On time bounds, the work-time scheduling principle, and optimality for BSR

Constant time solutions for many applications have been obtained on BSR, but some theoretical problems on BSR (broadcasting with selective reduction) that raised when BSR was proposed have not been solved. Three of them are: 1) No lower bound for any problem on BSR is known except trivial constant time, 2) is there any improvement with nonconstant BSR time but still better than the lower bound for CRCW?, and 3) how to characterize problems for which BSR achieves constant time performance. In this paper, we have solved these three problems. For Problem 1, a lower bound on BSR is shown for any computational problem with an optimal sequential solution. An efficient sorting algorithm answers the second problem. A necessary condition is given for the third problem. The work-time (WT) scheduling principle and optimality for BSR are also introduced for investigating the BSR performance when the number of processors available, p, is different from the input size, n, of problems