Abstract: An available bit rate scheduling method and apparatus for asynchronous transfer mode communication of a plurality of cells over a network characterized by a system clock frequency f and an allowed cell rate ACR. Each cell belongs to an assigned virtual circuit communication channel which is defined by a set of negotiated traffic parameters. The invention partitions the ACR's of the virtual circuits into a smaller subset of profiles/sub-profiles and conducts a deterministic search to service them. The scheduler incorporates a profile generator for iteratively generating a number p of the profiles by (i) outputting a k*modulo 2.sup.i th one of the profiles during each kth iteration of the profile generator, where 1.ltoreq.i.ltoreq.p and 1.ltoreq.k.ltoreq.p-1; (ii) outputting a null profile during each 2.sup.p th one of the iterations; and, (iii) dispatching the profiles from the profile generator to the profile queue such that a particular profile is dispatched at a time T=T.sub.0 +(1/ACR)*f, where T.sub.