The inverse shortest paths problem with upper bounds on shortest paths costs

We examine the computational complexity of the inverse shortest paths problem with upper bounds on shortest path costs, and prove that obtaining a globally optimum solution to this problem is NP-complete. An algorithm for finding a locally optimum solution is proposed, discussed and tested.

[1]  L. R. Ford,et al.  NETWORK FLOW THEORY , 1956 .

[2]  Richard Bellman,et al.  ON A ROUTING PROBLEM , 1958 .

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

[4]  Stephen A. Cook,et al.  The complexity of theorem-proving procedures , 1971, STOC.

[5]  Donald B. Johnson,et al.  Efficient Algorithms for Shortest Paths in Sparse Networks , 1977, J. ACM.

[6]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[7]  David S. Johnson,et al.  Computers and In stractability: A Guide to the Theory of NP-Completeness. W. H Freeman, San Fran , 1979 .

[8]  F. Natterer,et al.  Mathematical problems of computerized tomography , 1983, Proceedings of the IEEE.

[9]  Donald Goldfarb,et al.  A numerically stable dual method for solving strictly convex quadratic programs , 1983, Math. Program..

[10]  Said M. Easa,et al.  Shortest route algorithm with movement prohibitions , 1985 .

[11]  Pitu Mirchandani,et al.  Generalized Traffic Equilibrium with Probabilistic Travel Times and Perceptions , 1987, Transp. Sci..

[12]  Josef Stoer,et al.  Numerische Mathematik 1 , 1989 .

[13]  P. Bovy,et al.  ROUTE CHOICE: WAYFINDING IN TRANSPORT NETWORKS , 1990 .

[14]  T. Moser.  Shortest path calculation of seismic rays , 1991 .

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

[16]  Philippe L. Toint,et al.  On an instance of the inverse shortest paths problem , 1992, Math. Program..

[17]  T. J. Moser.  The shortest path method for seismic ray tracing in complicated media , 1992 .

[18]  P. Pardalos.  Complexity in numerical optimization , 1993 .

[19]  Philippe L. Toint,et al.  On the use of an inverse shortest paths algorithm for recovering linearly correlated costs , 1994, Math. Program..