Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
The auction algorithm: a distributed relaxation method for the assignment problem
Annals of Operations Research - Special Issue: Parallel Optimization on Novel Computer Architectures
The auction algorithm for the transportation problem
Annals of Operations Research
Linear network optimization: algorithms and codes
Linear network optimization: algorithms and codes
Polynomial auction algorithms for shortest paths
Computational Optimization and Applications
Shortest paths algorithms: theory and experimental evaluation
Mathematical Programming: Series A and B
Shortest Path Auction Algorithm Without Contractions Using Virtual Source Concept
Computational Optimization and Applications
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In this paper we consider the problem of finding a shortest path from a source node to a fixed target node (SSP) or to all the nodes (SPT) on a directed graph. A family of algorithms which derives from the known auction algorithm is introduced. The key feature of these algorithms is based on topological transformations operated on the graphs that replace an optimal sub-path with a single arc of the same length (graph collapsing concept). The same idea is applied both to the standard auction algorithm and to a modified version of the algorithm. In the last mentioned case a good saving in computation cost is obtained as shown by the reported numerical examples.