1. In a computing environment having multiple processing units, each processing unit having one or more cache memories associated therewith, a snoop filtering system comprising: a snoop filter sub-system associated with each of said multiple processing units, each snoop filter sub-system having a plurality of dedicated inputs for receiving snoop requests from dedicated memory writing sources in said multiprocessor computing environment and, a point-to-point interconnect means comprising communication links for directly connecting a memory writing source to a corresponding dedicated input of each snoop filter sub-system associated with each processing unit of said multiprocessor computing environment; wherein each said snoop filter sub-system further comprises: a plurality of snoop filter means each coupled to a corresponding one of said plurality of dedicated inputs for filtering respective received snoop requests from respective dedicated memory writing sources, each snoop filter means implementing one or more parallel operating sub-filter elements operative for determining those requests likely residing in a cache memory at said associated processing unit and filtering out those snoop requests for data that are determined not cached locally at said associated processing unit, whereby a number of snoop requests forwarded to a processing unit is significantly reduced thereby increasing performance of said computing environment.