Parallel VLSI-routing models for polymorphic processors array

This paper explores various parallel processing methods for concurrent multi-layer VLSI-routing. One approach is based on efficient execution of the maze routing algorithm on custom processing elements arranged in the form of a hexagonal array. The key features here are the mapping policy and the acceleration of three-dimensional search operations. Subsequently, parallel algorithms over a reconfigurable SIMD array is discussed to handle a wider range of routing applications. A routing framework is discussed that consolidates many of the existing specialized algorithms such as channel, switch-box and maze routers into one muting system. The concept of a total grid-graph is used to capture the state of the routing region and propose new and efficient parallel algorithms for cycle detection cycle elimination, and tree reduction on such graphs. The proposed algorithms scale well with increased problem sizes since they require only O (log(N)) time given a N²-node grid-graph. Based on these algorithms, the paper develops two types of generalized detailed routers, each capable of finding paths concurrently spanning multiple layers. The first, called a parallel chord router, has the ability to compute various “useful” route patterns in close to constant time; the second is an adaptation of maze routing capable of simultaneously expanding from multiple pins. In addition, a parallel hill-climbing algorithm is discussed that can be used to improve a given route, if possible, by iteratively identifying and rewiring bends in the route