A dual feasible forest algorithm for the linear assignment problem

Linear Assignment Problems and Extensions

“…It is easy to show that the identical permutation is an optimal solution of an LSAP with a cost matrix which fulfills (8). This remains true, even if condition (8) is relaxed to the so-called weak Monge property (cf.…”

“…Two other signature-guided algorithms were given by Paparrizos [135] and Akgül and Ekin [8]. Paparrizos' algorithm is similar to Balinski's competitive simplex algorithm [19].…”

“…Thus the overall complexity is O(n 4 ). Akgül and Ekin [8] give an efficient implementation of Paparrizos' algorithm, which maintains and updates a forest rather than a single tree. In this way only dual feasible trees are visited.…”

The Linear Assignment Problem

“…for some Xc N; where E is determined so that for some edge e E 8+(X) U 8-(X) we have We = 0 with respect to new dual variables, i.e. E is the amount of dual (in)feasibility of the edge e; E = ±We• Thus, dual variable (potential) change defined by (9) will cause the following changes in reduced costs:…”

“…Solution procedures vary from primal-dual/successive shortest paths [19,58,59,81,43,41,26,56] (see [35] for a survey), cost parametric [76], recursive [79], relaxation [39,52], signature based [15,16,48,9,66,67,68] to primal methods [17,31,6] to name just a few.…”