Abstract

This paper studies the relationship between parallel computation cost and communication cost for performing divide-and-conquer (D&C) computations on a parallel system of p processors. The parallel computation cost is the maximal number of the D&C nodes that any processor in the parallel system may expand, whereas the communication cost is the total number of cross nodes. A cross node is a node which is generated by one processor but expanded by another processor. A new scheduling algorithm is proposed, whose parallel computation cost and communication cost are at most dN=pe and pdh, respectively, for any D&C computation tree with N nodes, height h, and degree d. Also, lower bounds on the communication cost are derived. In particular, it is shown that for each scheduling algorithm and for each positive ffl C ! 1, which can be arbitrarily close to 0, there are values of N , h, d, p, and ffl T (? 0), for which if the parallel computation cost is between N=p (the minimum) and (1 + ffl T ...

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