An Efficient A* Algorithm for the Directed Linear Arrangement Problem

[[abstract]]In this paper we present an efficient A* algorithm to solve the Directed Linear Arrangement Problem. By using a branch and bound technique to embed a given directed acyclic graph into a layerwise partition search graph, the optimal directed ordering is then be identified through a A* shortest path search in the embedding graph. We developed a hybrid DC+BDS algorithm to approximate the optimal linear arrangement solution, which includes directed clustering and bidirectional sort technique. Along with a lower bound based on the maximum flow technique, this approximation solution is used as an upper bound to prune the state space during the A* search. In order to reduce the memory requirement of the A* search, we also discuss a implementation of the relay node technique from Zhou and Hansen