Average Case Analysis of a Hard Dial-a-Ride Problem
Amin Coja‐Oghlan, Sven Oliver Krumke, Till Nierhoff · 2003
In the dial-a-ride-problem (DARP) objects have to be moved between given sources and destinations in a transportation network by means of a server. The goal is to find a shortest transportation for the server. We study the DARP when the underlying transportation network forms a caterpillar. This special case is strongly NP-hard in the worst case. We prove that in a probabilistic setting there exists a polynomial time algorithm which almost surely finds an optimal solution. Moreover, with high probability the optimality of the solution found can be certified efficiently. We also examine the complexity of DARP in a semi-random setting and in the unweighted case.