Parallel heuristics for the Steiner tree problem in images without sorting or routing

The problem of determining a minimum-cost rectilinear Steiner tree when the input is an n×n binary array, I which is stored in an n×n mesh of processors is discussed. Several heuristic mesh algorithms are presented for this NP-hard problem. A major design criterion of the algorithms is to avoid sorting and routing, which are expensive operations in practice. All of the algorithms have an O(n log k ) worst-case running time, where k is the number of connected components formed by the entries of value 1. Two conceptually different methods for connecting components in an image and a method for improving subsolutions by making horizontal and vertical shortcuts are presented