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
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Polynomial auction algorithms for shortest paths
Computational Optimization and Applications
Shortest paths algorithms: theory and experimental evaluation
Mathematical Programming: Series A and B
Graph Collapsing in Shortest Path Auction Algorithms
Computational Optimization and Applications
Artificial Intelligence: Structures and Strategies for Complex Problem Solving
Artificial Intelligence: Structures and Strategies for Complex Problem Solving
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In this paper, the problem of finding a shortest path tree rooted at a given source node on a directed graph (SPT) is considered. A new efficient algorithm based on a primal-dual approach is presented, which improves both the convergence and the complexity of the best known auction-like algorithm. It uses the virtual source (VS) concept based on the following consideration: when a node i is visited for the first time by any algorithm which preserves verified the dual admissibility conditions, then the shortest path (SP) from the source node to i is found. Therefore, the SP from the source to the remaining nodes may be computed by considering i as a “virtual source”.We propose a very efficient implementation of an auction-like algorithm that uses this concept and enables us to obtain a computational cost of O(n2), where n is the number of nodes.Numerical experiments are reported showing that the new method outdoes previously proposed auction-like algorithms and is highly competitive with other state-of-art SP approaches.