Multi Purpose Routing: New Perspectives and Approximation Algorithms
share
The cost due to delay in services may be intrinsically different for various applications of vehicle routing such as medical emergencies, logistical operations, and ride-sharing. We study a fundamental generalization of the Traveling Salesman Problem, namely L_p TSP, where the objective is to minimize an aggregated measure of the delay in services, quantified by the Minkowski p-norm of the delay vector. We present efficient combinatorial and Linear Programming algorithms for approximating L_p TSP on general metrics. We provide several approximation algorithms for the L_p TSP problem, including 4.27 10.92-approximation algorithms for single multi vehicle L_2 TSP, called the Traveling Firefighter Problem. Among other contributions, we provide an 8-approximation and a 1.78 inapproximability for All-Norm TSP problem, addressing scenarios where one does not know the ideal cost function, or is seeking simultaneous approximation with respect to any cost function.
READ FULL TEXT