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 (,,).
The scope of this work is to provide an extensive treatment of shortest path problems. It starts covering the major classical approaches and proceedes focusing on the auction algorithm and some of its recently developed variants. There is a discussion of the theoretical and practical performance of the treated methods and numerical results are reported in order to compare their effectiveness.
KeywordsShortest path Auction technique Network optimization.
Unable to display preview. Download preview PDF.
- L.R.,Jr. Ford, Network Flow Theory,Report P-923, The Rand Corporation, Santa Monica, CA.Google Scholar
- D. Bertsekas, (1979), “A distributed Algorithm for the Assignment Problem”, Lab. for Information and Decision Systems Working Paper, MIT.Google Scholar
- D. Bertsekas, (1985), “A distributed asynchronous relaxation algorithm for the Assignment Problem”, 24th IEEE Conference on Decision and Control, Ft Lauderdale, Fla., 1703–1704.Google Scholar
- D. Bertsekas, D.A. Castanon, (1989), “The Auction Algorithm for minimum cost network flow problem”, Lab. For Information and Decision Systems, Report LIDS-P-1925, MIT.Google Scholar
- D. Bertsekas, D.A. Castanon, (1991), “A generic auction algorithm for the minimum cost network flow problem”, Lab. For Information and Decision Systems, Report LIDS-P-2084, MIT.Google Scholar
- D. Bertsekas, (1991), Linear networks optimization: Algorithms and Codes,MIT Press.Google Scholar
- R. Cerulli, R. De Leone, and G. Piacente, (1994), “A modified Auction Algorithm for the shortest path problem”, Optimization Methods and Software, v. 4.Google Scholar
- R. Cerulli, P. Festa, and G. Raiconi, (1997), “Graph Collapsing in Auction Algorithms”, Tech. Report 6/97, D.I.A. R. M. Capocelli, University of Salerno, submitted to Computational Optimization and Application.Google Scholar
- R. Cerulli, P. Festa, and G. Raiconi, (1997), “An Efficient Auction Algorithm for the Shortest Path Problem Using Virtual Source Concept”, Tech. Report 7/97, D.I.A. R. M. Capocelli, University of Salerno, submitted to Networks.Google Scholar
- R.B. Dial, “Algorithm 360: Shortest Path Forest with Topological Ordering”, Comm. ACM, vol. 12, 632–633.Google Scholar
- B.V. Chernassky, A.V. Goldberg, and T. Radzik, (1996), “Shortest path algorithms: Theory and experimental evaluation”, Math. Programm., vol. 73, 129–174.Google Scholar
- S. Pallottino, M.G. Scutellâ, (1991), “Strongly polynomial Auction Algorithms for shortest path”, Ricerca Operativa, vol. 21, No. 60.Google Scholar
- G. Gallo, S. Pallottino, C. Ruggeri, and G. Storchi, (1984), “Metodi ed algoritmi per la determinazione di cammini minimi”, Monografie di Software Matematico, n. 29.Google Scholar
- C.H. Papadimitriou, K. Steiglitz, (1982), Combinatorial Optimization: Algorithms and Complexity, Practice-Hall, Englewood Cliffs, NJ.Google Scholar