to look for her.
Police said she had suffered a particularly violent attack.
Despite several public appeals and a reconstruction on the BBC's Crimewatch programme, officers are still appealing to the public for their help.
DCI Colin Carey, the officer in charge of the investigation for Police Scotland, said: "Jean's family are devastated by the loss of their wife, mother and grandmother and they deserve answers."
Over the past six months, officers have taken more than 1500 DNA samples and carried out house-to-house inquiries, but the case remains unsolved.
The Crimestoppers charity has offered a reward of up to £5000 for information that leads to a conviction.