A parallel algorithm for EDT transform on linear array with reconfigurable pipeline bus system (LARPBS) is presented. For an image with n × n pixels, the algorithm can complete the EDT transform in O(nlogn/(c(n)logd(n))) time using n.d(n).c(n) processors, where c(n) and d(n) are parameters satisfying 1 ≤ c(n) ≤ n, and 1< d(n) ≤ n, respectively. By selecting different values for c(n) and d(n), the time complexity and the number of processors used can be adjusted. This makes the algorithm highly scalable and flexible. The algorithm also provides a general framework of EDT algorithms on LARPBS, and many existing and new parallel EDT algorithms can be deduced from this framework. In particular, if we let c(n) = n, d(n) = nε, the algorithm can be completed in O(1) time using n^{2 + \varepsilon} processors. To our best knowledge, this is the most efficient constant-time EDT algorithm on LARPBS.