One of the concepts behind community policing is familiarity. If members of a neighborhood become familiar with the officers assigned to the area a relationship of trust can be fostered. Also, if potential criminals see the same faces day after day some believe this deters criminal activity.
The regular shift and area assignments are so important, both for the officers and the community. Trust is such an issue and ways to build trust so limited if the police officers don't know the people in their area. People who live in the community begin to be part of the policing effort as they work with the officers to keep people safe. The officers learn to truly listen to people's issues and spend the time and effort to change what is wrong because these become their issues also as their part of the pact to work together. The key is a working partnership to solve crime and the other issues which affect the community in which the officers work.
The previous post is correct about this. The idea of the "beat cop" used to be very common. However, it was done away with at least in part because officers who came to "own" a certain beat had too much opportunity to become corrupt. This is one thing that stands in the way of community policing.