Complexity and experimental evaluation of primal-dual shortest path tree algorithms

The Shortest Path Tree problem (SPT) is a classical and important combinatorial problem. It has been widely studied in the past decades leading to the availability of a great number of algorithms adapted to solve the problem in various special conditions and/or constraint formulations ([1],[19],[20]).

[1]  Ravindra K. Ahuja,et al.  Network Flows: Theory, Algorithms, and Applications , 1993 .

[2]  D. Bertsekas.  The auction algorithm: A distributed relaxation method for the assignment problem , 1988 .

[3]  Dimitri P. Bertsekas,et al.  A generic auction algorithm for the minimum cost network flow problem , 1993, Comput. Optim. Appl..

[4]  Dimitri P. Bertsekas,et al.  The auction algorithm for the minimum cost network flow problem , 1989 .

[5]  Dimitri P. Bertsekas,et al.  Polynomial auction algorithms for shortest paths , 1995, Comput. Optim. Appl..

[6]  Robert B. Dial,et al.  Algorithm 360: shortest-path forest with topological ordering [H] , 1969, CACM.

[7]  Giorgio Gallo,et al.  Shortest path algorithms , 1988, Handbook of Optimization in Telecommunications.

[8]  R. Bellman.  Dynamic programming. , 1957, Science.

[9]  Dimitri P. Bertsekas,et al.  Network optimization : continuous and discrete models , 1998 .

[10]  Dimitri P. Bertsekas,et al.  An Auction Algorithm for Shortest Paths , 1991, SIAM J. Optim..

[11]  Andrew V. Goldberg,et al.  Shortest paths algorithms: Theory and experimental evaluation , 1994, SODA '94.

[12]  D. Bertsekas,et al.  The auction algorithm for the transportation problem , 1989 .

[13]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[14]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[15]  Darwin Klingman,et al.  NETGEN: A Program for Generating Large Scale Capacitated Assignment, Transportation, and Minimum Cost Flow Network Problems , 1974 .

[16]  Panos M. Pardalos,et al.  Network Optimization , 1997 .

[17]  G. Gallo,et al.  SHORTEST PATH METHODS: A UNIFYING APPROACH , 1986 .

[18]  R. Leone,et al.  A modified auction algorithm for the shortest path problem , 1994 .

[19]  D. Bertsekas.  A distributed asynchronous relaxation algorithm for the assignment problem , 1985, 1985 24th IEEE Conference on Decision and Control.