25th Annual Symposium onFoundations of Computer Science, 1984. (1984)
Singer Island, FL
Oct. 24, 1984 to Oct. 26, 1984
C.H. Papadirnitriou , Stanford University
We show a nontrivial tradeoff between the communication c and time t required to compute a collection of values whose dependencies form a grid, i.e., value (i,j) depends on the values (i-1,j) and (i,j-1). No matter how we share the responsibility for computing the nodes of the n x n grid among processors, the law ct = /spl Omega/(n/sup 3/) must hold. Further, there must be a single path through the grid along which there are d communication steps, where dt = /spl Omega/(n/sup 2/). Depending on the machine organization, either law may be the more significant.
J. Ullman and C. Papadirnitriou, "A Communication-Time Tradeoff," 25th Annual Symposium onFoundations of Computer Science, 1984.(FOCS), Singer Island, FL, 1984, pp. 84-88.