The body of mother-of-two Jean Campbell was discovered by her husband on the morning of Saturday December 14 in Glasgow's Cranhill Park.
The 53-year-old was last seen walking her dog the night before and police believe she suffered a particularly violent attack.
Officers last week turned to Facebook users to help find the killer and have now said they received a positive response to the appeal.
In what they described as a first for Scotland, police promoted the appeal via a sponsored Facebook post on the Police Scotland national site. This meant that people in the Glasgow area logging on to their Facebook page would find the appeal for information about the murder highlighted on their news feed.
The technique resulted in an additional 151,000 people in the city seeing the appeal, Police Scotland said.
Of those, more than 16,000 people checked the force website for further details, shared the appeal with Facebook friends or commented on the appeal, helping to raise awareness of the investigation and the continued hunt for the murderer.
Last night, the BBC's Crimewatch programme featured a short appeal for information about the killing.
CCTV footage shown during the appeal showed Mrs Campbell on the Friday afternoon in a local shop and walking her dog near the park later that night.
Door-to-door inquiries are still taking place in the Cranhill area and leaflets, which include details of a Crimestoppers £5,000 reward for information that leads to an arrest and conviction, are now being distributed.
Detective Chief Inspector Colin Carey, the officer leading the inquiry, said: "Our Facebook appeal was about awareness and making sure the appeal gets to as wide an audience as possible.
"The response to this appeal, and indeed for all of our appeals, has been positive - people are very keen to help officers solve this crime.
"All the information we get is followed up by the team of detectives involved in this inquiry with support for local officers. Nothing passed to officers will be ignored."
Extra police officers are patrolling the area to help reassure the public.
Anyone with information or concerns can talk to them or call into the incident caravan in Bellrock Street.
People can also call the incident room on 0141 532 4191 or the Police Scotland non-emergency number 101. Crimestoppers can be contacted anonymously on 0800 555 111.