Recoverable robust shortest path problem under interval budgeted uncertainty representations
For researchers in robust optimization, this provides polynomial-time algorithms for a previously NP-hard problem on acyclic digraphs, though the results are incremental as they extend known techniques.
The paper addresses the recoverable robust shortest path problem under interval uncertainty, proving it is polynomially solvable for acyclic digraphs with traditional interval uncertainty and all known neighborhoods, while strengthening negative results for general digraphs and proposing exact and approximate methods for budgeted interval uncertainty.
In this paper, the recoverable robust shortest path problem under interval uncertainty representations is discussed. This problem is known to be strongly NP-hard and also hard to approximate in general digraphs. In this paper, the class of acyclic digraphs is considered. It is shown that for the traditional interval uncertainty, the problem can be solved in polynomial time for all natural, known from the literature, neighborhoods. Efficient algorithms for various classes of acyclic digraphs are constructed. Some negative results for general digraphs are strengthened. Finally, some exact and approximate methods of solving the problem under budgeted interval uncertainty are proposed.