Determining adjacent vertices on assignment polytopes

To rank the solutions to the assignment problem using an extreme point method, it is necessary to be able to find all extreme points which are adjacent to a given extreme solution. Recent work has shown a procedure for determining adjacent vertices on transportation polytopes using a modification of the Chernikova Algorithm. We present here a procedure for assignment polytopes which is a simplification of the more general procedure for transportation polytopes and which also allows for implicit enumeration of adjacent vertices.