Consideration is given to a situation in which two processors, P1 and P2, are to evaluate a collection of functions f1,..., f]s of two vector variables x, y under the assumption that processor P1 (respectively, P2) has access only to the value of the variable x (respectively, y) and the functional form of f1, ..., fs. Bounds on the communication complexity (the amount of information that has to be exchanged between the processors) are provided. An almost optimal bound is derived for the case of one-way communication when the functions are polynomials. Lower bounds for the case of two-way communication that improve on earlier bounds are also derived. As an application, the case in which x and y are n × n matrices and f(x,y) is a particular entry of the inverse of x + y is considered. Under a certain restriction on the class of allowed communication protocols, an Ω(n2) lower bound is obtained. The results are based on certain tools from classical algebraic geometry and field extension theory.
|Original language||English (US)|
|Number of pages||2|
|Journal||Proceedings of the IEEE Conference on Decision and Control|
|State||Published - Dec 1 1989|
|Event||Proceedings of the 28th IEEE Conference on Decision and Control. Part 1 (of 3) - Tampa, FL, USA|
Duration: Dec 13 1989 → Dec 15 1989