Analysis of Backtracking A for Resource Constrained Shortest Path Problems - Ford, Bryce; Kumar, Mrinal (Proceedings of the American Control Conference, 2024)
The Resource Constrained Shortest Path Problem (RCSPP) requires a minimum-cost simple path between two nodes that is subject to a resource consumption constraint. In this paper, we consider the Backtracking A^{*} algorithm presented in previous works applied to the general RCSPP. Backtracking A^{*} attempts to solve the RCSPP by iterative modification of paths generated by a shortest path algorithm such as A^{*} . We consider the completeness of Backtracking A^{*} and demonstrate that it cannot be a complete algorithm. Then we propose a complete, modified version of Backtracking A^{*} . Finally, we give a result for the time complexity of Backtracking A^{*} , and demonstrate it under worst-case conditions applied to randomly generated graphs.