image query time algorithm for all pairs shortest distances on permutation graphs Original Research Article

We present an algorithm for the all pairs shortest distance problem on permutation graphs. Given a permutation model for the graph on n vertices, after image preprocessing the algorithm will deliver answers to distance queries in image time. In the EREW PRAM model, preprocessing can be accomplished in image time with image work. Where the distance between query vertices is k, a path can be delivered in image time. The method is based on reduction to bipartite permutation graphs, a further reduction to unit interval graphs, and a coordinatization of unit interval graphs.