Systems Theory ©1988 Springer-Verlag New York Inc. Minimum-Diameter Cyclic Arrangements in Mapping Data-Flow Graphs onto VLSI Arrays

Abstract. Regular arrays of processing elements in VLSI have proved to be suitable for high-speed execution of many matrix operations. To execute an arbitrary computational algorithm on such processing arrays, it has been suggested mapping the given algorithm directly onto a regular array. The computational algorithm is represented by a data-flow graph whose nodes are to be mapped onto processors in the VLSI array. This study examines the complexity of mapping data-flow graphs onto square and hexagonal arrays of processors. We specifically consider the problem of routing data from processors in a given (source) sequence to another (target) sequence. We show that under certain conditions, the above problem is equivalent to the one of finding a minimum-diameter cyclic arrangement. The complexity of the latter problem is analyzed and upper and lower bounds on the number of intermediate rows of processors (between the source and target rows) are derived