Multi Purpose Routing: New Perspectives and Approximation Algorithms
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.
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