On finding ranked assignments with application to multitarget tracking and motion correspondence

Within the target tracking community there is strong interest in computing a ranked set of assignments of measurements to targets. These k-best assignments are then used to determine good approximations to the data association problem. Much earlier work described algorithms which either had exponential worst case time or were not guaranteed to return the k-best assignments. Danchick and Newnam (1993) described a fast algorithm for finding the exact k-best hypotheses. However, in the worst case, k! linear assignment problems must be solved. This correspondence describes an algorithm originally due to Murty (1968) for optimally determining a ranked set of assignments in polynomial time and which is linear in k.<>