#### Abstract

In designing VLSI architectures for a complex computational task, the functional decomposition of the task into a set of computational modules can be represented as a directed task graph, and the inclusion of input data modifies the task graph to an acyclic data flow graph (ADFG). Due to different paths of traveling and computation time of each computational module, operands may arrive at multi-input modules at different arrival times, causing a longer pipelined time. Delay buffers may be inserted along various paths to balance the ADFG to achieve maximum pipelining. This paper presents an efficient decomposition technique which provides a more systematic approach in solving the optimal buffer assignment problem of an ADFG with a large number of computational nodes. The buffer assignment problem is formulated as an integer linear optimization problem which can be solved in pseudo-polynomial time. However, if the size of an ADFG increases, then integer linear constraint equations may grow exponentially, making the optimization problem more intractable. The decomposition approach utilizes the critical path concept to decompose a directed ADFG into a set of connected subgraphs, and the integer linear optimization technique can be used to solve the buffer assignment problem in each subgraph. In other words, a large-scale integer linear optimization problem is divided into a number of smaller-scale subproblems, each of which can be easily solved in pseudo-polynomial time. Examples are given to illustrate the proposed decomposition technique.

#### Date of this Version

6-1-1987

## Comments

Supported in part by the National Science Foundation Engineering Research Center Grant CDR-8500022.