A global router based on a multicommodity flow model

Abstract

The paper describes a new global router applicable for any object with a defined channel structure. This router can be used for the routing of chips and boards with rectilinear or nonrectilinear channel topology in a multilayer environment. This makes it more universal than other known global routers. The router is based on a multicommodity flow model in the graph form with hierarchical cost function. This model is proved to be NP-complete. An algorithm applied to this problem is based on minimax ideas. It moves from the solution optimal w/r to an initial cost function in the direction of the constraints by maximizing on each iteration the decrease in the number of channels at the highest level of overflow and the number of cells with overflown via count. If a solution exists for each iteration, then algorithm will converge in polynomially bounded number of steps to the solution of the multicommodity flow problem. If, for some iteration, a solution does not exist, then an escape procedure is applied and the process continues. Experimental results indicate that performance characteristics of this global router are not inferior to global routers applicable only to gate arrays.