The original form of the auction algorithm is an iterative method to find the optimal prices and an assignment that maximizes the net benefit in a bipartite graph, the maximum weight matching problem (MWM).
[4] A later variation of the auction algorithm that solves shortest path problems was introduced by Bertsekas in 1991.
Auction algorithms for shortest hyperpath problems have been defined by De Leone and Pretolani in 1998.
This is also a parallel auction algorithm for weighted bipartite matching, described by E. Jason Riedy in 2004.
[6] The (sequential) auction algorithms for the shortest path problem have been the subject of experiments which have been reported in technical papers.