多用途布线：新观点和近似算法
Multi Purpose Routing: New Perspectives and Approximation Algorithms
摘要：
由于服务延迟而导致的成本对于车辆路由的各种应用（诸如医疗紧急情况、物流操作和共乘）可能本质上不同。我们研究了旅行商问题，即$L_p$ TSP的基本推广，其目标是最大限度地减少在服务中的延迟的聚合措施，量化的Minkowski $p$ -范数的延迟向量。我们提出了有效的组合和线性规划算法近似$L_p$ TSP的一般度量。我们提供了几个近似算法的$L_p$ TSP问题，包括$4.27$和$10.92$ -近似算法的单和多车辆$L_2$ TSP，称为旅行消防员问题。在其他贡献中，我们提供了一个$8$近似和$1.78$不可近似的全范数TSP问题，解决的情况下，不知道理想的成本函数，或寻求同时近似的任何成本函数。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
