Christopher C. Skiscim and Bruce L. Golden. Solving k-shortest and constrained shortest path problems efficiently. Ann. Oper. Res., 20(1-4):249--282, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....researchers have resorted to several heuristics and approximation algorithms. 2 One common approach to the RSP problem is to find the k shortest paths w.r.t. a cost function defined based on the link weights and the given constraint, hoping that one of these paths is feasible and near optimal [20, 32, 15, 19]. The value of k determines the performance and overhead of this approach; if k is large, the algorithm has good performance but its computational cost is prohibitive. A similar approach to the k shortest paths is to implicitly enumerate all feasible paths [3] but this approach is also ....

Christopher C. Skiscim and Bruce L. Golden. Solving k-shortest and constrained shortest path problems efficiently. Ann. Oper. Res., 20(1-4):249--282, 1989.

....several common variations of the problem. In many of the papers cited above, the paths are restricted to be simple, i.e. no vertex can be repeated. This has advantages in some applications, but as our results show this restriction seems to make the problem significantly harder. Several papers [3, 13, 17, 24, 41, 42, 58, 59] consider the version of the k shortest paths problem in which repeated vertices are allowed, and it is this version that we also study. Of course, for the DAGs that arise in many of the applications described above including scheduling and dynamic programming, no path can have a repeated vertex ....

C. C. Skicism and B. L. Golden. Solving k-shortest and constrained shortest path problems efficiently. Network Optimization and Applications, pp. 249--282. Baltzer Science Publishers, Annals of Operations Research 20, 1989.

....paths is to generate many paths and discard all illegal ones. For some networks this may be a feasible approach, but in general it isn t, since there are usually way too many paths. The classical solution is to use specialized constrained shortest path algorithms as decribed in [Sai68, RM85, SG89, HG94, HG96, JBK96] These techniques either put additional information (labels or resources) into the shortest path codes or use Lagrangian relaxation techniques [HZ80] dynamic programming [DDS92] or branch and bound. For a number of reasons we prefer not to do this. For one, we don t like the ....

Christopher C. Skicism and Bruce Leonard Golden. Solving k-shortest and constrained shortest path problems efficiently. In Bala Shetty, editor, Network Optimization and Applications, number 20 in Annals of Operations Research, pages 249--282. Baltzer Science Publishers, 1989.

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